Solution Manual For Finance for Executives Managing for Value Creation, 7th Edition by Gabriel Hawaw

Solution Manual For Finance for Executives Managing for Value Creation, 7th Edition Gabriel Hawawini, Claude Viallet Chapter 2-18

Chapter 2 Answers to Review Problems Finance for Executives – 7th Edition

1. Finding the implicit interest rate If indifferent then the present values of the alternatives should be the same, that is, , and thus

from which we get k = 8.63%.

2. APR versus effective interest rate (

Using equation 2.4 we can write:

)

, thus:

from which we get APR = 6%.

With a financial calculator, enter N=12, PV=1, PMT=0, FV=

1.0617 and press I/YR. you

will find a monthly APR of 0.5% which multiplied by 12 gives you 6%.

3. Compounded value and compounded rate a. $1.1464. b.

For use with Finance for Executives: Managing for Value Creation 7th edition

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from which we get k = 4.66%.

4. Alternative financing plans PV(Plan 1) = $12,400 + $400 × ADF(T=35; k=6%/12) = $12,400 + $400 × 32.0354 = $25,214.

PV(Plan 2) = $492 × ADF(T=60; k=6%/12) = $492 × 51.7256 = $25,449.

The first plan is preferable because it is less expensive because it has a lower present value.

5. Annuity versus perpetuity The future value of the $100 a year for the next 10 years (see formula 2.13 for the future value of an annuity) at the rate ‗k‘ must be equal to the present value, at the end of 10, of a $100 perpetuity at the same rate ‗k‘, hence we have: [

]

, and thus [

]

, from which we get

Using a financial calculator we find k = 7.18%. (Enter N=10, PV=1, PMT=0, FV= 2 and press I/YR. you will find 7.18%.)

6. Valuing a loan a.

The loan will generate fixed interest income of $800,000 (8% of $10 million) every year over the next 4 years plus $10 million at the end of the fourth year. Its value is thus the sum of the present value of 4-year, $800,000 annuity at 7 percent (the prevailing market rate) and the present value of $10 million to be received in 4 years at 7 percent: Value of loan = [$800,000 × ADF(T=4; k=7%)] + [$10,000,000 × DF(T=4; k=7%)] Value of loan = [$800,000 × 3.3872] + [$10,000,000 × 0.7629] = $10,338,760. b.

Value of loan = [$400,000 × ADF(T=8; k=3.5%)] + [$10,000,000 × DF(T=8; k=3.5%)] Value of loan = [$400,000 × 6.8740] + [$10,000,000 × 0.7594] = $10,343,600.

For use with Finance for Executives: Managing for Value Creation 7th edition

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7. Perpetual cash flows a.

If the current membership is renewed every year in perpetuity with fees growing at 3 percent annually, its the present value at 6 percent is

. This is a

higher amount than the proposed price of $65,000 for life-long family membership. The lifelong family membership is thus a better deal. b.

The interest rate that makes you indifferent is the one that equates the present value of the two choices, that is,

, from which we get k = 6.17%.

c.

The annual fee, call it X, that makes you indifferent is giving by the equation: , from which we get X = $1,893.20 d. $68,667, which is the present value of the current membership if it were an annuity growing at 3 percent.

8. American Airlines AAirpass a. [

*

]

(

) +

We have the following information: For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

  

Payment amount ( = $1,000,000 Discount rate (k) = 10% or 0.10 Periods (T) = 2008 – 1987 = 21

The present value (PV) of these payments can be now calculated as: [

]

Hence, it costs the company $8,648,694.29 for the AAirpass and this should have been the lowest value at which it should have been sold. b. The information required is as follows:    

Payment amount ( = $1,100,000 Discount rate (k) = 10% or 0.10 Growth rate (g) = 5% or 0.05 Periods (T) = 20 *

(

) +

The price of the pass should therefore be ideally higher than $13,323,292.46.

9. Growing annuities versus growing perpetuities a.

It is the present value, at 8 percent, of an annuity of $80 million growing at 3 percent for 5 years. Using formula 2.12 you get: *

(

) +

b.

It is the present value, at 8 percent, of a perpetuity growing at 3 percent, that is, which is $1,600 million.

For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

10. Mortgage loan a.

The monthly mortgage payment, call it X, is the solution to the equation: $80,000 = X × ADF[T=360; 8%/12] = X × 136.2783 from which we get X = $587.03. b.

Interest payment in first installment =

$533.33.

Principal repayment = $587.03 – $533.33 = $53.70. c.

Total interest payments = Total payments – Principal repayment = ($587.03 × 360) – $80,000 Total interest payments = = $211,330.80

$80,000 = $131,330.80.

11. Retirement planning a.

The capital needed at 65, call it X, is an immediate annuity such as: X = $50,000 + $50,000 × ADF[T=19; 6%] = $50,000 + $50,000 × 11.1581 = $607,905.82 The lump sum needed today is the present value at DF (T=40; k=6%): Lump sum = $609,905.82 × DF[T=40; k=6%] = $609,905.82 × 0.0972 = $59,088.45. b.

Amount to invest every month is an annuity, call it X, whose present value (including the immediate payment) must be equal to the lump sum $59,088.45, that is: $59,088.45 = X + X × ADF[T=40×12; k=6%/12] = X + X × 181.7476, from which we get X = $323.33.

For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

12. Annuity versus annuity due The relation for the future value of the net income will be calculated as per the formula.

However, since the rent is paid at the start of the month and each of the cash flows will be compounded for one more period, we need to adjust the first cash flow by compounding it for one period.

For Rent:   

Discount rate (k) = 6% or 0.50% monthly = 0.005 CF1 = $2,000 (1 + 0.005) = $2,010.00 T = 12

[

]

The formula for the rent which is a type of annuity due can therefore be adjusted to:

[

]

For net income, the future value can be calculated as:   

Discount rate (k) = 0.005 CF1 = $10,000 T = 12

[

]

For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

Chapter 3 Answers to Review Problems Finance for Executives – 7th Edition

1. Attitudes toward risk a. She is either risk averse or risk neutral because stock A has a higher expected return with less risk. b. He is a risk seeker because stock B has a lower expected return with more risk. c. A risk neutral investor will buy stock B if it offers more than 13 percent. d. A risk-averse investor will buy stock B if its volatility is 25 percent.

2. Characteristics of a two-stock portfolio a. b.

For use with Finance for Executives: Managing for Value Creation 7th edition

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c.

√

√

√

√

d.

e. No, portfolio P2 is not efficient because it has the same expected return as portfolio P1 with more risk. To be efficient, portfolio P2 must have a volatility of 24.23 percent, the volatility of portfolio P1.

3. Risk reduction through diversification a. The expected return of the equally-weighted portfolio is the same as the expected return of the three individual stocks, that is, E(RP) = (1/3)10% + (1/3)10% + (1/3)10% = 10%. b. The variance of the 3-stock portfolio has the following structure: three variances each equal to 20 percent and three covariances each equal to 0.0200 (0.50×0.20×0.20). Given one-third investment in each stock, the variance of the portfolio is thus: Var (RP) = [(1/3)2 × (0.20)2 + (1/3)2 × (0.20)2 + (1/3)2 × (0.20)2] + [2 × (1/3)2 × (0.02) + 2 × (1/3)2 × (0.02) + 2 × (1/3)2 × (0.02)] = 0.026667 Volatility of the portfolio is thus √

The risk of the portfolio is thus

significantly lower than the risk of the individual stocks in the portfolio.

4. Correlations, covariances and betas a. Re-arrange the SML equation, E(R) = 4% + 6%β, as

Using the expected

returns in Exhibit 3.12, row 5, you can infer the betas of the 5 stocks. We have Use the same procedure you get βB = 0.50, βC = 0.90, βD = 1.30 and βE = 1.50.

For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

b. We have

from which you get

Using the same procedure you get We have

Using the same

procedure you get c. (

)

(

)

. d.

( )

The portfolio beta is lower than

the market beta because there are more stocks with betas lower than one than higher.

Recall that the market beta is a value-weighted portfolio, not an equally-weighted one.

5. Negative betas

a.

(

)

(

)

. The negative sign indicates that the stock

returns have a tendency to move in the opposite direction to those of the market. b. E(RA) = 4% + ( 0.20

(9%

4%)) = 3%. The expected return of stock A is lower than

the risk-free rate because the demand for this stock is high (because its negative beta allows investors to reduce their market risk). The strong demand raises its price which lowers its expected return.

6. The CML versus the SML a. If the portfolio is efficient, its expected return is given by the CML equation. Its composition must be a combination of the risk-free rate and the market portfolio. In practice, it must be one of the following four cases: (1) A proxy for the market portfolio and a riskless bank deposit or government bond; (2) A proxy for the market portfolio held without any debt (purchased exclusively with my own money); (3) A proxy for the market portfolio purchased partly with money borrowed at the risk-free rate; (4) An asset For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

that is perfectly positively correlated with the market portfolio (either held exclusively or held with a riskless asset or with some debt borrowed at the risk-free rate). b. If the portfolio is inefficient, its expected return is given by the SML equation. Its composition is any investment other than those listed in the answer to question (a). c. To show that the correlation

of an efficient portfolio E with the market portfolio M is

one, start with

and note that

and

.

We thus have:

d. To show this, rewrite the SML equation and replace beta with its definition given in equation 3.11b: (

)

(

)

Because the efficient portfolios along the CML are all perfectly positively correlated with the market portfolio, the correlation coefficient

is equal to one and the above SML

equation becomes the CML equation 3.9a.

7. The Capital Asset Pricing Model and investment allocation a.

If wM is the proportion of funds invested in the market portfolio, we must have: [

]

[

]. Solving for wM you get wM = 2/3 and wF = 1/3. The

$180,000 should thus be invested as follows: $120,000 in the market portfolio and $60,000 in the in a risk-free asset. b. The volatility of the efficient portfolio in the previous question is given by the CML equation. We have you get

(

)

Solving for

The portfolio beta is given by the SML equation. We have Solving for

you get

For use with Finance for Executives: Managing for Value Creation 7th edition

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c. The portfolio expected return is given by the CML equation. We have: If wM is the proportion of funds [

invested in the market portfolio, we must have: [

]. Solving for wM you get wM = 120% and wF =

]

20%. The $200,000

is thus invested as follows: $40,000 is borrowed at 5 percent, added to the initial $200,000 and the total of $240,000 is invested in the market portfolio. d. The portfolio beta is given by the SML equation. We have Solving for

you get

20.

8. Estimating a firm’s cost of capital a. According to the CAPM, PEC‘s estimated cost of equity capital is Cost of equity capital = 3% + (5% × 1.10) = 8.5% b. PEC‘s weighted average cost of capital = (50% × 8.5%) + (50% × 6%) = 7.25%

9. Evaluating portfolio efficiency The portfolios on the EIL will have the highest Sharpe‘s ratio. Therefore, to identify the portfolio which does not lie on the EIL, we need to calculate the Sharpe ratio for all portfolios.

Portfolio A Expected Return Volatility Sharpe’s Ratio

B 15.30% 25.80%

C 12.60% 19.64%

D 17.70% 33.56%

E 11.90% 18.04%

9.30% 12.10%

Portfolio C has a Sharpe‘s ratio which is lower than other portfolios. Consequently, it does not lie on the EIL. It should lie below the EIL.

10. Evaluating asset returns For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

To justify inclusion in the portfolio, both stocks should have the same risk and return characteristics. [ (

)]

Substituting the values for Microsoft, we have: [

]

After substituting the value of the expected market return ( [

), we have: ]

Given the amount of market risk (beta), Tesla should return 33.50 percent in the same period to justify its inclusion in the portfolio.

For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

11. Evaluating portfolio performance a. The market has a beta of one; the risk-free asset has a zero beta and a zero volatility b. αA = 7.90% αA = 7.90%

E(R) = 7.90% 8.48% =

[3.2% + (9.2%

3.2%)βA] = 7.90%

[3.2% + (6% × 0.88)]

0.58% (underperformed relative to the market index)

applying the same procedure for the other investment funds, you get: αB = 10.10%

10.40% = 0.30% (underperformed relative to the market index)

αC = 9.80%

9.44% = +0.36% (overperformed relative to the market index)

αD = 7.20%

8.60% =

1.40% (underperformed relative to the market index)

12. Testing for informational efficiency a. The alphas of company A and company B are calculated below using the SML equation: Company A has a beta of 1

2 days

1 day

(1) Excess return on shares of A

1.99%

0.19%

Event Day 1.00%

(2) Excess return on the market

2.00%

0.50%

(3) Expected excess return = βA×(2)

2.00%

(4) Alpha of company A = (1) – (2)

+1 day

+2 days

1.27%

0.45%

0.50%

1.00%

0.50%

0.50%

0.50%

1.00%

0.50%

0.01%

0.31%

0.27%

0.05%

Company B has a beta of 2

2 days

1 day

+1 day

+2 days

(5) Excess return on shares of B

2.25%

1.01%

0.50% Event Day 0.50%

1.01%

2.00%

(6) Excess return on the market

1.00%

0.50%

2.00%

0.50%

1.00%

(7) Expected excess return = βB×(6)

2.00%

1.00%

4.00%

1.00%

2.00%

(8) Alpha of company B = (5) – (6)

0.25%

0.01%

3.50%

0.01%

0.00%

b. and c. The average alphas of the two companies and their cumulative values over the 5 days are shown below:

Average alphas = [(4) + (8)]/2

2 days

1 day

0.13%

0.15%

Event Day 2.00%

+1 day

+2 days

0.14%

0.03%

For use with Finance for Executives: Managing for Value Creation 7th edition

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Cumulative average alphas

0.13%

1.98%

0.02%

1.84%

1.87%

d. The plot of the cumulative average alphas indicates that the market is informationally efficient: share prices adjust instantly and completely on the announcement day with no further adjustments on the days following the announcements.

2.50%

2.00%

Chapter 4

CAAR

1.50%

1.00%

0.50%

Answers to Review Problems

Finance for Executives – 7th Edition

0.00%

-2

-1

0

1

2

-0.50%

Event Day

1. Missing accounts Assets, beginning of period Assets, end of period Owner‘s equity, beginning of period Owners‘ equity, end of period Liabilities, beginning of period Liabilities, end of period Revenues of the period Expenses of the period Earnings after tax of the period Dividends (from earnings of the period) Shares issued ($ amount) during the period

Firm 1

Firm 2

Firm 3

$1,000 1,100 500 600 500 500 2,000 1,800 200 100 0

$400 500 200 260 200 240 200 180 20 10 50

$1,500 1,500 900 1,000 600 500 600 500 100 0 0

For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

Firm 1 Liabilities beginning of period = Assets beginning of period – Owners‘ equity beginning of period = $1,000 – $500 = $500 Earnings of the period

= Revenues of the period – Expenses of the period = $2,000 – $1,800 = $200

Owners‘ equity end of period = Owners‘ equity beginning of period + Earnings after tax of then period – Dividends + $Amount of shares issued during the period = $500 + $200

$100 + $0 = $600

= Assets end of period – Owners‘ equityend of period

Liabilities end of period

= $1,100 – $600 = $500 Firm 2 Assets beginning of period

= Liabilities beginning of period + Owners‘ equity beginning of period = $200 + $200 = $400

Revenues of period

= Earnings after tax of period + Expenses of period = $20 + $180 = $200

Owners‘ equity end of period

= Owners‘ equity beginning of period + Earnings after tax of the period – Dividends + $Amount of shares issued during the period = $200 + $20

Liabilities end of period

$10 + $50 = $260

= Assets end of period – Owners‘ equityend of period

For use with Finance for Executives: Managing for Value Creation 7th edition

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= $500 – $260 = $240

Firm 3 Owners‘ equity beginning of period = Owners‘ equity end of period period

+ Dividends

Earnings after tax of the

$Amount of shares issued during the

period = $1,000

$100 + $0

$0 = $900

= Liabilities beginning of period + Owners‘ equitybeginning of period

Assets beginning of period

= $600 + $900 = $1,500 = Liabilities end of period + Owners‘ equityend of period

Assets end of period

= $500 + $1,000 = $1,500 Expenses of the period

= Revenues of the period – Earnings after tax of the period = $600 – $100 = $500

2. Balance sheet changes

a. Figures in millions End-of-year for balance sheet items

Year 1

Current assets Noncurrent assets Total assets Current liabilities Noncurrent liabilities Paid-in capital

$16,870 24,066 40,936 13,466

Year 2

Year 3

Year 4

$18,732 $19,950 $19,976 29,318 29,920 31,094 48,050 49,870 51,070 15,284 16,574 16,080 14,624 17,326 2,298 18,414 2,798 11,998 th 2,034for Value Creation 72,584 For use with Finance for Executives: Managing edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

Retained earnings Earnings (loss) after tax Dividends Owners‘ equity Total liabilities and owners’ equity

2,014 13,438 1,580 15,472

15,844 4,446 2.040 18,142 48,050

(1,312) 12,298 2,234 14,882 49,870

40,936

Year 1 Total assets

= Total liabilities and Owners‘ equity = $40,936

Noncurrent assets

= Total assets – Current assets = $40,936 – $16,870 = $24,066

Owners‘ equity

= Total assets – (Current Liabilities + Noncurrent liabilities) = $40,936 – ($13,466 + $11,998) = $15,472

Paid-in capital

= Owners‘ equity – Retained earnings = $15,472 – $13,438 = $2,034

Year 2 For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

14,866 5,048 2,480 17,664 51,070

Noncurrent assets = Total assets – Current assets = $48,050 – $18,732 = $29,318 Total liabilities and owners‘ equity = Total assets = $48,050 Earnings after tax = Dividends + (Accumulated earnings Year 2 –Accumulated Earnings Year 1) = $2,040 + ($15,844 – $13,438) = $4,446 Owners‘ equity = Paid-in capital + Accumulated earnings = $2,298 + $15,844 = $18,142 Noncurrent liabilities = Total assets – Current liabilities – Owners‘ equity = $48,050 – $15,284 – $18,142 = $14,624 Year 3 Total assets = Current assets + Noncurrent assets = $19,950 + $29,920 = $49,870 Total liabilities and owners‘ equity = Total assets = $49,870 Owners‘ equity = Total assets – (Current Liabilities + Noncurrent liabilities) = $49,870 – ($16,574 + $18,414) = $14,882 Retained earnings Year 3 = (Retained earnings Year 2 + Earnings (loss) after tax) – Dividends = ($15,844 – $1,312) – $2,234 = $12,298 Paid-in capital = Owners‘ equity – Retained earnings = $14,882 – $12,298 = $2,584

Year 4 Noncurrent assets = Total liabilities and owners‘ equity – Current assets = $51,070 – $19,976 = $31,094 Total assets = Total liabilities and owners‘ equity = $51,070 For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

Retained earnings Year 4 = (Retained earnings Year 3 + Earnings (loss) after tax) – Dividends = ($12,298 + $5,048) – $2,480 = $14,866 Owners‘ equity = Paid-in capital + Retained earnings = $2,798 + $14,866 = $17,664 Noncurrent liabilities = (Total liabilities & owners‘ equity – Owners‘ equity) – Current liabilities = ($51,070 – $17,664) – $16,080 = $17,326

b.

A large investment (e.g., the acquisition of another firm) would explain the increase in total assets between Years 1 and 2. A mix of debt and equity financing was used to finance the investment.

c.

The decrease in retained earnings was the result of the year‘s net loss and dividend payments.

The resulting decrease in internal funding was financed by an increase in long-term financing in the form of long-term debt.

d.

The firm became profitable again in Year 4. A portion of the cash generated by the renewed profitability was used to repay debt.

3. Balance sheet changes For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

Figures in millions End-of-year for balance sheet items

Year 1

Year 2

Year

Year

Current assets Noncurrent assets Total assets Current assets/current liabilities Current liabilities Noncurrent liabilities Owners‘ equity Total liabilities and owners‘ equity

$ 3,092

$ 3,022

3 $

4 $

2,932 20,928 17,996 1.023 2,866 10,004 8,058 20,928 8,058

3,122 23,408 20,286 1.04 3,002

a.

18,002 1.038 21,094 2,978 9,286 8,830 21,094

18,160 1.217 21,182 2,484 9,830 21,182 8,868

12,322 8,084 23,408

Year 1 Noncurrent assets = Total assets – Current assets = $21,094 – $3,092 = $18,002 Total liabilities and owners‘ equity = Total assets = $21,094 Owners‘ equity = Total liabilities & owners‘ equity – (Current liabilities + Noncurrent liabilities = $21,094 – ($2,978 + $9,286) = $8,830 Current assets/current liabilities = $3,092/$2,978 = 1.038 Year 2 Total assets = Total liabilities and owners‘ equity = $21,182 Current assets = Total assets – Noncurrent assets = $21,182 – $18,160 = $3,022 Current liabilities = (Total liabilities & owners‘ equity – Owners‘ equity) – Noncurrent liabilities = $21,182 – $8,868 – $9,830 = $2,484 Current assets/current liabilities = $3,022/$2,484 = 1.217

Year 3 For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

Total assets = Current assets + Noncurrent assets = $2,932 + $17,996 = $20,928 Total liabilities and owners‘ equity = Total assets = $20,928 Current liabilities = Current assets/(Current assets/current liabilities) = $2,932/1.023 = $2,866 Noncurrent liabilities = (Total liabilities & owners‘ equity – Owners‘ equity) – Current liabilities = ($20,928 – $8,058) – $2,866 = $10,004 Year 4 Current assets = Current liabilities × (Current assets/current liabilities) = $3,002 × 1.04 = $3,122 Total assets = Current assets + Noncurrent liabilities = $3,122 + $20,286 = $ 23,408 Total liabilities and owners‘ equity = Total assets = $23,408 Noncurrent liabilities = (Total liabilities & owners‘ equity – Owners‘ equity) – Current liabilities = ($23,408 – $8,084) – $3,002 = $12,322 b.

The noncurrent assets (fixed assets)-to-current assets ratio stayed remarkably constant over the four-year period, varying between 5.8 (Years 1, 2, and 3) and 6.5 (Year 4). The large value of this ratio indicates that the firm belongs to a capital intensive industry. The noncurrent liabilities-to-owners‘ equity ratio kept increasing, from 1.05 (Year 1) to 1.52 (Year 4). This suggests that the firm is using more and more debt relative to equity in financing its growth.

For use with Finance for Executives: Managing for Value Creation 7th edition

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For use with Finance for Executives: Managing for Value Creation 7th edition

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4. Reconstructing an income statement

Year 1

Year 2

$21,184

$31,036

Year 3

Sales $49,308

Cost of goods sold

24,372

16,916

38,420

Gross profit

4,268

10,888

6,664

Administrative and selling expenses

Research & development expenses

2,380

380

504

1,508

2,856

1,508

2,856

24

132

1,532

2,988,

3,304

816 Operating profit 5,264 Earnings before interest and tax (EBIT) 5,264 Interest income Earnings before tax (EBT) 5,472

Income tax expense

444

208

864

1,696 Earnings after tax (EAT)

1,088

2,124

3,776

Year 1 Gross profit = Sales – Cost of goods sold = $21,184 – $16,916 = $4,268 Operating profit = Gross profit – (Administrative and selling expenses + R&D expenses) For use with Finance for Executives: Managing for Value Creation 7th edition

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= $4,268 – ($2,380 + $380) = $1,508 Earnings before interest and tax (EBIT) = Operating profit = $1,508 Earnings before tax (EBT) = Earnings before interest and tax (EBIT) + Interest income = $1,508 + $24 = $1,532 Earnings after tax (EAT) = Earnings before tax (EBT) – Income tax expense = $1,532 – $444 = $1,088 Year 2 Sales = Earnings after tax + Income tax expense – Interest income + R&D expenses + Administrative and selling expenses + Cost of goods sold = $2,124 + $864 – $132 + $504 + $3,304 + $24,372 = $31,036 Gross profit = Sales – Cost of goods sold = $31,036 – $24,372 = $6,664 Operating profit = Gross profit – (Administrative and selling expenses + R&D expenses) = $6,664 – ($3,304 + $504) = $2,856 Earnings before interest and tax (EBIT) = Operating profit = $2,856 Earnings before tax (EBT) = Earnings before interest and tax (EBIT) + Interest income = $2,856 + $132 = $2,988 Earnings after tax (EAT) = Earnings before tax (EBT) – Income tax expense = $2,988

$864 = $2,124

Year 3 Earnings before tax (EBT) = Earnings after tax (EAT) + Income tax expense For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

= $3,776 + $1,696 = $5,472 Earnings before interest and tax (EBIT) = Earnings before tax (EBT) – Interest income = $5,472 – $208 = $5,264 Operating profit = Earnings before interest and tax (EBIT) = $5,264 Gross profit = Operating profit + Administrative and selling expenses + R&D expenses = $5,264 + $4,808 + $816 = $10,888 Cost of goods sold = Sales – Gross profit = $49,308 – $10,888 = $38,420

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5. Reconstructing an income statement

Year 1

Year 2

$21,087

$22,992

16,182

17,709

4,905

5,283

3,966

4,533

939

750

Earnings before interest and tax (EBIT) 939

750

3 Sales $26,613 Cost of goods sold 20,481 Gross profit 6,132 Administrative and selling expenses 5,547 Operating profit 585

585 Interest expense

75

90

864

660

324

252

540

408

81 Earnings before tax (EBT) 504 Income tax expense 192 Earnings after tax (EAT) 312

Year 1

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Year

Gross profit = Sales – Cost of goods sold = $21,087 – $16,182 = $4,905 Operating profit = Gross profit – Administrative and selling expenses = $4,905 – $3,966 = $939 Earnings before interest and tax (EBIT) = Operating profit = $939 Earnings before tax (EBT) = Earnings before interest and tax (EBIT) – Interest expense = $939 – $75 = $864 Earnings after tax (EAT)

= Earnings before tax (EBT) – Income tax expense = $864 – $324 = $540

Year 2

Earnings before tax (EBT) = Earnings after tax (EAT) + Income tax expense = $408 + $252 = $660 Earnings before interest and tax (EBIT) = Earnings before tax (EBT) + Interest expense = $660 + $90 = $750 Operating profit = Earnings before interest and tax (EBIT) = $750 Gross profit = Operating profit + Administrative and selling expenses = $750 + $4,533 = $5,283 Sales = Gross profit + Cost of goods sold = $5,283 + $17,709 = $22,992

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Year 3

Earnings before tax (EBT) = Earnings after tax (EAT) + Income tax expense = $312 + $192 = $504 Earnings before interest and tax (EBIT) = Earnings before tax (EBT) + Interest expense = $504 + $81 = $585 Operating profit = Earnings before interest and tax (EBIT) = $585 Gross profit = Operating profit + Administrative and selling expenses = $585 + $5,547 = $6,132 Cost of goods sold = Sales – Gross profit = $26,613 – $6,132 = $20,481

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6. Reconstructing a balance sheet

Beginning of year

End of year

Assets Current assets $ 450

$ 5007

Accounts receivable

250

4508

Inventories

300

4009

Cash

1,000

Total current assets

1,350

Noncurrent assets Property, plant, and equipment Gross value

$3,0001

$4,00010

Less: Accumulated depreciation

(1,000)

(1,200)11

Total noncurrent assets

2,000

2,800 $3,000

$4,150

Short-term debt

$400

$15017

Owed to banks

3003

50

Current portion of long-term debt

1002

1002

Accounts payable

3006

40012

Accrued expenses

100

30013

Total assets

Liabilities and owners’ equity Current liabilities

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Total current liabilities

800

850

500

40014

1,300

1,250

Owners’ equity

1,7004

2,90015

Total liabilities and owners’ equity

$3,0005

$4,15016

Noncurrent liabilities Long-term debt Total liabilities

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1

16 + 17

2

5

Equals total assets

6

Total liabilities and owners’ equity 18 – 19 – 20 – 21 – 22

7

13 + 7

8

5

14 + 8

3

9

18 – 5

4

21 + 22

15 + 9

10

Gross value, beginning of year + 4

12

Accounts payable, beginning of year + 10

13

19 + 11 + 12

15

Owners’ equity, beginning of year + 1 + 3 – 6

16

Equals total assets

17

Total liabilities and owners’ equity – Accounts payable – Accrued expenses – Long-term debt – Owners’ equity.

14

11

17 + 2

20 – 5

7. Changes in cash flow and working capital requirement

a. What is the net outflow from net interest expense in 20X1?

[

]

   [

]

b. Calculate cash outflow from purchases for 20X1.

For use with Finance for Executives: Managing for Value Creation 7th edition

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  

51

c. What is the increase or decrease in working capital requirements for 20X1?

    

There is a net increase in working capital requirement of 9.

d. Calculate the total cash outflow from operating activities in 20X1 [

    

51

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   [

]

8. Effect of transactions on working capital requirement

a. Decrease (less receivables) b. Increase (less payables) c. Increase (more receivables) d. Increase (more inventories)

9. Constructing a managerial balance sheet

Invested capital (in millions) Cash

Cash and cash equivalents + Short-term investments Merchandise inventories + Deferred income taxes + Other current assets – Accounts payable 1,589 – Accrued compensation & employees benefits – Self-insurance liabilities – Deferred revenue – Other current liabilities Property and equipment 23,435 + Intangible assets + Goodwill 661

Working capital requirement

Net assets

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+ Other assets Total invested capital

$25,685

Capital employed (in millions) Short-term borrowing Short-term debt

1,021 + Current portion of long-term debt

Long-term debt

5,039 Long-term debt

Long-term liabilities

1,570

Deferred income taxes, net + Other liabilities Owners‘ equity

18,055 Shareholders‘ equity

Total capital employed

$25,685

10. Transactions

Owners’

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

Shares are issued for cash Goods from inventory are sold for cash A fixed asset is sold for cash at a loss Corporate income tax is paid Cash is obtained through a bank loan A cash dividend is paid Accounts receivable are collected Minority interest in a firm acquired for cash A fixed asset is depreciated Obsolete inventory is written off Insurance premium is paid Merchandise is purchased on account

WCR 0 0 + 0 0 0 0 + 0

CF0OPE + 0 0 0 + 0 0 0 0

CF0INV 0 + 0 0 0 0 0 0 0 0

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CF+FIN 0 0 0 + 0 0 0 0 0 0

Equity +

+ 0 0 0 0 0

0 0

11. Free cash flow estimation

EBIT = ($840

$336

EBIT (1 – T) = $252

$112 (1

$140) = $252

0.30) = $176.40

Depreciation expense = $140

Net capital expenditure = ($1,120

$896)

$140 = $364

Free cash flow = $176.40

$28

$364 = $75.60

$140

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12. Profits, losses, and cash flows A company can show a profit, while, during the same period, the cash flows from operating activities are negative because the investment component of the operating cycle (working capital requirement) increased more than the margin component of the operating cycle.

At the opposite, a firm can show a loss when its cash flows from operating activities is positive in two cases:

a. b.

The margin component of the operating cycle is negative and the working capital requirement decreased more than the absolute value of the margin component.

The margin component is positive and the working capital requirement increased less than the margin component.

Chapter 5 Answers to Review Problems Finance for Executives – 7th Edition

1. Transactions

NLF

WCR

NSF

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NET PROFIT

Shares are issued for cash.

+

0

–

0

Goods for inventory are sold for cash.

+

–

–

+

Goods from inventory are sold on account.

+

+

0

+

A fixed asset is sold for cash for less than book value.

+

0

–

–

A fixed asset is sold for cash for more than book value.

+

0

–

+

Corporate income tax is paid.

0

+

+

0

Payment is made to trade creditors.

0

+

+

0

Cash is obtained through a short-term bank loan.

0

0

0

0

Cash is obtained through a long-term bank loan.

+

0

–

0

A cash dividend is declared and paid.

–

0

+

0

Accounts receivable are collected.

0

–

–

0

Merchandise is purchased on account.

0

0

0

0

Cash advances are made to employees.

0

+

+

0

Minority interest in a firm is acquired for cash.

–

0

+

0

Equipment is acquired for cash.

–

0

+

0

2. Reconstructing a balance sheet

Sales:

20 days of sales

= $400,000

360 days of sales

= ($400,000/20) × 360 = $7,200,000

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Accounts receivable:

40 days of sales

= ($7,200,000/360) × 40 = $800,000

Inventory:

Inventory

= Sales/6 = $7,200,000/6 = $1,200,000

Working capital requirement (WCR):

WCR

= 0.20 × Sales = 0.20 × $7,200,000 = $1,440,000

Accounts payable:

Given that WCR

= (Accounts receivable + Inventory) – Accounts payable,

Accounts payable

= (Accounts receivable + Inventory) – WCR = ($800,000 + $1,200,000) – $1,440,000 = $560,000

Net fixed assets:

Net fixed assets

= Total assets – Current assets

For use with Finance for Executives: Managing for Value Creation 7th edition

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Net fixed assets

= Total assets – Inventory – Accounts receivable – Cash = $5,000,000 – $1,200,000 – $800,000 – $400,000 = $2,600,000

Short-term debt:

Liabilities

= 0.60 × total assets = 0.60 × $5,000,000 = $3,000,000

Financial debt

= Liabilities – Accounts payable = $3,000,000 – $560,000 = $2,440,000

Short-term debt

= 0.10 × $2,440,000 = $244,000

Long-term debt:

Long-term debt

= Financial debt – Short-term debt = $2,440,000 – $244,000 = $2,196,000

Owners’ equity:

Owners‘ equity

= Total assets – Liabilities = $5,000,000 – $3,000,000 = $2,000,000

Assets

Liabilities For use with Finance for Executives: Managing for Value Creation 7th edition

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Cash

$ 400,000

Short-term debt

$ 244,000

800,000

Accounts payable

560,000

Accounts receivable Inventory

1,200,000

Total current assets

$2,400,000

Net fixed assets

$2,600,000

Total assets

$5,000,000

Total current liabilities

$ 804,000

Long-term debt

$2,196,000

Owners‘ equity

2,000,000

Total liabilities and owners’ equity

$5,000,000

Balance Sheet:

3. Measuring liquidity

a.

For 2020 Current assets Current liabilities Current ratio

= Accounts receivables + Inventories + Cash = 50 + 200 +100 = 350 = Accounts payables + Short-term debt = 100 + 50 = 150 = 350/150 = 2.33

For 2021 Current assets

= Accounts receivables + Inventories + Cash

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Current liabilities Current ratio

= 100 + 250 + 50 = 400 = Accounts payables + Short-term debt = 50 + 50 = 100 = 400/100 = 4.00

b. The current ratio is a measure of liquidity which means that it should ideally increase the liquidity when it increases. However, in this case the liquidity seems to be decreasing because cash is being used to pay off payables. While receivables increase, they are not as good as cash for the liquidity position.

4. Managing liquidity

a. Wrong.

From where would the cash come from to repurchase shares or reimburse short-term debt?

The relationship is a tautology. As such, it cannot be used for causality relations.

b. Wrong.

By writing down inventories, profits will go down and as a consequence, so will owner‘s equity and net long-term financing. Net short-term financing, and as a result the liquidity of the business unit liquidity will not be affected (before tax effects).

c. Wrong.

Accounts receivable will increase, as will working capital requirement and, as a result the cash holdings of the business unit will decrease.

d. Right.

The bank will receive less income from the firm but, since the decrease in working capital requirement is a signal of better management, it will feel more secure in the ability of its client to service its debt.

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5. Trade credit terms

Assume a $100 invoice. La Tierra Inc. has the choice to pay $99 in 30 days or $100 in 60 days.

The early payment is equivalent to lending $99 and receiving $100 thirty days later (60 days – 30 days). The effective annual interest rate is thus:

6. Optimal credit policy

a. The NPV of selling for cash is: 100 × $100 – 100 × $50 = $10,000 × $5,000 = $5,000

b. The NPV of selling at credit is the difference between the present value (PV) of the expected payments from customers in one month time and the cost of the computer programs sold.

Since 10 percent of the customers are not expected to pay their bills, 90 percent will. Thus, the expected cash flows to be received by Algebra Ltd in one month time are:

0.90 × 130 × $100 = $11,700

The PV of $11,700 at a cost of capital of 1 percent is:

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The cost of the programs sold is:

100 × $55 = $5,500 And the NPV of offering credit is:

$11,584 – $5,500 = $6,084

c. The NPV of offering credit ($6,084) is higher than selling only for cash ($5,000). Algebra Ltd should adopt the credit policy strategy.

7. The consequences of the 2008 financial crisis

Not necessarily. The cash held by your firm would have been deposited in one or several banks.

If one, or more, of these banks would have gone bankrupt as did Lehmann Brothers, your firm could not have access to some of its cash, even losing it.

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8. Industry effect on the working capital requirement

All dollars in millions a.

Firm 1

Firm 2

Firm 3

Firm 4

WCR

$1,489

($4,250)

$8,942

$1,207

WCR/Sales

53.3%

–27.6%

15.7%

0.3%

Collection period

61.5 days

17.3 days

67.8 days

5.3 days

Inventory turnover

1.9

39.4

6.7

10.7

Working capital requirement (WCR) = Accounts receivable + Inventories + Prepaid expenses + Other current assets – Accounts payable – Accrued expenses – Other current liabilities

Firm 1

WCR = $471 + $1,481 + $187 + $0 – $650 – $0 – $0 = $1,489

Working capital requirement-to-revenue ratio = $1.489/$2,796 = 0.53

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Collection period days =

Accounts receivable $471 = = 61.5 days $2,796 / 365 Re venue / 365

Inventory turnover

$2,796 Re venue = = 1.9 Inventorie s $1,481

=

Firm 2

WCR = $730 + $390 + $0 + $236 – $1,977 – $3,629 – $0 = ($4,250)

Working capital requirement-to-revenue ratio = ($4,250)/$15,382 = (0.276)

Collection period days

=

Accounts receivable $730 = = 17.3 days $15,382 / 365 Re venue / 365

Inventory turnover

=

Re venue $15,382 = = 39.4 $390 Inventorie s

Firm 3

WCR = $10,556 + $8,476 + $0 + $334 – $10,425 – $0 – $0 = $8,942

Working capital requirement-to-revenue ratio = $8,942/$56.786 = 0.157

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Collection period days

=

Accounts receivable $10,556 = = 67.8 days $56,786 / 365 Re venue / 365

Inventory turnover

=

$56,786 Re venue = = 6.7 Inventorie s $8,476

Firm 4

WCR = $6,768 + $43,803 + $0 + $1,588 – $50,952 – $0 – $0 = $1,207

Working capital requirement-to-revenue ratio = $1,207/$469,162 = 0.003

Collection period days

=

Accounts receivable $6,768 = = 5.3 days $469,162 / 365 Re venue / 365

Inventory turnover

=

Re venue $469.162 = = 10.7 Inventorie s $43,803

b.

Firm 1 is Constellation Brands Inc.: Inventory turnover is low, reflecting aging wine. As a result, working capital requirement is high relative to sales (53.3 cents out of one dollar of sales is locked in the firm‘s operating cycle).

Firm 2 is Carnival Corporation: The negative working capital requirement is the result of a large amount of other current liabilities, which in turn, reflects the accumulation of the deposits, or advanced payments, made by customers booking cruises.

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Firm 3 is The Dow Chemical Company: The working capital requirement-to-revenue ratio is positive and represents 17.3 percent of the annual sales, a value typical of chemical manufacturing companies. For these companies, clients are billed on account. In the case of Dow Chemical, they pay on average more than two months later.

Firm 4 is Wal-Mart Stores, Inc.: The working capital requirement-to-revenue ratio is very low and reflects the main characteristics of the non-grocery sector of the retail industry—high inventory turnover, very low collection period, and high level of accounts payable compared to accounts receivable.

9. Financing strategies

The managerial balance sheet of the three firms can be directly constructed from the data with Working capital requirement = Accounts receivable + Inventories – Accounts payable:

Firm A

Firm B

Firm C

Invested capital Cash Working capital requirement Net fixed assets Total invested capital

$ 0 25 50 $75

$10 15 50 $75

$ 0 25 50 $75

Capital employed Short-term debt Long-term financing Total capital employed

$ 0 75 $75

$ 0 75 $75

$10 65 $75

It follows that:

Firm A

Firm B

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Firm C

Net long-term financing [Long-term financing – Net fixed assets] Net short-term financing [Short-term debt – Cash]

$25

$ 25

$15

0

(10)

10

Firm A has an excess of long-term financing of $25 after funding its net fixed assets, which is exactly equal to its working capital requirement: the firm‘s operating cycle is financed exclusively with long-term funds. The firm has no cash and no short-term debt. The firm follows a matching finance strategy.

Firm B has an excess of long-term financing of $25 after funding its net fixed assets, which is exactly equal to the sum of its working capital requirement and cash holdings. Not only is its operating cycle is financed exclusively with long-term funds but also is the totality of its cash holdings. The firm follows a conservative financing strategy.

Firm C has an excess of long-term financing of $15 after funding its net fixed assets of $50, which is lower than its working capital requirement of $25. Thus, its operating cycle is partially financed by short-term funds, up to $10. The firm follows an aggressive financing strategy.

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10. The financial effect of the management of the operating cycle

All dollars in thousands a.

Working capital requirement (WCR) = Accounts receivable + Inventories + Prepaid expenses – Accounts payable – Accrued expenses

Year-end 1:

WCR = $2,730 + $2,800 + $0 – $1,400 – $200 = $3,930

Year-end 2:

WCR = $3,100 + $3,200 + $0 – $1,600 – $260 = $4,440

Year-end 3:

WCR = $4,200 + $4,300 + $0 – $2,050 – $350 = $6,100

b.

Managerial balance sheets

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Year-end 1

Year-end 2

Year-end 3

Invested capital Cash

$ 600

$ 350

$ 300

Working capital requirement (WCR)

3,930

4,440

6,100

Net fixed assets

1,200

1,300

1,450

Total invested capital

$5,730

$6,090

$7,850

Short-term debt

$ 300

$ 500

$1,900

Long-term financing

5,430

5,590

5,950

Capital employed

Long-term debt

$1,300

$1,200

$1,100

Owners‘ equity

4,130

4,390

4,850

Total capital employed

$5,730

$6,090

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$7,850

c.

Net long-term financing (NLF) = Long-term debt + Owners‘ equity – Net fixed assets

Year-end 1: NLF = $1,300 + $4,130 – $1,200 = $4,230

Year-end 2: NLF = $1,200 + $4,390 – $1,300 = $4,290

Year-end 3: NLF = $1,100 + $4,850 – $1,450 = $4,500

Net short-term financing (NSF) = Short-term debt – Cash

Year-end 1: NSF = $300 – $600 = ($300)

Year-end 2: NSF = $500 – $350 = $150

Year-end 3: NSF = $1,900 – $300 = $1,600

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Note that net short-term financing (NSF) went up drastically from Year-end 1 to Year-end 3. In the third year, the firm‘s financing strategy changed from a matching one to a very aggressive one. During that year, each extra dollar invested in the operating cycle which was not financed either by retained earnings or long-term debt was funded by short-term debt. NSF can increase only if the firm‘s net long-term financing (NLF) decreases, and/or its working capital requirement increase. It is clear from the data that the change in the financing strategy was triggered by an increase in the firm‘s investment in its operating cycle (increase in WCR) that was not matched by a corresponding increase in long-term financing (NLF).

d.

Pro forma working capital requirement (WCR)Year-end 3

Accounts receivable Year-end 3 =

Inventory Year-end 3

=

Net sales 365

 30 days 

Cost of goods sold 8

Accounts payable Year-end 3 =





$31,600  30 days  $2,597 365

$25,100  $3,138 8

Purchases  33 days 365

Cost of goods sold  Change in inventorie s  33 days 365

Working capital requirement Year-end 3 = Accounts receivable + Inventories + Prepaid expenses – Accounts payable – Accrued expenses For use with Finance for Executives: Managing for Value Creation 7th edition

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= $2,597 + $3,138 + $0 –$2,264– $350 = $3,121

Pro forma managerial balance sheet Year-end 3 Invested capital Cash Working capital requirement (WCR) Net fixed assets Total invested capital Capital employed Short-term debt Long-term financing Long-term debt Owners‘ equity Total capital employed

$1,379 3,121 1,450 $5,950 $

0 5,950

$1,100 4,850 $5,950

Note that the amount of long-term financing ($5,950) would have been higher than the investment in fixed assets and in the operating cycle ($1,450 + $3,121 = $4,571). Sentec Inc. would not have needed any short-term debt, and would have $1,379 million ($5,950 – $44,571) in cash.

Net long-term financing (NLF) = Long-term debt + Owners‘ equity – Net fixed assets NLF = $1,100 + $4,850 – $1,450 = $4,500 Net short-term financing (NSF) = Short-term debt – Cash NSF = $0 – $1,484 = ($1,484) Sentec Inc. would have exhibited a conservative finance strategy instead of an aggressive one.

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11. Seasonal business

All dollars in thousands a.

Working capital requirement (WCR) = Inventories + Accounts receivable + Prepaid expenses – Accounts payable – Accrued expenses

Collection period days =

Accounts receivable Re venues / 180

Inventories turnover =

Cost of goods sold  2 Inventorie s

Payment period days =

Accounts payable Accounts payable  Purchases / 180 [Cost of goods sold  Change in inventorie s] / 180

June 30, Year 1

WCR = $1,986 + $1,953 + $80 – $1,450 – $98 = $2,471

Collection period days =

$1,953 = 33 days (rounded) $10,655 / 180

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$8,940  2 = 9.0 $1,986

Inventories turnover

=

Payment period

= 29 days (given)

December 31, Year 1

WCR = $2,694 + $2,616 + $42 – $1,950 – $114 = $3,288

Collection period days =

Inventories turnover =

Payment period

$2,616 = 34 days (rounded) $13,851 / 180

$11,671  2 = 8.7 $2,694



$1,950 $1,950  [$11,671  ($2,694  $1,986)] / 180 [$11,671  $708] / 180



$1,950 = 28.4 days (rounded) $12,379 / 180

June 30, Year 0

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WCR = $2,085 + $2,100 + $25 – $1,650 – $138 = $2,422

Collection period days =

Inventories turnover =

Payment period

$2,100 = 32.3 days (rounded) $11,720 / 180

$9,834 x 2 = 9.4 $2,085



$1,650 $1,650  [$9,834  ($2,085  $2,694)] / 180 [$9,834  ($609)] / 180



$1,950 = 32.2 days (rounded) $9,225 / 180

b.

Managerial balance sheet June 30, Year 0 Invested capital Cash Working capital requirement (WCR) ((WC(WCR) Net fixed assets Total invested capital Capital employed Short-term debt Long-term financing Long-term debt Owners‘ equity

December 31, Year 1

June 30, Year 1

$ 70 2,422 830 $3,322

$

60 3,288 818 $4,166

$

$

$ 880 3,286

$

50 3,272

$ 700 2,572

$ 750 2,536

160 2,471 733 $3,364 50 3,314

$ 800 2,514

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Total capital employed

$3,322

$4,166

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$3,364

c.

Net long-term financing (NLF) = Long-term debt + Owners‘ equity – Net fixed assets

June 30, Year 1: NLF = $800 + $2,514 – $733 = $2,581

December 31, Year 1:

NLF = $750 + $2,536 – $818 = $2,468

June 30, Year 0: NLF = $700 + $2,572 – $830 = $2,442

Net short-term financing (NSF) = Short-term debt – Cash

June 30, Year 1: NSF = $50 – $160 = ($110)

December 31, Year 1:

NSF = $880 – $60 = $820

June 30, Year 0: For use with Finance for Executives: Managing for Value Creation 7th edition

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NSF = $50 – $70 = ($20)

Mars Electronics has a matching strategy since its short-term financing needs are funded with short-term debt and its permanent financing needs are funded with long-term debt and equity.

The firm has a seasonal activity: its sales and working capital requirement are larger in the second part of the year than in the first part of the year. During the first part of the year, net short-term financing is negative since there is enough long-term financing to fund the firm‘s fixed assets and working capital requirement, while it is positive in the second part of the year when short-term debt is used to finance the seasonal increase in working capital requirement.

Note that the amount of net short-term financing at the trough of the season (Year 0) is lower than a year before (–$20 million versus $110 million). If the firm continues to grow at the same rate in the years to come, the permanent part of its working capital requirement (its value at the trough of the season) would continue to grow, and if no long-term funds are raised, the firm‘s financing strategy may change from matching to aggressive.

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12. Comparative analysis

a. Since KTS Enterprises has the highest inventory turnover ratio of 3.8, it is most efficient in utilizing its inventories. This means that to make a sale of $3.8, it must maintain an inventory of $1. For 1$ inventory, ARM Contractors and the industry make a sale of only $3.3 and $3.7. b. No, ARM contractors are less efficient than KTS Enterprises as well as the industry because they have a higher working capital requirement as a percentage of sale. ARM Contractors require 29 percent of their sales as working capital whereas KTS Enterprises need only 24 percent. The corresponding requirement for the industry is 25 percent. c. ARM Contractors has a lower credit risk because they have the least Days receivables outstanding ratio of 30 days. This signifies that ARM Contractors have sold 30 days‘ worth of their product based on their average daily sales volume. The corresponding figure for KTS Enterprises in higher at 38 days which means they have more sale on credit. d. Some reasons for days payables outstanding being the same for all companies can include:  Industry practice of following the credit terms strictly.  Only one seller dictating the terms to all the companies.

Chapter 6 Answers to Review Problems Finance for Executives – 7th Edition

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1. Transactions

Operating margin

Invested capital turnover

Debt ratio

1. Shares are issued for cash.

0

–

–

2. Goods from inventory are sold for cash at a profit.

+

+

–

3. A fixed asset is sold for cash at its book value.

0

0

0

4. A fixed asset is sold for more than its book value.

0

–

–

5. A dividend is declared and paid.

0

+

+

6. Cash is obtained through a bank loan.

0

–

+

7. Accounts receivable are collected.

0

0

0

8. Minority interest in a firm is acquired for cash.

0

0

0

9. A fixed asset is depreciated.

–

+

+

10. Obsolete inventory is written off.

–

+

+

11. Merchandise is purchased on account.

0

0

0

12. Shares are repurchased.

0

+

+

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2. ROICBT , ROCEBT, ROBA, and ROTA

Measure

Definition

Value

ROICBT

EBIT/Invested capital

$24.0/$138.0 = 17.4%

ROCEBT

EBIT/Capital employed

$24.0/$138.0 = 17.4%

ROBA

EBIT/Business assets

$24.0/($77.0 + $53.0) = 18.5%

ROTA

EBIT/Total assets

$24/$190.0 = 12.6%



ROICBT and ROCEBT are the same. The former refers to the return on the assets used to generate the 17.4 percent return while the second refers to the amount of capital that was needed to generate the same return.



ROBA is higher than ROICBT because it does not include the amount of cash held by OS Distributors, while it is accounted for in ROICBT.



ROTA is the lowest of the four measures of return, because, unlike the other measures, it ignores the investment reduction effect of the accounts payable and accrued expenses.

3. Book versus market return on equity

The two ratios are different because the book value is estimated using past data, up to the end of the accounting period, while the market value is determined by the investors‘ expectation regarding future earnings/cash flows. Further, financial accounting data is very sensitive to the accounting principles used to estimate it.

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The book return on equity is a valuable measure of profitability because it can be structured in a way to show the impact of different activities of the firm, such as operations, financial, and tax activities. By analysing this impact, the financial analyst is able to identify the contribution of these activities on the firm‘s ability to generate profitability.

4. Estimating ROE

We have the following formula for ROE:

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EBIT can be calculated as:

Sales

$ 10,287.00

COGS

$ 4,851.00

SG&A

$

EBIT

$ 4,458.00

Invested capital = Cash = $580

978.00

Working capital requirements ($5,525

$1,020)

Net fixed assets

$485 = $5,570

Substituting the values in the equation, we have:

5.

The structure of a firm profitability

a. 7.5 percent (0.075 × 2 = 0.15 or 15 percent) b. The financial structure effect is 1.67 (0.10 × 0.9 × 1.67 = 0.15 or 15 percent). Since the financial structure effect is Invested capital/Owners‘ equity, it is also equal to (Owners‘ equity + Debt)/Owners‘ equity or 1 + Debt/Owners‘ equity. If 1 + Debt/Owners‘ equity = 1.67, the debt-to-equity ratio is equal to 0.67.

c. This can occur when the firm receives more financial income than it pays interest charges.

6.

Misuse of the structure of the return on equity For use with Finance for Executives: Managing for Value Creation 7th edition

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a. If the firm decides not to replace existing fixed assets, its invested capital will decrease as the book value of fixed assets will decrease due to increased accumulated depreciation. Its capital turnover ratio will increase, and as a result, its return on equity will increase.

b. If the firm decides to increase its debt-to-equity ratio to a very high level when interest rates are lower than the return on invested capital before tax.

7.

Financial leverage

When the cost of debt is lower than the return on invested capital before tax: it pays to borrow when the cost of borrowing is lower than the return expected from the investment made by the firm. A formal proof is given by the ROE equation shown in the chapter‘s section entitled How Does Financial Leverage Work?

The return on equity relationship described what would happen to the return on equity if the return on invested capital will be higher or lower than the cost of borrowing, but does not provide any clue on what is the optimal capital structure decision.

8. Industry effect on the structure of the return on equity

All dollars in millions

a.

Working capital requirement (WCR) = Accounts receivable + Inventories + Prepaid expenses For use with Finance for Executives: Managing for Value Creation 7th edition

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– Accounts payable – Accrued expenses

Firm 1 WCR = $1,341 + $19,793 + $1,366 – $13,105 – $7,290 = $2,105

Firm 2 WCR = $770 + $223 + $237 – $616 – $158 = $456

Firm 3 WCR = $3,250 + $0 + $3,260 – $1,083 – $8,672 = ($3,245)

Managerial balance sheets Firm 1 INVESTED CAPITAL Cash Working capital requirement (WCR) Net fixed assets Total invested capital CAPITAL EMPLOYED Short-term debt Long-term financing Long-term debt Owners‘ equity Total capital employed

Firm 2

Firm 3

$ 1,856 2,105 45,993 $49,954

$

485 456 13,816 $14,757

$23,798 (3,245) 21,842 $42,395

$ 5,408 44,546

$ 890 13,867

$ 0 42,395

$8,205 5,662

$18,712 25,834 $49,954

$1,027 41,368 $14,757

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$42,395

b.

Operating margin

= EBIT/Sales

Invested capital turnover

= Sales/Invested capital

Return on capital employed = EBIT/Capital employed

Financial multiplier

= (EBT/EBIT) × (Invested capital/Owners‘ equity)

Tax effect

= EAT/EBT

Return on equity

= EAT/Owners‘ equity

Firm 1

Operating margin

= $10,105/$166,809 = 6.1% (rounded)

Invested capital turnover

= $166,809/$49,954 = 3.34 (rounded)

Return on invested capital

= $10,105/$49,954 = 20.2%

Financial multiplier

= ($9,083/$10,105) × ($49,954/$25,834)= 0.90 × 1.93 = 1.74

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Tax effect

= $5,745/$9,083 = 0.63

Return on equity

= $5,745/$25,834 = 22.2%

Firm 2

Operating margin

= $1,419/$7,132 = 19.9% (rounded)

Invested capital turnover

= $7,132/$14,757 = 0.48

Return on capital employed = $1,419/$14,757 = 9.6%

Financial multiplier

= ($1,114/$1,419) × ($14,757/$5,662)= 0.79 × 2.61 = 2.06

Tax effect

= $714/$1,114 = 0.64

Return on equity

= $714/$5,662 = 12.6%

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Firm 3

Operating margin

= $10,937/$22,956 = 47.6%

Invested capital turnover

= $22,956/$42,395 = 0.54

Return on invested capital

= $10,937/$42,395 = 25.8% (rounded)

Financial multiplier

= ($14,275/$10,937) × ($42,395/$41,368)= 1.31 × 1.02 = 1.34

Tax effect

= $9,421/$14,275 = 0.66

Return on equity

= $9,421/$41,368 = 22.8%

The relationship between these ratios and the firms‘ return on equity is that ROE is equal to the product of the operating margin, invested capital turnover, financial multiplier, and tax effect.

c.

Firm 1 is in the retail (non-grocery) industry, Firm 2 is a utility firm, and Firm 3 is in the computer (software industry).

The most striking feature of Firm 1 is its invested capital turnover of 3.34, which means that the firm generates $3.34 of revenue per dollar of invested capital, while the other two firms generate only around half a dollar of revenue. Among the three industries to which Firm 1 can belong, only the retail industry can exhibit such a relatively high invested capital turnover.

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Firm 2 has a slow invested capital turnover, like Firm 3. However, the net fixed assets turnover of Firm 2 is equal to 0.52 ($7,132/$13,816), which is half of that of Firm 3, itself equal to 1.05 ($22,956/$21,842). This means that Firm 2 is using twice as many fixed assets as Firm 3 to generate the same amount of revenue. Since the utilities industry is using more capital intensive plant facilities than the software industry, Firm 2 must be a utility firm. Furthermore, the financial multiplier of Firm 2 is much higher than that of Firm 3, with a financial structure ratio of 2.61 ($14,757/$5,662) versus 1.02 ($42,395/$41,368). A relatively high financial leverage ratio is also a characteristic of a utility firm since firms in this industry bear low risk due to regulation and guaranteed returns.

The most salient feature of Firm 3 is its operating margin, which is close to 50 percent. Such an extremely high level of operating margin can only be found in industries where there exists some level of unregulated monopoly power. This situation is most likely to be found in the software industry than that of the retail or utility industries. Furthermore, note that the working capital requirement of Firm 3 is negative. The company does not have any inventory and carries a high level of unearned revenues, the latter representing paid subscription to future services such as systems update and technical support, both unique characteristics of industries such as the computer industry.

9. The effect of the management of the operating cycle on the firm’s profitability

All dollars in thousands a.

Working capital requirement (WCR) = Accounts receivable + Inventories + Prepaid expenses – Accounts payable – Accrued expenses

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Year-end 1 WCR = $2,730 + $2,800 + $0 – $1,400 – $200 = $3,930 Year-end 2 WCR = $3,100 + $3,200 + $0 – $1,600 – $260 = $4,440 Year-end 3 WCR = $4,200 + $4,300 + $0 – $2,050 – $350 = $6,100

Managerial balance sheets

Year-end 1

Year-end 2

Year-end 3

Cash

$ 600

$ 350

$ 300

Working capital requirement (WCR)

3,930

4,440

6,100

Net fixed assets

1,200

1,300

1,450

Total invested capital

$5,730

$6,090

$7,850

Year-end 1

Year-end 2

Year-end 3

$ 300

$ 500

$1,900

Invested capital

Capital employed Short-term debt Long-term financing Long-term debt Owners‘ equity Total capital employed

5,430 $1,300 4,130

5,590 $1,200 4,390

$5,730

5,950 $1,100 4,850

$6,090

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$7,850

b.

Operating margin

= EBIT/Sales

Invested capital turnover

= Sales/Invested capital

Return on capital employed = EBIT/Capital employed

Financial multiplier

= (EBT/EBIT) × (Invested capital/Owners‘ equity)

Tax effect

= EAT/EBT

Return on equity

= EAT/Owners‘ equity

Year 1

Operating margin

= $650/$22,100 = 2.94%

Invested capital turnover

= $22,100/$5,730 = 3.86

Return on capital employed = $650/$5,730 = 11.34%

Financial multiplier

= ($540/$650) × ($5,730/$4,130) = 0.83 × 1.39 = 1.15

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Tax effect

= $320/$540 = 0.59

Return on equity

= $320/$4,130 = 7.75%

Year 2

Operating margin

= $900/$24,300 = 3.70%

Invested capital turnover

= $24,300/$6,090 = 3.99

Return on capital employed = $900/$6,090 = 14.78%

Financial multiplier

= ($770/$900) × ($6,090/$4,390)= 0.86 × 1.39 = 1.19

Tax effect

= $460/$770 = 0.60

Return on equity

= $460/$4,390 = 10.48%

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Year 3

Operating margin

= $1,350/$31,600 = 4.27%

Invested capital turnover

= $31,600/$7,850 = 4.03

Return on invested capital

= $1,350/$7,850 = 17.20%

Financial multiplier

= ($1,090/$1,350) × ($7,850/$4,850) = 0.81 × 1.62 = 1.31

Tax effect

= $660/$1,090 = 0.61

Return on equity

= $660/$4,850 = 13.61%

The relationship between these ratios and the firm‘s return on equity is that ROE is simply equal to the product of the operating margin, invested capital turnover, financial multiplier, and tax effect.

c.

Note the drastic increase of the return on equity which nearly doubles between Year 1 and Year 3, from 7.75 percent to 13.61 percent. This change in profitability can be attributed either to the tax effect, a change in the financial policy or in the return on invested capital.

The tax effect, which stayed between 0.59 to 0.61 (i.e., reducing the profitability by 41 to 39 percent), had no significant impact on the change in the return on equity.

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The financial multiplier, which increased the return on invested capital by 15 percent in Year 1, increased it by 31 percent in Year 3, thus improving the profitability of the firm. Had the return on invested capital been 11.34 percent in Year 3 as in Year 1, the return on equity would have been equal to 9.06 percent (11.34%  1.31  0.61), which indicates that the change in the financial multiplier explains 22.35 percent of the change in the return on equity ([9.06% – 7.75%]/[13.61% – 7.75%]). The increase in the financial multiplier was the result of the increase in the firm‘s short-term debt, which went up from $300,000 at Year-end 1to $1.9 million at Year-end 3. At the same time, the firm‘s equity went up only from $4.13 million to $4.85 million. In other words, the firm was relying more on debt financing at Year-end 3 than at Yearend 1 with two effects. First, the return on equity increased because during the three-year period, the firm‘s return on invested capital was higher than the rate at which the firm borrowed its short-term fund. Second, the financial risk of the firm increased. Had the return on invested capital been lower than the cost of borrowing in Year 3, the financial multiplier would have still worked, but would have drowned the return on equity deeper than if it had stayed at its Year 1 level of 1.15.

The return on invested capital (ROIC), which increased drastically from 11.34 percent in Year 1 to 17.20 percent in Year 3 was the main driver of the increase of the firm‘s profitability during that period. Furthermore, most of the ROIC increase comes from the operating margin which went up from 2.94 percent in Year 1 to 4.27 percent in Year 3, while the invested capital turnover increased only marginally from 3.86 to 4.03 during the same period. d.

From the data on the industry, we can compute what Sentec‘s working capital requirement would have been at Year–end 3 if it had the same activity ratios as the average of its competitors, prepare a new managerial balance sheet at that date, and analyse the impact on Sentec‘s return on equity structure in Year 3.

Pro forma working capital requirement (WCR)Year-end 3

Accounts receivable Year-end 3=

Net sales Year3 $31,600  30 days =  30 days = $2,597 365 365

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Inventories Year-end 3

=

Cost of goods sold Year3 $25,100   $3,138 8 8

Accounts payable Year-end 3 =

PurchasesYear 3  33 days 365

=

Cost of goods sold Year3  Change in inventorie s Year3  33 days 365

=

$25,100  ($3,138  $3,200)  33 days = $2,264 365

Working capital requirement (WCR) = Accounts receivable + Inventories + Prepaid expenses – Accounts payable – Accrued expenses

WCR = $2,597 + $3,138 + $0 – $2,264 – $350 = $3,121

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Pro forma managerial balance sheet Year-end 3 Invested capital Cash

$ 1,379

Working capital requirement (WCR)

3,121

Net fixed assets

1,450

Total invested capital

$5,950

Capital employed Short-term debt

$

Long-term financing Long-term debt

$1,100

Owners‘ equity

4,850

0 5,950

Total capital employed

$5,950

Note that the amount of long-term financing ($5,950) would have been higher than the investment in fixed assets and in the operating cycle ($1,450 + $3,121 = $4,571). Sentec Inc. would not have needed any short-term debt, and had $1,379 million (5,950 – $4,571) in cash.

THE STRUCTURE OF THE PRO FORMA RETURN ON EQUITY YEAR 3 OPERATING MARGIN

EBIT/Sales

4. 27%

multiplied by Invested capital turnover

Sales/Invested Capital

5.31

equals For use with Finance for Executives: Managing for Value Creation 7th edition

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RETURN ON INVESTED CAPITAL

EBIT/Invested capital

22. 67%

multiplied by EBT/EBIT)1x(Invested FINANCIAL MULTIPLIER

capital/Owners‘ equity

1.18

multiplied by EAT/EBT

TAX EFFECT

0.6

equals EAT/Owners‘ equity

RETURN ON EQUITY 1

16. 05%

If the interest charges to EBIT ratio is 4 percent, then the ratio EBT/EBIT is 0.96.

Note the drastic impact of a better management of the operating cycle on the return on invested capital, which would have jumped from 4.03 to 5.31. As a result, the return on invested capital would have reached 22.7 percent and the return on equity 16.05 percent, instead of 17.2 percent and 13.61 percent, respectively. This improvement would have been realized with a financial multiplier not significantly different from what it was at Year-end 1 (1.18 vs 1.15). In other words the drastic profitability increase would have been reached without any increase in financial risk. As the pro forma balance sheet shows, Sentec not only would not have had any short-term debt, but would have had a substantial amount of cash which could have been used for business expansion, to pay higher dividends to its shareholders or to repurchase shares.

10. Seasonal business

All dollars in thousands

a.

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Working capital requirement (WCR) = Accounts receivable + Inventories + Prepaid expenses – Accounts payable – Accrued expenses

June 30, Year 1 WCR = $1,953 + $1,986 + $80 – $1,450 – $98 = $2,471

December 31, Year 1

WCR = $2,616 + $2,694 + $42 – $1,950 – $114 = $3,288

June 30, Year 0 WCR = $2,100 + $2,085 + $25 – $1,650 – $138 = $2,422

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Managerial balance sheets

June 30, Year 1

in thousands Invested capital Cash Working capital requirement (WCR) Net fixed assets Total invested capital Capital employed Short-term debt Long-term financing Long-term debt Owners‘ equity Total capital employed

December 31, Year 1

June 30, Year 0

$ 160 2,471 733 $3,364

$

60 3,288 818 $4,166

$

$ 50 3,314

$ 880 3,286

$

$ 800 2,514

$ 750 2,536 $3,364

70 2,422 830 $3,322

50 3,272

$ 700 2,572 $4,166

b.

Operating margin

= EBIT/Sales

Invested capital turnover

= Sales/Invested capital

Return on invested capital

= EBIT/Invested capital

Financial multiplier

= (EBT/EBIT) × (Invested capital/Owners‘ equity)

Tax effect

= EAT/EBT\

Return on equity

= EAT/Owners‘ equity

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$3,322

6 Months to June 30, Year 1

Operating margin

= $117/$10,655 = 1.1% (rounded)

Invested capital turnover

= $10,655/$3,364 = 3.17 (rounded)

Return on invested capital

= $117/$3,364 = 3.48%

Financial multiplier

= ($55/$117) × ($3,364/$2,514) = 0.47 × 1.34 = 0.63 (rounded)

Tax effect

= $32/$55 = 0.58

Return on equity

= $32/$2,514 = 1.3%

6 Months to December 31, Year 1

Operating margin

= $200/$13,851 = 1.4%

Invested capital turnover

= $13,851/$4,166 = 3.32

Return on invested capital

= $200/$4,166 = 4.80%

Financial multiplier

= ($110/$200) × ($4,166/$2,536) = 0.55 × 1.64 = 0.90

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Tax effect

= $66/$110 = 0.60 (rounded)

Return on equity

= $66/$2,536 = 2.6%

6 Months to June 30, Year 0

Operating margin

= $133/$11,720 = 1.1%

Invested capital turnover

= $11,720/$3,322 = 3.53 (rounded)

Return on invested capital

= $133/$3,322 = 4.00%

Financial multiplier

= ($63/$133) × ($3,322/$2,572) = 0.47 × 1.29 = 0.61 (rounded)

Tax effect

= $37/$63 = 0.59

Return on equity

= $37/$2,572 = 1.4%

c.

Return on equity is higher in the second part of the year than in the first half (2.6 percent versus 1.3/1.4 percent) for the following reasons:

For use with Finance for Executives: Managing for Value Creation 7th edition

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1) Operating margin is higher in the second half of the year as a result of higher sales and operational leverage (fixed costs effect).

2) A higher financial multiplier in the second half of the year as a result of a higher level of short-term debt. Short-term debt is used to finance the firm‘s seasonal cash needs.

For use with Finance for Executives: Managing for Value Creation 7th edition

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11. Self-sustainable growth rate a.

The five percent target growth rate would be attainable only if the firm‘s self-sustainable growth rate is at least equal to 5 percent. Ambersome‘s self-sustainable rate can be computed as follows:

1. Assets turnover ratio

Sales/Total assets

0.9

2. Profit margin

Earnings before interest and tax/Sales

8%

3. Return on equity

Earnings after tax/ Owners‘ equity [(2)  (1 – 0.4)  (1)]1

4. Payout ratio

Dividends/ Earnings after tax

5. Self-sustainable growth rate

[(3)  [1 – (4)]

4.32%

0.4 2.59%

1

Since Ambersome has not debt, its Earnings after tax is Earnings before interest and Tax  (1 – Tax rate of 40 percent) and owners‘ equity = Total assets.

Since the self-sustainable growth rate (2.59 percent) is lower than the target sales growth rate (5 percent), Ambersome will not able to meet its target growth rate.

b.

Ambersome would have to increase its asset turnover ratio or its profit margin so that its return on equity is equal to at least 5 percent, which represents an increase of 93 percent (5%/2.59% – 1) from its current level. This requires that either the assets turnover ratio must increase to 1.737 (0.9  1.93) or the profit margin to 15.44 percent (8%  1.93), or that both of them increase in such a way that their product, which is equal to the return on equity, reaches 5 percent.

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c.

The firm‘s return on equity, and as a result, its self-sustainable rate, would increase through debt financing only if the rate at which the firm can borrow is lower than the return on assets. Since the interest rate after tax that will be charged to Ambersome is 10 percent, and its return on assets before tax is 7.2 percent, borrowing will not help in meeting the sales target of 5 percent.

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12. Ratio calculation P/E calculation:

Turnover

1,100

Cost of Goods Sold

(530)

Gross Profit

570

SG&A

(125)

Depreciation and Amortization

(225)

Operating Income

220

Other Income

27

Interest Expense

(30)

PBT

217

Tax

(52)

PAT

164

EPS 1.64

As a measure of profitability this means that the shareholders or the owners of the company have to pay $18.29 for $1 worth of income.

Market-to-book value calculation: Cash

310

Working capital requirements

130

Net fixed assets

685 For use with Finance for Executives: Managing for Value Creation 7th edition

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Invested capital

1,125

Short-term debt

(70)

Long-term debt

(185)

Owner's equity

870

This means that the market values the company at 3.44 times the value calculated as per the balance sheet.

Chapter 7 Answers to Review Problems Finance for Executives – 7th Edition

1. Future values of an investment For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

a.

Timeline:

0

1

2

3

$1,000

$2,000

$3,000

4

5

Let FV($amount)Year N = future value of the $ amount at the end of Year N.

Value at Year-end 5 = FV($1,000)4 + FV($2,000)3 + FV($3,000)3

= $1,000 × (1 + 0.04)4 + $2,000 × (1 + 0.04)3 + $3,000 × (1 + 0.04)2

= $1,000 × 1.16986 + $2,000 × 1.12486 + $3,000 × 1.08160

= $6,664 b.

Timeline: 0

1

2

3

4

$1,000

$2,000

$3,000

$1,500

5

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Value at Year-end 5 = FV($1,000)4 + FV($2,000)3 + FV($3,000)3 – FV($1,500)1

= $6,664 – $1,500 × 1.04

= $6,664 – $1,560 = $5,104

2. Present value of a contract Timeline: 0

1

2

3

$5M

$5M

$8M

$12M

Using a calculator

Contract value = $5M 

$5M $8M $12M   2 (1  0.10) (1  0.10) (1  0.10) 3

= $5M + $5M × 0.90909 + $8M × 0.82645 + $12M × 0.7513

= $25,172,802

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Using a spreadsheet

A

B 0 $5,000,000

C 1 $5,000,000

1 2 Cash flows 3 4 Cost of capital 10.00% 5 6 Present value $25,172,802 7 8 The formula in cell B6 is: =B2 + NPV(B4,C2:E2).

9 10

D 2 $8,000,000

E 3 $12,000,000

3. Buying a machine The investment is worth undertaking if its net present value is positive.

Timeline:

0

1

2

3

4

5

–$500,000

$150,000

$150,000

$150,000

$150,000

– $20,000

– $20,000

– $20,000 – $20,000 – $20,000

$150,000 + $100,000

–$520,000

$130,000

$130,000

Using a calculator

$250,000 $130,000

$130,000

For use with Finance for Executives: Managing for Value Creation 7th edition

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NPV  $520,000 

$130,000 $130,000 $130,000 $130,000 $250,000     (1  0.10) (1  0.10) 2 (1  0.10) 3 (1  0.10) 4 (1  0.10) 5

NPV  $520,000  $130,000  

1 1 1 1    2 3 (1  0.10) (1  0.10) (1  0.10) (1  0.10) 4

  $250,000

(1  0.10) 5

= –$520,000 + $130,000 × [0.90909 + 0.82645 + 0.75131 + 0.68301] + $250,000 × 0.62092

= –$520,000 + $130,000 × 3.16986 + $250,000 × 0.62092

= $47,313

Using a spreadsheet

A B C 1 0 1 2 Purchase cost of the machine -$500,000 3 Net revenues $150,000 4 Resale value of machine 5 Maintenance costs -$20,000 -$20,000 6 7 Net cash flow -$520,000 $130,000 8 9 Cost of capital 10% 10 11 Net present value $47,313 12 13 The formula in cell B6 is: =B7 + NPV(B9,C7:H7).

14 15

D 2

E 3

F 4

G 5

$150,000

$150,000

$150,000

$150,000 $100,000

-$20,000

-$20,000

-$20,000

$130,000

$130,000

$130,000

For use with Finance for Executives: Managing for Value Creation 7th edition

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$250,000

NPV is positive, so the machine should be purchased.

For use with Finance for Executives: Managing for Value Creation 7th edition

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4. Buying a car a.

Timeline of No Better Deals offer: 0

$9,500 Timeline of Best Deals offer:

0

$4,000

1

2

$6,000

The cash flows related to the two offers cannot be directly compared since they do not take place at the same time. To make them comparable you have to imagine a financial transaction which, combined with the Best Deals offer, will result in a single cash outflow at time zero. This cash outflow could then be directly compared with the $9,500 of the No Better Deals offer.

This financial transaction is straightforward: lend at 12 percent a $ amount at time zero, such that you will get $6,000 at the end of Year 2, interest included. This amount is

$6,000 = $4,783.

(1  .12) 2

Then, if you choose the Best Deals offer you would have to pay $4,000 to the dealer, get your car, and drive to your bank where you would invest $5,237 at 12 percent. In two years‘ time, you For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

would go to your bank and take your savings out. You would get exactly $6,000 that you would immediately give to Best Deals, as final payment for your car. The combination of the two transactions—buying the car and investing at your bank—would result in a net cash outflow of $4,000 + $4,783 = $8,783 at time zero and zero net cash flow at the end of Year 2. These $8,783 are now comparable to the $9,500 of the No Better Deals offer since these cash outflows would take place at the same time. You will obviously prefer the Best Deals offer.

b.

Timeline of New Best Deals offer:

0

1

2

$2,000

$3,000

$5,000

Timeline of Old Best Deals offer:

0

$4,000

1

2

$6,000

We showed in part a. that the old Best Deals offer is equivalent to spending $8,783 at time zero.

Using the same approach to value the new offer, you would have to invest at your bank For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

$3,000 $5,000  = $6,665 at the same time you get your car and pay $2,000 to the dealer. In one 1  .12 (1  .12) 2

year's time, you would go to the bank and retrieve $3,000 that you would immediately turn to Best Deals. You would have to go again to the bank in two years‘ time, take out what is left of your savings (i.e., $5,000), and give it to the dealer as the last payment. These transactions would involve only one cash outflow at time zero equals to $8,665 ($2,000 to the dealer and $6,665 invested at your bank). Since this is less than the $9,500 deal offered by No Better Deals, you would prefer to buy the car from Best Deals.

c.

1. For No Better Deals, the present value of the 36 monthly payments must be equal to $10,000 at 0.5 percent per month. Since the present value of an annuity of $1 at 0.5 percent per period $10,000 over 36 periods is $, the monthly payments would have to be  $304.22 .

32.871 2. The present value of 36 monthly payments of $302.71 when you can invest at 1 percent per month is $9,114. This is the present value of 36 annuities of $302.71 at 1 percent per period over 36 periods. This would be the net cost of the car to you. The transaction implies investing $9,114 in the bank at 1 percent per month and have the bank make 36 payments of $302.71 to the car dealer.

5. Saving for college Timeline: 0

1

2

3

9

10

$X

$X

$X

$X

$X

$160,000

where X is the annual payment to the saving account.

For use with Finance for Executives: Managing for Value Creation 7th edition

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Using a calculator

First, find the present value of $160,000 and second, using the annuity formula A6.1.2, compute the annuity.

PV($160,000, 10 years at 4 percent) =

$160,000 = $160,000 × 0.675564 = $108,090 (1  0.04)10

From equation 2.11 in Chapter 2:

$108,090 = Annuity × Annuity discount factor (ADF)

Annuity =

$108,090 ADF

From Appendix 1:

ADF 

1  0.675564  8.11 .04

So that:

Annuity =

$108,090 = $13,327 8.11

Using a spreadsheet For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

A

B

1 2 3 Future value $160,000 4 Numper of payments 10 5 Interest rate 4% 6 7 Annuity $13,327 8 9 The formula in cell B7 is: =PMT(B5,B4,0,B3).

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6. Saving for retirement a.

Timeline ($ thousands):

$100

$100

$100 $100

42

58

$100 0

1

2

39

3

40 $In $In $In

$In

41

59

$In

where $In is the annual payment to the pension fund.

Using a calculator

To get $100,000 at the end of each year from the end of year 40 to the end of year 59, the amount that needs to be saved by the end of year 39 is the present value of the $100,000 annuity discounted for 20 years, at either 12 or 6 percent depending upon the investment strategy chosen.

The annual payment to the savings account from now to the end of year 39 is an annuity for which the future value at the end of year 39 must be equal to the present value of the amount needed to be saved at that date.

For use with Finance for Executives: Managing for Value Creation 7th edition

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For use with Finance for Executives: Managing for Value Creation 7th edition

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Using a spreadsheet A

B C Now to Year-end 39 Year-end 39 to Year 64

D E Savings Needed Annual payments Year-end 39 to Year 39

1 2 3 4 Investment rates 6% 6% $1,146,992 $7,411 5 Investment rates 12% 12% $746,944 $974 6 Investment rates 12% 6% $1,146,992 $1,495 7 Investment rates 6% 12% $746,944 $4,826 8 Years of annuities 20 9 Annuities at retirement $100,000 10 Years of contribution 40 11 12 The formula in cell D4 is: =PV(C4,$C$8,$C$9). For D5, D6, D7, change C4 to C5, C6, C7.

13 14 The formula in cell E4 is: =PMT(B4,$B$10,D4). For E5, E6, E7, change B4 to B5, B6, B7 15 and change D4 to D5, D6, D7.

16

b.

The strategy to adopt depends upon your attitude towards risk. The 12 and 6 percent returns used in the computations are based on historical average returns. These are returns that can be expected over a long period of time. However, the probability that the investor will experience an actual return different from the expected one is higher with the aggressive investment (12 percent average) than it is with the conservative one (6 percent average return). A ―reasonable‖ strategy might be to invest in the aggressive portfolio during the work-related income-producing years from the age of 25 to 65, and then in the conservative portfolio after retirement.

7. Financial deals For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

a.

Timeline: 0

1

2

3

8 9

$250M

$50M m

$50M

$50M m

$50M m

$50M m

The objective is to compute the discount rate implicit in the proposed ―deal.‖ The aunt would receive $250,000 now [present value] and give up $50,000 per year [annuity] for the next 9 years.

Using a calculator

The implicit discount rate k is the solution of:

 1 1 1 1 1  $250,000  $50,000      ......   2 3 8 (1  k ) (1  k ) (1  k ) 9  1  k (1  k )

A trial-and-error calculation will show that the discount rate would be 13.7%.

For use with Finance for Executives: Managing for Value Creation 7th edition

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Using a spreadsheet

A B C D E F G H I J K 1 0 1 2 3 4 5 6 7 8 9 2 3 Cash flows -$250,000 $50,000 $50,000 $50,000 $50,000 $50,000 $50,000 $50,000 $50,000 $50,000 4 5 Discount rate 13.7% 6 7 The formula in cell B5 is: =IRR(B3:K3).

8 9

b.

The question is whether this would be satisfactory for the aunt. If she would not be able to obtain the $250,000 from any other source, then she has little choice. If she were able to borrow the $250,000 from a bank or other lender at a lower interest rate, then she should tell the finance company to get lost.

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8. Value of a firm Timeline: 0

1

2

3

$100,000 $120,000 $150,000

4

5

$150,000

$500,000 + $150,000 $650,000

The value of the firm is the present value of this series of cash flows discounted at 10 percent.

Using a calculator

Value of the firm =

$100,000 $120,000 $150,000 $150,000 $650,000     2 3 4 1  0.10 (1  0.10) (1  0.10) (1  0.10) (1  .010) 5

= $100,000 × 0.9090909 + $120,000 × 0.82644463 + $150,000 × 0.7513148 + $150,000 × 0.6830135 + $650,000 × 0.6209213

= $808,831

Using a spreadsheet

For use with Finance for Executives: Managing for Value Creation 7th edition

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A

B 0

C 1

1 2 3 Cash flows $100,000 4 5 Discount rate 10.0% 6 7 Value of the firm $808,831 8 9 The formula in cell B7 is: =NPV(B5,C3:G3).

10

D 2

E 3

F 4

G 5

$120,000

$150,000

$150,000

$650,000

For use with Finance for Executives: Managing for Value Creation 7th edition

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9. Investment analysis There are two approaches to this question. You could calculate the IRR for the cash flows and check if it is more than 15 percent. Additionally, checking whether the NPV at 15 percent is positive means the project might be accepted or rejected. The cash flows can be represented as:

Period

Cash flow (million)

DF (15%)

PV (million)

0

$(400.00)

1

$(400.00)

1

$(400.00)

0.869565

$(347.83)

2

$(400.00)

0.756144

$(302.46)

3

$ 300.00

0.657516

$ 197.25

4

$ 300.00

0.571753

$ 171.53

5

$ 300.00

0.497177

$ 149.15

6

$ 300.00

0.432328

$ 129.70

7

$ 300.00

0.375937

$ 112.78

8

$ 300.00

0.326902

$ 98.07

9

$ 300.00

0.284262

$ 85.28

10

$ 300.00

0.247185

$ 74.16

NPV

$ (32.37)

Since the NPV at 15 percent is negative, this project will not lead to value creation given the amount of risk.

Using a spreadsheet to calculate the IRR, we get 14.27 percent as the IRR, which is less than the 15 percent required return. Hence the project should not be invested in.

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10.Competing investment projects a.

Timelines:

Project I

0

1

2

3

4

5

–$25M

$3M

$5M

$8M

$10M

$13M

For use with Finance for Executives: Managing for Value Creation 7th edition

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Project II

0

–$25M Using a calculator

NPV(I)  $25M 

1

2

3

4

5

$12M

$9M

$7M

$4M

$3M

$3M $5M $8M $10M $13M     2 3 4 1  0.10 (1  0.10) (1  0.10) (1  0.10) (1  0.10)5

= –$25M + $3M × 0.90909 + $5M × 0.82645 + $8M × 0.75131 + $10M × 0.68301 + 13M × 0.62092

= $2.772M

NPV(II)  $25M 

$12M $9M $7M $4M $3M     2 3 4 1  0.10 (1  0.10) (1  0.10) (1  0.10) (1  0.10) 5

= –$25M + $12M × 0.90909 + $9M × 0.82645 + $7M × 0.75131 + $4M × 0.68301 + $3M × 0.62092

= $3.201M

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Using a spreadsheet

A

B 0

1 2 3 Cash flows – Project I -$25,000,000 4 5 Cash flows – Project II -$25,000,000 6 7 Discount rate 10.0% 8 9 Net present value – Project I $2,772,134 10 11 Net present value – Project II $3,201,129 12 13 The formula in cell B9 is: =B3 + NPV(B7,C3:G3).

14 15 The formula in cell B11 is: =B5 + NPV(B7,C5:G5).

16

C 1

D 2

E 3

F 4

G 5

$3,000,000

$5,000,000

$8,000,000

$10,000,000

$13,000,000

$12,000,000

$9,000,000

$7,000,000

$4,000,000

$3,000,000

Project II must be preferred to Project I since its net present value is higher.

b.

It is not necessarily the case that Project II would be always better than Project I when the cost of capital changes from 10 percent. Since the cash flows increase in size over time for Project I, they are worth less in present value terms than the cash flows of Project II when the discount rate increases. However, at low discount rates, the higher cash flows of Project I are more valuable than the low cash flows of Project II. As a result, at a sufficiently low cost of capital, Project I could have a higher net present value than Project II. By trial and error, we found that the breakeven point is 8.7 percent, with a net present value of $3.949 million for both projects.

11.Comparing projects with unequal economic life For use with Finance for Executives: Managing for Value Creation 7th edition

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Timelines:

Standard Model 0

1

2

3

4

–$50M

–$4M

–$4M

–$4M

–$4M

0

1

2

3

4

–$90M

–$2.5M

–$2.5M

Superior Model

–$2.5M –$2.5M

5

6

–$2.5M –$2.5M

a.

Using a calculator

For use with Finance for Executives: Managing for Value Creation 7th edition

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PV(Standard) =  $50M 

$4M $4M $4M $4M    2 3 1  0.08 (1  0.08) (1  0.08) (1  0.08) 4

= –$50M – $4M × (.92593 + 0.85734 + 0.79383 +0.73503)

= –$63.25M

PV(Superior) =  $90M 

$2.5M $2.5M $2.5M $2.5M $2.5M $2.5M      2 3 4 5 1  0.08 (1  0.08) (1  0.08) (1  0.08) (1  0.08) (1  0.08) 6

= –$90M – $2.5M × (0.92593 + 0.85734 + 0.79383 + 0.73503 + 0.68058 + 0.63017)

= –$101,557M

For use with Finance for Executives: Managing for Value Creation 7th edition

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Using a spreadsheet

A B 1 0 2 3 Cash flows – standard model -$50,000 4 5 Cash flows – superior model -$90,000 6 7 Discount rate 8.0% 8 9 Present value – standard machine -$63,249 10 11 Present value – superior machine -$101,557 12 13 The formula in cell B9 is: =B3 + NPV(B7,C3:F3).

14 15 The formula in cell B11 is: =B5 + NPV(B7,C5:H5).

16

C 1

D 2

E 3

F 4

-$4,000

-$4,000

-$4,000

-$4,000

-$2,500

-$2,500

-$2,500

-$2,500

G 5

H 6

-$2,500

-$2,500

b.

The cash flows obviously cannot be directly compared because the standard model would have to be replaced at the end of the fourth year whereas the superior model would still have two years before needing replacement. In order to be able to evaluate them on the basis of equal lives, one would have to have a sequence of six standard models against four superior models. Besides it being a tedious calculation, it is essentially a waste of time to project cash flows over such a long period of time since technological changes are virtually certain to occur.

c.

The constant annuity-equivalent cash flow cost of each model [at an 8 percent discount rate], using the following equation (see equation 2.11 in Chapter 2):

For use with Finance for Executives: Managing for Value Creation 7th edition

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Constant annuity-equivalent cash flow 

Pr esent value of original cash flow Annuity discount factor

The present value of initial cash flow for the standard model is –$63,248 and –$101,557 for the superior one.

The annuity discount factor is given by equation 2.11 in Chapter 2:

1 Annuity discount factor 

1 (1  k ) N k

where k is the cost of capital (8 percent for Rollon) and N is the useful life of the equipment (4 years for the standard model and 6 years for the superior model).

Applying the formula, we get:

1

1 (1  .08) 4  3.312 .08

1

1 (1  .08) 6  4.623 .08

Annuity discount factor standard 

Annuity discount factor superior 

and

Constant annuity-equivalent cash flow standard 

 $63,249 = –$19,097 3.312

For use with Finance for Executives: Managing for Value Creation 7th edition

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Constant annuity-equivalent cash flow superior 

 $101,557 = –$21,968 4.623

d.

On the basis of expected costs, the company should purchase the standard model. This may also be desirable because in four years‘ time, the changes in technology or in the markets may render the superior model obsolete or useless.

For use with Finance for Executives: Managing for Value Creation 7th edition

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12.Comparable NPV analysis a.

Cash flow

Project A

Project B

DF @ 10%

PV Project A

PV Project B

0

–$10 million

–$25 million

1.00

$ –10,000,000.00

$ –25,000,000.00

1

$4 million

$8 million

0.91

$

3,636,363.64

$

7,272,727.27

2

$5 million

$10 million

0.83

$

4,132,231.40

$

8,264,462.81

3

$6 million

$12 million

0.75

$

4,507,888.81

$

9,015,777.61

4

$4 million

$10 million

0.68

$

2,732,053.82

$

6,830,134.55

NPV

$

5,008,537.67

$

6,383,102.25

As per the NPV rule, since the NPV of project B is higher, we would choose project B.

b.

Project A has significantly less investment requirement than B. As a result, one can use other metrics to determine if project B is more attractive considering that we could invest in each project more than once. We can use the profitability index which adjusts for the differences in initial investments.

For use with Finance for Executives: Managing for Value Creation 7th edition

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Since the profitability index of project A is higher, it should yield a better return.

Chapter 8 Answers to Review Problems Finance for Executives – 7th Edition

1. Using appropriate metric a. Net present value – the initial investment amount would be the discounted present value of the future required cash flows. b. Payback – the number of periods it takes to recoup the investment. c. IRR – the IRR for two sets of cash flows are compared and the higher selected. d. Net present value – the NPV of the annuity is calculated and compared with the winnings receivable today if such an option is chosen. e. Net present value – of all future pension payments.

For use with Finance for Executives: Managing for Value Creation 7th edition

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f. IRR – for the set of cash flows.

2. Investment criteria a.

Impact on earnings per share (EPS) is an accounting measure of performance. Its main drawbacks are that it ignores capital investment required for the project, penalizes projects whose earnings are not immediately realized, and is subject to accounting manipulation. Yet there is a strong belief among managers that changes in EPS have a primary influence on share prices, and consequently that the impact of an investment proposal should be taken into account when making the decision to undertake the project.

The payback period measures the number of years to recover the capital investment outlay. It is easy to compute and understand. It is often considered a proxy for risk—the faster the payback, the less risky the project. However, the payback period criterion does not account for all the project‘s cash flows, is biased against long-term projects, does not take the cost of capital into account (although a discounted payback period would do), and does not properly adjust for risk.

Internal rate of return (IRR) takes into account all of the cash flows related to the project. It is liked by managers because it provides a performance measure which can be easily compared to the cost of capital. Its drawbacks are that it may lead to the wrong choice when used to compare two mutually exclusive projects that it may not be unique for some types of projects, and finally, that it has no particular economic significance.

Net present value (NPV) takes into account all of the cash flows related to the project and discounts them at the cost of capital to account for the time value of money and risk. The result is either a positive or negative number reflecting the creation or destruction of wealth that would result from making the investment. It requires that an explicit cost of capital be specified. It avoids most, if not all, of the drawbacks of the other measures. Some managers profess to find it somewhat abstract—not as intuitively obvious as IRR. For use with Finance for Executives: Managing for Value Creation 7th edition

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b.

Global Chemicals uses all of these measures, no doubt, because the various managers (and also board members for large project decisions) want them. Some of those taking part in the investment decision process are more comfortable with certain measures than others. If the project meets all of the minimum requirements, they presumably will feel more comfortable when accepting a project where the future outcome is generally subject to some uncertainty.

3. Relationship between investment criteria

The information given tells:    

Nothing about the discounted payback period That the project‘s internal rate of return is higher than its cost of capital That the profitability index is higher than one Nothing about the average accounting return

4. Net present value and payback period

If the payback period is less than the economic life of the project, its net present value can be either positive or negative. This is because the relevant cash flows in the computation of the payback period are actual cash flows while those in the computation of the net present value are discounted cash flows. The only certain case is the trivial case when the cost of capital of the project is zero. In that case, the project‘s net present value is, by definition, equal to zero at its payback period. Since it lasts longer, its net present value is positive.

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If the discounted payback period is less than the useful life of the project, its net present value is always positive. This is because the project‘s net present value being equal to zero at its discounted payback period, it must be positive if this period is less than the duration of the project. The positive expected cash flows after the payback period adds value to the project above zero.

5. The internal rate of return of mutually exclusive projects

a.

The intersection of Project A and Project B‘s NPV lines represents the discount rate which produces the same NPV for the two projects. Assuming the risk of each project is the same, and the firm‘s cost of capital is the discount rate at the intersection point, one should be indifferent between the two projects.

b.

The point at which each project crosses the zero-NPV line represents the internal rate of return (IRR) of that project. It is the discount rate at which the present value future stream of cash flows expected from the project is equal to the initial cash outlay.

c.

The difference in NPVs between the two projects at each discount rate is due to the size and timing of the cash flows. Project A has larger cash flows during the latter part of the project relative to the beginning. Hence at higher discount rates they are worth less. The larger cash flows of project B occur earlier in its life.

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d.

The choice depends on the cost of capital. When the cost of capital is lower than the breakeven rate (the point where the project NPV lines intersect), Project A is better, and Project B is better when the cost of capital is higher than the breakeven rate. Note that the choice between the two projects cannot be made by comparing their internal rates of return because those rates have no particular economic significance.

For use with Finance for Executives: Managing for Value Creation 7th edition

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6. The case of multiple internal rates of return

This project shows cash flows with alternating negative and positive signs. Though the project is perhaps unrealistically simple, it is designed to illustrate a weakness of the internal rate of return approach. a. and b.

Using a spreadsheet

A

B 0 -$200

C 1

D 2 -$400

E

F

G

1 2 Cash flows $600 3 4 Cost of capital 0% 25% 50% 100% 5 6 Net present value $0 $24 $22 $0 7 8 The formula in cell B6 is: =$B$2 + NPV(B4,$C$2:$D$2). Then copy formula in cell B6 to cells C6, D6, and E6.

9 10 Internal rate of return 0% 100% 11 12 The formula in cell B10 is: =IRR(B2:D2,.1), where .1 is a guess value for IRR. 13 The formula in cell C10 is: =IRR(B2:D2,.9), where .9 is a guess value for IRR. 14

There are two internal rates of return (IRR)—at 0 percent and 100 percent discount rates. Rates between 0 percent and 100 percent produce positive net present values (NPV). Rates below 0 percent and above 100 percent will produce negative NPVs. Even if both are mathematically ―correct,‖ neither IRRs are economically meaningful measures, and cannot be used to decide if the project will create value or not.

c.

For use with Finance for Executives: Managing for Value Creation 7th edition

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The project should be accepted if its net present value is positive. This will be the case if the cost of capital is above 0 percent and less than 100 percent.

For use with Finance for Executives: Managing for Value Creation 7th edition

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7. NPV versus IRR for same initial outlay

a.

b.

Since the NPV of project B is higher, it should be chosen based on NVP analysis. c.

The IRR of project A is higher and hence it should be chosen based on IRR analysis. d.

Since NPV provides value addition as a result of undertaking a specific project, it is a better measure when compared to IRR. Project B should be chosen as it provides a higher NPV. IRR has drawbacks because it assumes that the receipts would be invested at IRR which is not always possible. Since the discount rate here is 8 percent, the receipts would ideally be invested at 8 percent and not at 9.20 percent or 8.91 percent.

For use with Finance for Executives: Managing for Value Creation 7th edition

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8. The net present value rule versus the internal rate of return rule

Note that this is an ―either or‖ type of problem and that the two projects are of different scale.

a.

Using a spreadsheet

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A

B

C

D

1 0 1 2 2 PROJECT A 3 Cash flows -$12,000 $7,900 $6,850 4 5 Cost of capital 10% 6 7 Net present value 8 9 Net present value $843 10 11 The formula in cell B9 is: =B3 + NPV(B5,C3:D3).

12 13 Internal rate of return 14 15 Internal rate of return 15.3% 16 17 The formula in cell B15 is: =IRR(B3:D3,.1), where .1 is a guess value for IRR. 18 19 PROJECT B 20 Cash flows -$2,400 $2,500 $950 21 22 Net present value 23 24 Net present value $658 25 26 The formula in cell B24 is: =B20 + NPV(B5,C20:D20).

27 28 Internal rate of return 29 30 Internal rate of return 33.8% 31 32 The formula in cell B30 is: =IRR(B20:D20,.1), where .1 is a guess value for IRR. 33

b.

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Project B is a better choice based on internal rate of return, while project A is a better choice based on net present value.

c.

Project A is the larger of the two projects and promises to create more wealth. That it has a lower internal rate of return reflects the timing and size of its cash flows. They are large enough to produce the largest absolute net present value, but a relatively larger portion of the cash flows occurs in Year 2 as compared to Project B.

d.

The net present value rule is the least ambiguous assuming that the cost of capital rate has been estimated correctly and that the firm does not have any capital constraints.

e.

The internal rate of return of the incremental cash flows (Project A’s minus Project B’s cash flows) is 11.4 percent. At any discount rate below 11.4 percent, Project A will produce the highest net present value; at any discount rate above 11.4 percent, Project B promises the higher net present value. This is consistent with the answer given in d. above; it strengthens the importance of estimating the correct discount rate used in mutually exclusive types of investments.

For use with Finance for Executives: Managing for Value Creation 7th edition

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9. The internal rate of return rule and the net present value rule

a. and b.

Using a spreadsheet A B C D 1 0 1 2 2 PROJECT A 3 Cash flows -$150,000 $120,000 $80,000 4 5 Cost of capital 12% 6 7 Net present value 8 9 Net present value $20,918 10 11 The formula in cell B9 is: =B3 + NPV(B5,C3:D3).

12 13 Internal rate of return 14 15 Internal rate of return 23.3% 16 17 The formula in cell B15 is: =IRR(B3:D3,.1), where .1 is a guess value for IRR. 18 19 PROJECT B 20 Cash flows -$300,000 $200,000 $180,000 21 22 Net present value 23 24 Net present value $22,066 25 26 The formula in cell B24 is: =B20 + NPV(B5,C20:D20).

27 28 Internal rate of return 29 30 Internal rate of return 17.7% 31 32 The formula in cell B30 is: =IRR(B20:D20,.1), where .1 is a guess value for IRR. 33 34 PROJECT C 35 Cash flows -$150,000 $110,000 $90,000 36 37 Net present value 38 39 Net present value $19,962 40 41 The formulaFor in cell B35 + NPV(B5,C35:D35). useB39 withis:Finance for Executives: Managing for Value Creation 7th edition 42 43 Internal rate of return

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 44 45 Internal rate of return ©22.4% 2022 Cengage Learning EMEA 46 47 The formula in cell B45 is: =IRR(B35:D35,.1), where .1 is a guess value for IRR. 48

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c.

The three projects should be accepted since their net present value is positive and their internal rate of return is higher than the cost of capital (12 percent).

d.

Project B should be selected since its net present value ($22,066) is the highest of the three.

e.

Projects A and B should be selected since their accumulated net present values ($20,918 + $22,066 = $42,984) is the highest of any combination of projects within the budget of $450,000.

10. The net present value rule versus the profitability index rule

Note that this is an ―either or‖ type of problem and that the two projects are of different scale.

a.

Using a spreadsheet (see next page)

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A 1

B

C 0

D

E

1

2 PROJECT A 3 Cash flows -$16,000 $10,500 4 5 Cost of capital 10% 6 7 Net present value 8 9 Net present value $3,320 10 11 The formula in cell B9 is: =B3 + NPV(B5,C3:E3).

12 13 Profitability index 14 15 Profitability index 1.21 16 17 The formula in cell B15 is: =NPV(B5,C3:E3)/-B3.

18 19 PROJECT B 20 Cash flows -$3,200 $3,300 21 22 Net present value 23 24 Net present value $1,292 25 26 The formula in cell B24 is: =B20 + NPV(B5,C20:E20).

27 28 Profitability index 29 30 Profitability index 1.40 31 32 The formula in cell B30 is: =NPV(B5,C20:E20)/-B20.

33

2

3

$9,100

$3,000

$1,260

$600

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b.

Project B is a better choice based on the profitability index rule, while project A is a better choice based on net present value.

c.

Project A is the larger of the two projects and promises to create more wealth. That it has a lower profitability index reflects the timing and size of its cash flows. They are large enough to produce the largest absolute net present value, but a relatively larger portion of the cash flows occurs in Year 2 as compared to Project B.

d.

The net present value rule is the least ambiguous assuming that the cost of capital rate has been estimated correctly and that the firm does not have any capital constraints.

11. The average accounting return

Using a spreadsheet

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A B C D E F G 1 1 2 3 4 5 2 Initial cash outlay $2,000,000 3 4 Annual depreciation $400,000 5 Net book value $2,000,000 $1,600,000 $1,200,000 $800,000 $400,000 $0 6 Average net book value $1,000,000 7 8 The formula in cell B4 is: +SLN(B2,0,5), where 0 is the salvage value of the machine at the end of year 5 and 5 is the life of the machine.

9 The formula in cell C5 is: =B5-$B$4. Then copy formula in cell C5 to cells D5, E5, F5, and G5.

10 The formula in cell B6 is: =average(B5:G5).

11 12 Earnings after-tax – Year 1 $200,000 13 Growth rate after Year 1 10% 14 Earnings after-tax $200,000 $220,000 $242,000 $266,200 $292,820 15 Average earnings after-tax $244,204 16 17 The formula in cell D14 is: =C14*(1+$B$13). Then copy formula in cell D14 to cells E14, F14, and G14.

18 The formula in cell B15 is: =average(C14:G14).

19 20 Average accounting return 24.4% 21 22 The formula in cell B20 is: =B15/B6.

According to the average accounting return rule, the machine should be bought since the average accounting return is higher than the target return (24.4 percent versus 20 percent). However, you should question the approach on the basis of the following considerations:

1. The approach ignores the time value of money. To account for it, the approach should have used cash flows instead of earnings and discount those cash flows to present.

2. The target return is not a market return which would be needed to discount the cash flows from the project.

12. Investment criteria

a.

For use with Finance for Executives: Managing for Value Creation 7th edition

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Using a spreadsheet (see next page)

A B C D E F G 1 0 1 2 3 4 5 2 Cash flows -$18,000 $5,200 $5,200 $5,200 $5,200 $7,200 3 4 Payback period 5 6 Accumulated cash inflows $5,200 $10,400 $15,600 $20,800 $28,000 7 8 Payback period 3.46 9 10 The formula in cell C6 is: =C2. The formula in cell D6 is: =C6+D2. Then copy formula in cell D6 to cells E6, F6, and G6.

11 The formula in C8 is: =IF(OR(C6<=-$B$2,B6>-$B$2),"-",B1+(-$B$2-B6)/C2. Then copy formula in cell C8 to cells D8, E8, F8, and G8.

12 13 Discounted payback period 14 15 Cost of capital 10% 16 17 Discounted cash inflows $4,727 $4,298 $3,907 $3,552 $4,471 18 Accumulated discounted cash flows $4,727 $9,025 $12,932 $16,483 $20,954 19 20 Discounted payback period 4.34 21 22 The formula in cell C17 is: =C2/(1+$B$15)^C1. Then copy formula in cell C17 to cells D17, E17, F17, and G17.

23 The formula in cell C18 is: =C17. The formula in cell D18 is: =C18+D17. Then copy formula in cell D18 to cells E18, F18, and G18.

24 The formula in cell C20 is: =IF(OR(C18<=-$B$2,B18>-$B$2),"-",B1+(-$B$2-B18)/C17). Then copy formula in cell C20 to cells D20, E20, F20, and G20.

25 26 Net present value 27 28 Net present value $2,954 29 30 The formula in cell B28 is: =B2 + NPV(B15,C2:G2).

31 32 Internal rate of return 33 34 Internal rate of return 16.0% 35 36 The formula in cell B34 is: =IRR(B2:G2,.1), where .1 is a guess value for IRR. 37 38 Profitability index 39 40 Profitability index 1.16 41 42 The formula in cell B40 is: =NPV(B15,C2:G2)/-B2.

43

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The discounted payback period at a 10 percent discount rate, given the expected annual cash flows, might appear to be 4.34 years—if the final year‘s cash flow were realized evenly over the year. However, since we are told that a significant part of the final year‘s cash flow represents a recovery of working capital needed for the project, the discounted payback would not be realized before the end of the fifth year.

b.

Considering the above measures, the project appears to be satisfactory since the net present value is positive, the profitability index is greater than 1.0, the internal rate of return is above 10 percent (assuming that 10 percent is the cost of capital), and the payback periods indicate the investment outlay will be recovered during the life of the project.

Chapter 9 Answers to Review Problems Finance for Executives – 7th Edition

1. Cash-flow equation deviation

We have the EBIT equation as: For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

Substituting ―EBIT‖ by ―EBITDA – Depreciation‖ we have:

Multiplying the brackets, we have:

Cancelling out the depreciation, we have:

Taking EBITDA within the brackets, we have the final equation:

For use with Finance for Executives: Managing for Value Creation 7th edition

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Let‘s take a small example to check if our equations are correct: Sales

$ 100.00

COGS

$ 40.00

SG&A

$ 20.00

Depreciation

$ 10.00

WCR

$

Capex

$ 10.00

5.00

Assuming a tax rate of 25 percent.

Using the EBIT equation, we have: EBIT = $100

$40

$20

$10 = $30

Similarly using EBITDA, we have: EBITDA = $100

$40

$20 = $40

Hence we can see that using both equations, the amount of cash flow is the same.

2. Pondering an investment offer The offer is not ―ridiculous.‖ The problem is that the cash flows in the deal have been incorrectly specified. The $15,000 investment promises a $17,000 payoff in one year. The ―less than 4 percent‖ return calculation is presumably based on a payoff of $17,000 less 12 percent interest on $12,000 or a net of $15,560. This sum related to the total investment of $15,000 is indeed less than 4% [it is 3.7%]. However, your investment [equity] would only be $3,000, if the bank will lend you $12,000 for one year at 12 percent. So at time 0, your net outflow will be $3,000. At the end of the year, you would receive $17,000 from your brother-in-law and repay For use with Finance for Executives: Managing for Value Creation 7th edition

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the $12,000 loan plus $1,440 of interest, which leaves you with a net $3,560. This yields an 18.7% return.

3. The effect of inflation on the investment decision The financial manager is correct. Why? The accountant is arguing that the projected cash flows (the numerator in the equation) are nominal amounts. That is, they assume some rate of inflation.

It is impossible to predict inflation rates very far into the future, so taking the most recent government figures seems to be reasonable. If the discount rate of 12 percent is based on the firm‘s expected borrowing rate and its cost of equity estimate (which itself is most likely to be based on market rates), then an inflation component is implicitly taken into account already in the denominator of the equation. To add another 5 percent to the standard discount rate will bias downward the project‘s net present value—effectively the inflation component is counted twice.

4. Changing machines in a world without taxes For all questions from a. to d., the first issue is the estimation of the project‘s economic or useful life. The existing machine can last another 10 or more years. However, the new one, which will perform exactly the same operations, has an economic life of only 5 years, which means that it will be obsolete within 5 years. It follows that the existing machine cannot have a useful life longer than 5 years. For the base case scenario, we use 5 years as the economic life of the project. The second issue is the estimation of the relevant cash flows. The right question to ask is: What will be the impact of changing machines on the cash flows of Clampton, excluding financially-related cash flows?

a.

By changing machines, the cash position of Clampton will immediately decrease by $110,000, the difference between the purchase price of the new machine ($110,000) and the resale price ($0) of the existing one. And then, each year for the following 5 years, the cash flow of Clampton will increase by $30,000.

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For use with Finance for Executives: Managing for Value Creation 7th edition

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Using a spreadsheet

A

B

1

C

D

E

F

G

Year-end

Year-end

Year-end

Year-end

Year-end

Now

1

2

3

4

5

–$110,000

$30,000

$30,000

$30,000

$30,000

$30,000

2 3 Cash flow from project 4 5

Cost of capital

10%

Net present value

$3,724

6 7 8 9 The formula in cell B7 is: =B3 + NPV(B5,C3:G3).

10

According to the net present value rule, the machine should be changed. Note that the depreciation expenses related to the new machine have no effect on the decision, although it will negatively affect its net profit in the next 5 years. This is totally rational since depreciation expenses are not cash expenses.

b.

The impact of changing machines on the relevant cash flows of the Clampton Company will be exactly the same as in question a. Book values and depreciation expenses have no impact on the investment decision in the absence of taxes.

For use with Finance for Executives: Managing for Value Creation 7th edition

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For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

c.

Using a spreadsheet

A

B

C

D

E

F

G

Year-end 3

Year-end 4

Year-end 5

Year-end 1

Now

1

Year-end 2

–$150,000

$40,000

$40,000

$40,000

$40,000

$40,000

1

2

3

4

5

$36,364

$33,058

$30,053

$27,321

$24,837

$36,364

$69,421

$99,474

$126,795

$151,631

–

–

–

–

4.93

2 3 Cash flow from project 4 5

Cost of capital

10%

Net present value

$1,631

6 7 8 9 The formula in cell B7 is: =B3 + NPV(B5,C3:G3).

10 11 12 Discounted cash inflows 13 Accumulated discounted 14 cash flows 15

16

Discounted payback period

17

For use with Finance for Executives: Managing for Value Creation 7th edition

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The formula in cell C12 is: =C3/(1+$B$5)^C10. Then copy formula in cell C12 to cells D12, E12, F12, 18

and G12.

The formula in cell C14 is: =C12. The formula in cell D14 is: =C14+D12. Then copy formula in cell 19 D14 to cells E14, F14, and G14.

The formula in cell C16 is: =IF(OR(C14<=–$B$3,B14>–$B$3)," –",B10+(–$B$3–B14)/C12). Then 20 copy formula in cell C16 to cells D16, E16, F16, and G16.

21

According to the net present value rule, machine B should be purchased.

d.

If a mistake has been made, it is in the estimation of the economic life of Machine A. The decision taken two years ago was taken with the assumption that its economic life was 5 years, when actually it was 2 years. Had the net present value analysis been done for 2 years instead of 5 years, Machine A would not have been a positive net present value proposition.

Was a mistake made? Not necessarily. The useful life estimation was simply off the mark. From a decision-making perspective, an investigation into the process of determining economic life of pieces of equipment at Clampton is in order. The estimation of the discounted payback period would be helpful (4.93 years), because it indicates the minimum value of the economic life of the new machine for which the investment is a positive net present value one.

5. Changing machines in a world with taxes a.

For use with Finance for Executives: Managing for Value Creation 7th edition

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Using a spreadsheet A

B

C

D

E

F

G

Year-end

Year-end

Year-end

Year-end

Year-end

1

2

3

4

5

Savings before depreciation 4 and tax

$30,000

$30,000

$30,000

$30,000

$30,000

Change in Clampton's 5 depreciation allowances

$22,000

$22,000

$22,000

$22,000

$22,000

Change in Clampton‘s 6 operating profit

$8,000

$8,000

$8,000

$8,000

$8,000

40%

40%

40%

40%

40%

$4,800

$4,800

$4,800

$4,800

$4,800

$26,800

$26,800

$26,800

$26,800

$26,800

1

Now

2 3 Purchase of new machine

–$110,000

7 Tax rate Change in Clampton‘s 8 operating profit after tax 9 Cash flow from project

–$110,000

10 11

Cost of capital

8%

Net present value

–$2,995

12 13 14 15 The values in rows 3, 4, and 7 are data.

16 The formulas in cell C5 to G5 is: =SLN(–$B$3,0,5), where 5 the depreciation period.

17 The formula in cell C6 is: =C4–C5. Then copy formula in cell C6 to cells D6, E6, F6, and G6.

18 The formula in cell C8 is: =C6*(1–C7). Then copy formula in cell C8 to cells D8, E8, F8, and G8.

For use with Finance for Executives: Managing for Value Creation 7th edition

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19 The formula in cell B9 is: =B3+B8+B5. Then copy formula in cell B9 to cells C9, D9, E9, F9, G9.

20 The formula in cell B13 is: =B9 + NPV(B11,C9:G9).

21

According to the net present value rule, the machine should not be changed, contrary to the case when the company is not taxed, because the net present value is negative (minus $2,995). Taxes have three effects on the estimation of the net present value:

 They decrease the cash flow after tax and before depreciation.  They increase the cash flow by the amount of the depreciation tax shield (Tax rate × Depreciation expenses).

 They reduce the cost of capital by the amount of the interest tax shield (Tax rate × Cost of borrowing). b.

Using a spreadsheet A

B

C

D

E

F

G

Year-end

Year-end

Year-end

Year-end

Year-end

1

2

3

4

5

4 Savings before depreciation and tax

$30,000

$30,000

$30,000

$30,000

$30,000

Increase in depreciation allowances 5 from new machine

$22,000

$22,000

$22,000

$22,000

$22,000

Decrease in depreciation allowances 6 from old machine

–$8,000

–$8,000

–$8,000

–$8,000

–$8,000

Change in Clampton‘s depreciation 7 allowances

$14,000

$14,000

$14,000

$14,000

$14,000

1

Now

2 –$110,000

3 Purchase of new machine

For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

Change in Clampton‘s operating 8 profit 9 Tax rate

$16,000

$16,000

$16,000

$16,000

$16,000

40%

40%

40%

40%

40%

$9,600

$9,600

$9,600

$9,600

$9,600

$23,600

$23,600

$23,600

$23,600

$23,600

40%

Change in Clampton‘s operating 10 profit after tax 11 Book value of old machine

$40,000

Tax credit from writing off old 12 machine

$16,000

13 Cash flow from project

–$94,000

14 15

Cost of capital

8%

Net present value

$228

16 17 18 19 The values in rows 3, 4, 6, 9, 11, and 15 are data.

20 The formulas in cell C5 to G5 is: =SLN($B$3,0,5), where 5 the depreciation period.

21 The formula in cell C7 is: =C5+C6. Then copy formula in cell C7 to cells D7, E7, F7, and G7.

22 The formula in cell C8 is: =C4–C7. Then copy formula in cell C8 to cells D8, E8, F8, and G8.

23 The formula in cell C10 is: =C8*(1–C9). Then copy formula in cell C10 to cells D10, E10, F10, and G10.

24 The formula in cell C12 is: =C11*C9.

25 The formula in cell B13 is: =B3+B10+B7+B12. Then copy formula in cell B13 to cells C13, D13, E13, F13, G13.

26 The formula in cell B17 is: =B13 + NPV(B15,C13:G13).

27

According to the net present value rule, the machine should be changed because the net present value is positive, although nearly insignificantly positive ($228).

Note that the difference in the net present value between the question in part a. and the question in part b. is explained by the write off of the old machine. By writing off the book value of the machine right now, For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

Clampton can immediately benefit from the remaining depreciation tax shield rather than having it spread over the next five years. The gain is $3,223 – the difference between the net present values ($228 – (– 2,995)).

6. Infrastructure investment analysis We need to calculate the cash flows for each year: Year 0:

$215 million

Year 1: $0 Year 2: $0

From Year 3 to 9 cash flow would include: Depreciation = ($50 million $60 million (revenue)

$5 million)/10 = $4.5 million

$10 million (costs)

$4.5 million (0.25) = $51.125 million

Year 10 cash flow: $51.125 million

$5 million = $56.125 million

The cash flows can be represented here with their present value calculations:

Year

Cash Flow (millions)

DF @ 15%

Present Value

0

$

(215.00)

1

$

215.00)

1

$

–

0.869565217

$

–

2

$

–

0.756143667

$

–

3

$

51.125

0.657516232

$

33.62

4

$

51.125

0.571753246

$

29.23

For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

5

$

51.125

0.497176735

$

25.42

6

$

51.125

0.432327596

$

22.10

7

$

51.125

0.37593704

$

19.22

8

$

51.125

0.326901774

$

16.71

9

$

51.125

0.284262412

$

14.53

10

$

56.125

0.247184706

$

13.87

NPV

$

(40.29)

For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

At 10 percent rate of return, we have:

Year

Cash Flow (millions)

DF @ 15%

Present Value

0

$

(215.00)

1

$

(215.00)

1

$

–

0.909091

$

–

2

$

–

0.826446

$

–

3

$

51.125

0.751315

$

38.41

4

$

51.125

0.683013

$

34.92

5

$

51.125

0.620921

$

31.74

6

$

51.125

0.564474

$

28.86

7

$

51.125

0.513158

$

26.24

8

$

51.125

0.466507

$

23.85

9

$

51.125

0.424098

$

21.68

10

$

56.125

0.385543

$

21.64

$

12.34

NPV

The investment is profitable at 10 percent. The IRR of the cash flows calculated (using a spreadsheet) is 11.03 percent, and any required return above this will lead to the cancellation of the project.

7. Investing in the production of toys a.

The cash flows (CFt) generated by the project can be estimated from equation 9.2: CFt = EBITt(1 – Taxt) + Dept – WCRt – Capext For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

where EBITt, Taxt, Dept, WCR, and Capext are the contribution of the project to the firm‘s earnings before interest and tax, its tax rate, its deductible depreciation expenses, and its capital expenditures, respectively. Note that inventories are the only working capital requirement item considered, so that we can write: CFt = EBITt(1 – Taxt) + Dept – Inventories – Capext

For use with Finance for Executives: Managing for Value Creation 7th edition

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Using a calculator $ thousands 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

Revenues Unit produced in thousands (3,000 per month) Raw material cost per thousand units Total material cost (line 2 × line 3) Direct cost ($130,000 per month) Depreciation expenses ($16 million/5) EBIT (line 1 – line 4 – line 5 – line6) Tax rate (Taxt) EBITt(1 – Taxt) (line 7  (line 1 – line 8)) Increase in raw material inventory (line 3  3) Increase in work-in-progress inventory Increase in inventories Capital expenditures Resale of equipment Tax on resale of equipment (line 8  line 14) CFt = (line 9 + line 6 – line 12 – line 13 + line 14 – line 15)

Now

Year 1 to 4

Year 5

$285 $150 $435 $16,000

$10,800 36 $95 $3,420 $1,560 $3,200 $2,620 40% $1,572 $0 $0 $0 $0

–$16,435

$4,772

$10,800 36 $95 $3,420 $1,560 $3,200 $2,620 40% $1,572 –$285 –$150 –$435 $0 $800 $320 $5,687

b.

The net present value (NPV) in thousand dollars of the project is:

NPV  $16,345 

$4,772 $4,772 $4,772 $4,772 $5,687     2 3 4 (1  .12) (1  .12) (1  .12) (1  .12) (1  .12)5

= $1,286,188

For use with Finance for Executives: Managing for Value Creation 7th edition

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A

B

C

D

E

F

G

Year-end

Year-end

Year-end

Year-end

Year-end

1

2

3

4

5

$10,800

$10,800

$10,800

$10,800

$10,800

4 Units produced

36

36

36

36

36

Raw material cost per 5 thousand units

$95

$95

$95

$95

$95

6 Total material cost

$3,420

$3,420

$3,420

$3,420

$3,420

7 Direct cost

$1,560

$1,560

$1,560

$1,560

$1,560

8 Depreciation allowance

$3,200

$3,200

$3,200

$3,200

$3,200

9 Operating profit or EBIT

$2,620

$2,620

$2,620

$2,620

$2,620

40%

40%

40%

40%

40%

$1,572

$1,572

$1,572

$1,572

$1,572

1 in thousands

Now

2 3 Revenues

10 Tax rate (T) After-tax operating profit or 11 EBITt(1 – Taxt) 12 Raw material inventory

$285

$285

$285

$285

$285

$0

Working process and finished 13 goods inventories

$150

$150

$150

$150

$150

$0

14 Total inventories

$435

$435

$435

$435

$435

$0

$435

$0

$0

$0

$0

–$435

15

Change in inventories

16 Capital expenditure

$16,000

17 Resale of equipment

$800

18 Tax on resale of equipment

$320

19

Total cash flow

–$16,435

$4,772

$4,772

$4,772

20 For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

$4,772

$5,687

21

Cost of capital

12%

Net present value

$1,286.188

22 23 24 25 The values in rows 3, 4, 5, 7, 10, 12, 13, 16, 17, and 21 are data.

26 The formula in cell C6 is: =C4*C5. Then copy formula in cell C6 to cells D6, E6, F6, and G6.

27 The formula in cell C8 is: =SLN($B$16,0,5), where 5 is the product’s economic life.

The formula in cell C11 is: =C9*(1–C10). Then copy formula in cell C11 to cells D11, E11, F11, and G11.

28 The formula in cell B14 is: =B12+B13. Then copy formula in cell B14 to cells C14, D14, E14, F14, and G14.

The formula in cell B15 is: =B14. The formula in C15 is =C15–B15. Then copy formula in cell C15 to cells D15, 29 E15, F15, and G15.

30 The formula in cell G18 is: =G10*G17.

The formula in cell B19 is: =B11+B8–B15–B16+B17–B18. Then copy formula in cell B19 to cells C19, D19, 31 E19, F19, and G19.

32 The formula in cell B23 is: =B19 + NPV(B21,C19:G19).

33

Using a spreadsheet

8. The effect of accounts receivable, accounts payable, overhead, and For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

financial costs on the investment decision a.

The new product would increase both accounts receivable and accounts payable. Annual sales of $12 million spread evenly over the year would mean $32,877 per day ($12 million/365 days). If the collection period on average were 50 days, this would mean an extra investment (an increase in the firm‘s accounts receivable) of $1,643,836 ($32,877  50). For simplicity, let us assume that this would take place at time 0. The firm should expect to get some financing from its suppliers. Annual purchases of $4 million of raw material spread evenly over the year would mean $10,959 per day ($4 million/365 days). If suppliers were paid on average in 36 days, this would amount to financing by suppliers of $394,521 ($10,959  36). The net increase in working capital would then be $1,249,315 ($1,643,836 – $394,521), which would add up to the initial cash outlay of $20,400,000. Finally let us assume that this sum would be recovered at the end of the project—the end of Year 5. At a discount rate of 11 percent, the impact on the present value of the cash flows would be +$741,408. In total, the net present value of the project would be reduced by $507,907 ($1,249,315 – $741,408) to $766,093.

Using a spreadsheet

A

B

1

Now

C

D

E

F

G

Year-end

Year-end

Year-end

Year-end

Year-end

1

2

3

4

5

2 Increase in firm's accounts 3 receivable

$1,643,836

$0

$0

$0

– $0 $1,643,836

Increase in firm's accounts 4 payable

$394,521

$0

$0

$0

$0

$1,249,315

$0

$0

$0

– $0 $1,249,315

Increase in firm's working capital 5 requirement

For use with Finance for Executives: Managing for Value Creation 7th edition

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–$394,521

6 7

Cost of capital

11%

Reduction in net present value of project

–$507,907

8

9 10

11 The values in rows 3 and 4 are explained in the text.

12 The value in cell B7 is data.

13 The formula in cell B5 is: =B3–B4. Then copy formula in cell B5 to cells C5, D5, E5, F5, and G5.

14 The formula in cell B9 is: –B5 – NPV(B7,C5:G5).

15

b.

The standard charge of one percent of revenues needs a careful look. While it is reasonable to expect some impact on general overheads from the addition of a new product, an incremental cost amounting to one percent of revenues ($120,000 p.a.) may be too high or too low. It sounds arbitrary. The present value of over five years of estimated increase in overheads would be $443,508. Let us take this figure for lack of a better estimate. This would reduce the net present value of the project by $443,508 to $322,585 ($766,093 – $443,508).

Using a spreadsheet

A

B

1

Now

C

D

E

F

G

Year-end

Year-end

Year-end

Year-end

Year-end

1

2

3

4

5

$120,000

$120,000

$120,000

$120,000

$120,000

2 3 Overhead charges increase

For use with Finance for Executives: Managing for Value Creation 7th edition

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4 5

Cost of capital

11%

Reduction in net present value of project

–$443,508

6

7 8

c.

The financing charge of 10 percent levied against the book value of assets used in the project is a ―red herring.‖ We should not bring financing costs into the cash flows since they are already included in the discount rate. To deduct them from the cash flows would result in doublecounting.

9. The effect of depreciation for tax purposes Using a spreadsheet

A move imposed by the tax authorities from MACRS to the straight-line method of depreciation will systematically decrease the net present value of any investment project. In our case, the net present value will decrease by $805 ($13,145 – $12,340) for an investment of $50,000.

Note that the change would be a zero-sum game: the loss for the corporation would be a gain for the government.

For use with Finance for Executives: Managing for Value Creation 7th edition

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A

B

C

D

E

F

G

H

Year-end

Year-end

Year-end

Year-end

Year-end

Year-end

1

2

3

4

5

6

5 MACRS allowances

20.00%

32.00%

19.20%

11.52%

11.52%

5.76%

6 Depreciation allowance

$10,000

$16,000

$9,600

$5,760

$5,760

$2,880

34%

34%

34%

34%

34%

34%

$3,400

$5,440

$3,264

$1,958

$1,958

$979

15 Depreciation allowance

$8,333

$8,333

$8,333

$8,333

$8,333

$8,333

16 Depreciation tax shield

$2,833

$2,833

$2,833

$2,833

$2,833

$2,833

1

Now

2 3 Cost of automobile

$50,000

4 I. Under MACRS

7 Tax rate 8 Depreciation tax shield 9 10

Cost of capital

10%

11

12

Present value of tax shield $13,145

13

14 II. Under straight-line system

17

18

Present value of tax shield $12,340

19 20 The values in rows 3, 5, 7, and10 are data

For use with Finance for Executives: Managing for Value Creation 7th edition

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21 The formula in cell C6 is: =C5*$B$3. Then copy formula in cell C6 to cells D6, E6, F6, G6, and H6.

22 The formula in cell C8 is: =C6*C7. Then copy formula in cell C8 to cells D8, E8, F8, G8, and H8.

23 The formula in cell C12 is: =NPV(B10,C8:H8).

24 The formula in cells C15 to H15 is: =SLN($B$3,0,6), where 6 is the depreciation life.

The formula in cell C16 is: =C15*C7. Then copy formula in cell C16 to cells D16, E16, F16, G16, and H16.

25 The formula in cell C18 is: =NPV(B10,C16:H16).

26

10.The effect of cannibalization These three items must each be handled differently. The $500,000 market study is a sunk cost. It has already been made and paid for. Whether the new project is taken or not, the cash flow has occurred. Therefore, this sum should be left out of the analysis.

The charge for the use of the company’s unoccupied building represents an opportunity cost. It apparently could be rented for $100,000 per year. There is no information, but it is conceivable that the building could be rented for more at a later date, or otherwise used by the company more profitably. On the other hand, if it is rented then, it could not be used by the company. For lack of any other data, let us assume that the company would forego the rental if it occupied the space. The present value of the $100,000 additional annual cost over five years at a cost of capital of 11 percent would be $369,590.

The possible ―cannibalization‖ of existing product sales if the new project is taken appears to be a major source of uncertainty. This often happens and is difficult to estimate. If we take the CEO‘s ―worst-case‖ scenario, the present value of the cash-flow impact from lost sales on existing products would be as much as $2,402,033 at a discount rate of 11 percent. Taking this ―worst-case scenario‖ valuation together with the cost of production space into account results in a negative impact of $2,771,923 ($2,402,333 + $369,590) on the net present value of the project.

This means that the Avon company‘s project would have had to promise a net present value before taking into account these items of at least $2.772 million to be acceptable.

For use with Finance for Executives: Managing for Value Creation 7th edition

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Using a spreadsheet

A

B

1

Now

C

D

E

F

G

Year-end

Year-end

Year-end

Year-end

Year-end

1

2

3

4

5

$100,000

$100,000

$100,000

$100,000

$100,000

$650,000

$650,000

$650,000

$650,000

$650,000

2 3 Loss of rental revenue 4 5

Cost of capital

11%

Effect on net present value of project

–$369,590

6

7 8

9 Loss to cannibalization 10

11

Effect on net present value of project

–$2,402,333

12

For use with Finance for Executives: Managing for Value Creation 7th edition

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11. Breakeven analysis Using a spreadsheet

A

B

1

Now

C

D

E

F

G

Year-end

Year-end

Year-end

Year-end

Year-end

1

2

3

4

5

2 I. Base case – $1,000,000

3 Initial investment 4 Number of snowmobiles sold 5 Unit sale price 6 Revenues

100

100

100

100

100

$10,000

$10,000

$10,000

$10,000

$10,000

$1,000,000 $1,000,000 $1,000,000 $1,000,000

$1,000,000

7 Variable costs per unit

$5,000

$5,000

$5,000

$5,000

$5,000

8 Total variable costs

$500,000

$500,000

$500,000

$500,000

$500,000

9 Total fixed costs

$125,000

$125,000

$125,000

$125,000

$125,000

10 Depreciation expense

$200,000

$200,000

$200,000

$200,000

$200,000

11 Operating profit (EBIT)

$175,000

$175,000

$175,000

$175,000

$175,000

40%

40%

40%

40%

40%

$105,000

$105,000

$105,000

$105,000

$105,000

$305,000

$305,000

$305,000

$305,000

$305,000

12 Tax rate 13 Operating profit after tax

14 Cash flow from the project

– $1,000,000

15 16 Cost of capital

10%

17 18

Net present value

$156,190

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19 20 The values in rows 3, 4, 5, 7, 9, 12, and 16 are data.

21 The formula in row C6 is: =C4*C5. Then copy formula in cell C6 to cells D6, E6, F6, and G6.

22 The formula in cell C8 is: =C7*C4. Then copy formula in cell C8 to cells D8, E8, F8, and G8.

23 The formula in cells C10 to G10 is: =SLN(–$B$3,0,5), where 5 is the depreciation life.

24 The formula in cell C11 is: =C6–C8–C9–C10. Then copy formula in cell C11 to cells D11, E11, F11, and G11.

25 The formula in cell C13 is: =C11*(1–C12). Then copy formula in cell C13 to cells D13, E13, F13, and G13.

26 The formula in cell B14 is: =B3+B13+B10. Then copy formula in cell B14 to cells C14, D14, E14, F14, and G14.

27 The formula in cell C18 is: =B14 + NPV(B16,C14:G14).

28 29 II. Breakeven analysis Number of snowmobiles 30 sold per year 31 Net present value

50

60

70

80

–$412,428

–$298,704

–$184,981

–$71,257

90

100

$42,466

$156,190

32 33 The values in cells B31 to G31 are net present values obtained by changing the number in row 4 to those in row 30.

34 The graph function in the spreadsheet menu is used to obtain the graph below.

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Net present value

Number of units

a.

The spreadsheet analysis indicates that the project should be undertaken for the expected sale of 100 snowmobiles per year since the net present value is positive under this assumption ($156,190).

b.

The graph shows that the breakeven sales level, which is the number of snowmobiles to sell every year over the five-year period to make the project acceptable is 87 units. Below that level, the project‘s net present value is negative.

The exact breakeven sales could also be obtained from the following relationships:

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Cash Flow = Operating profit after tax + Depreciation expenses

but

Operating profit after tax = [Revenues – Variable costs – Fixed costs – Depreciation expenses] × (1 – Tax rate) so that

Cash flow = [Revenues – Variable costs – Fixed costs – Depreciation expenses] × (1 – Tax rate) + Depreciation expenses

Let Q be the number of snowmobiles sold per year. Then:

Cash flow = [Q × Unit sales price – Q × Unit variable cost – Fixed costs – Depreciation expenses] × (1 – Tax rate) + Depreciation expenses or

Cash flow = Q × (Unit sales price – Unit variable cost) × (1 – Tax rate) – (Fixed costs + Depreciation expenses) × (1 – Tax rate) + Depreciation expenses

From the data, in thousands of dollars:

Unit sales price = $10 Unit variable cost = $5 Tax rate = 40 percent For use with Finance for Executives: Managing for Value Creation 7th edition

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Fixed costs = $125 Depreciation expenses = $200

Replacing the variables in the above equation by their values, we get:

Cash flow = Q × ($10 – $5) × (1 – 0.40) – ($125 + $200) × (1 – 0.40) + $200 or Cash flow = $3Q + $5

At the breakeven point we have:

Present value of [$3Q + $5] = $1,000 where $1,000 is the initial investment, or Q × PV($3) = $1,000 – PV($5)

from which we get

Q = [$1,000 – PV($5)]/PV($3)

The present value of an annuity of $5 per year at 10 percent is $18.95, that of an annuity of $3 is $11.37, so that:

Q = [$1,000 – $18.95]/$11.37 = 87

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c.

At the breakeven level, the payback period is equal to the project‘s economic life and the internal rate of return is equal to the project‘s cost of capital. This follows directly from the definition of the discounted payback period (the number of years of running the investment so that its net present value is equal to zero) and the definition of the internal rate of return (that discount rate for which the net present value is equal to zero).

12. Bid price The cash flows of the project are: A

B

1

Now

C

D

E

F

G

Year-end

Year-end

Year-end

Year-end

Year-end

1

2

3

4

5

2 Purchase of equipment

–$100,000

Change in working 3 capital requirement

–$30,000

+$30,000

–$130,000

CF $30,000

4 After-tax cash flow

CF

CF

CF

CF

5

The value of the cash flow, CF, for which the project‘s net present value is zero, must verify the following equation:

0  $130,000 

CF CF CF CF CF $30,000      2 3 4 5 (1  .10) (1  .10) (1  .10) (1  .10) (1  .10) (1  .10) 5

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or

CF × [5-year annuity of $1 at 10 percent] = $130,000 – $30,000 × [Present value of $1 in 5 years or 0.62092]

= $111,372

which implies that

CF = $111,372/3.7908 = $29,380

From equation 9.2:

CF = EBIT (1 – Tax) + Depreciation expenses

(Note there is no change in working capital requirement nor any new capital expenditure expected over the five-year period.)

The depreciation allowance is $20,000 ($100,000/5). Given this, we can write:

$29,380 = EBIT(1 – 0.40) + $20,000

EBIT 

$29,380  $20,000 $9,380   $15,633 .6 .6

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but, by definition:

EBIT = Revenues – Labor and other costs – Depreciation expenses

so that

$15,633 = Revenues – $80,000 – $20,000

Revenues = $80,000 + $20,000 + $15,633 = $115,633

Maintainit Inc. must submit a bid of no less than $115,633 per year for the project to have a positive net present value.

Chapter 10 Answers to Review Problems Finance for Executives – 7th Edition

1. Bond pricing and risk a. The 2-year spot rate is

√

√

The 1-year corporate spot rate = 3% +1% = 4% and the 2-year corporate spot rate = 4% + 1% = 5%. The corporate bond price is thus Expressed as a percentage of face value the price is 99.08.

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b. Using a financial calculator with N = 2, PV = –99.08, PMT = 4, FV = 100 we find that the yield to maturity is 4.489%.

c.

d.

Cash Flow

PV(CF) at 4.49 %

PV(CF)/Bond Price

$40

$38.2812

$38.2812/$990.8226= 3.86%

$1,040

$952.5414

$952.5414/$990.8226 = 96.14%

$990.8226

100.00%

Dur = (38.6% × 1 year) + (96.14 × 2 years) = 1.9614 years e. The maturity of the equivalent zero-coupon bond must be 1.9614 years because the term to maturity of a zero-coupon is the same as its duration. f.

g.

Because the change in yield is small, the change in price based on the duration formula is very close to the actual change in price.

2. Bond quotation a. The bond is quoted at $1,000. It excludes the last coupon payment.

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b. The bond‘s flat price is $1,000. Like the quoted price, it excludes the last coupon payment.

c. Accrued interest is $30; it is equal to the last coupon payment that will be made tomorrow. Whoever holds the bond at maturity will receive the last coupon and its face value. d. The bond‘s invoice price is $1,030; it is equal to the flat price plus accrued interest.

3. The cost of debt Thalin‘s cost of debt is the interest rate Thalin‘s would pay today if it issued new bonds. That rate must be equal to the yield to maturity on the 10-year, 10-percent coupon bond whose price is $1,065. Using a calculator, we find a yield of 8.99% (enter N = 10; P = –1065; PMT = 100; F = 1000 and you get I/YR = 8.99%). Thalin‘s cost of debt is thus 8.99%.

4. Reinvestment risk a. The yield to maturity is the same as the coupon rate (5%) because the bond is selling at par. The assumption is that the $50 coupon payment is reinvested at 5% for one year. b. If the $50 are reinvested at 7% for one year, they will be worth $53.50 in one year. At the end of the second year, the bondholder will receive a total cash flow of $1,103.50 ($1,000 + $50 + $53.50). Her return ‗k‘ (given that she paid to $1,000 for the bond) is thus the solution to:

from which we get k = 5.0476%. The return ‗k‘ is higher

than the yield to maturity because the reinvestment rate (7%) is higher than the bond yield (5%).

c. If the $50 are reinvested at 3% for one year, they will be worth $51.50 in one year. At the end of the second year, the bondholder will receive a total cash flow of $1,101.50 ($1,000 + $50 + $51.50). Her return ‗k‘ (given that she paid to $1,000 for the bond) is thus the For use with Finance for Executives: Managing for Value Creation 7th edition

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from which we get k = 4.9524%. The return ‗k‘ is lower

solution to:

than the yield to maturity because the reinvestment rate (3%) is lower than the bond yield (5%).

5. Bond stripping a. The 4-year, 5-percent coupon bond (with a face value of $1,000) is a portfolio of four zero-coupon bonds: (1) a 1-year zero with a face of $50, (2) a 2-year zero with a face value of $50, (3) a 3-year zero with a face value of $50 and (4) a 4-year zero with a face value of $1,050. A holder of the coupon bond can deposit that bond with a depository institution and issue the four zero-coupon bonds. When the first coupon is paid it is transferred to the holder of the 1-year zero, when the second coupon is paid, it is transferred to the holder of the 2-year zero, etc. b. Twenty coupon bonds are required to create zeros with a minimum face value of $1,000 ($1,000/$50). There will be one 1-year zero-coupon bond with a face value of $1,000, one 2-year zero-coupon bond with a face value of $1,000, one 3-year zero-coupon bond with a face value of $1,000, and twenty-one 4-year zero-coupon bonds ($1,050×20 = $21,000 and $21,000/$1,000 = 21).

6. Bond arbitrage The prices of the three zero-coupon bonds are:

Taken together, the three bonds constitute a portfolio that is the same as the 3-year, 4-percent bond. That portfolio has a value of $1,001.4757 ($39.2157 + $37.7038 + $924.5562). There is an arbitrage opportunity because two identical investments have different price: selling the

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expensive one for $1,002 (the coupon bond) and using the proceeds of the sale to buy the three zero-coupon bonds for $1,001.4757 generates a riskless profit of $0.5243 per bond.

7. Forward rates a. There are six forward rates. They are 1f2, 1f3, 1f4, 2f3, 2f4 and 3f4.

b. (1 + y2)2 = (1 + y1) × (1 + 1f2) from which we get 1f2 =

4.01%

(1 + y3)3 = (1 + y1) × (1 + 1f3)2 from which we get 1f3 = *

+

5.01%

(1 + y4)4 = (1 + y1) × (1 + 1f4)3 from which we get 1f4 = *

+

6.02%

(1 + y3)3 = (1 + y2)2 × (1 + 2f3) from which we get 2f3 = (1 + y4)4 = (1 + y2)2 × (1 + 2f4)2 from which we get 2f4 = *

6.03% 7.04%

+

(1 + y4)4 = (1 + y3)3 × (1 + 3f4) from which we get 3f4 =

8.05%

c. The rate at which you can lock the 3-year ‘forward’ borrowing is 1f4 = 6.02%. You borrow today $9,803.92 for 4 years at 5% (the 4-year spot rate) and invest that sum for one year at 2% (the 1-year spot rate) to get the $10,000 you need in one year. At the end of the fourth year you have to reimburse $11,916.66 which is $9,803.92(1+5%)4. You have, in effect, borrowed $10,000 for 3 years, paying back $11,916.66 three years later.

Your annual borrowing rate (k) is thus fixed at

. Solving for k, you

find that k is equal to 6.02% which is exactly the 3-year forward rate one year from now (1f4 = 6.02%).

8. Growth stocks versus income stocks

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a.

Because the firm pays out all of its earnings in dividends, its share price is .

b.

If the firm plows back 40% of its earnings with an expected return of 10%, its earnings will grow at a rate of 4% (10%  0.40). So will its dividend per share, which will be 60% of $5, that is, $3. Under this scenario, Therol‘s stock price is the present value of a perpetuity of $3 growing at 4% and discounted at an expected return of 10%, that is, . The stock price is the same as the one found in the previous question because Therol would reinvest its earnings at a rate which is the same as the 10% rate required by the shareholders from their investment in the firm. The new investment would result in higher growth in dividends but the growth is applied to a lower starting dividend ($3 versus $5).

c.

If the return on 40% of earnings is 15% instead of 10%, the dividends would grow at a rate of 6% (15% 0.40) and Therol‘s stock price would be

The $25

difference in stock price is the present value of the extra cash-flow provided by the new investments made by the firm with its retained earnings. It is generated by the expectation that Therol would be able to reinvest a portion of its earnings at a rate of return (15%) that is higher than the return required by Therol‘s shareholders (10%).

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9. Free cash flow valuation of stock

Year 0 $ 11.20

Year 1 $ 12.88

Total cash flow

$ 12.88 $ 11.93

Enterprise value Cash Debt Equity value #Stocks Stock price

$ 511.81 $40 ($100) $ 451.81 100 $ 4.52

Values in millions except stock price Year 2 Year 3 Year 4 $ 14.81 $ 16.29 $ 17.92 Terminal value $ 14.81 $ 16.29 $ 17.92 $ 12.70 $ 12.93 $ 13.17

Year 5 $ 18.82

Year 6 $ 19.76

$ 658.65 $ 677.47 $ 461.08

10. Dividend-discount model The expected stream of dividend per share (DPS) for the next 5 years is:

The share price is the discounted value of this dividend stream at 12% assuming that DPS will continue to grow at 6% after Year 5. It can be expressed as follows:

The numerator in last term is the present value, at the end of Year 5, of DPS6 ($2.491) that is assumed to grow in perpetuity at a constant rate of 6%. It is equal to $41.52.

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11. Stock valuation with the dividend-discount model We need to calculate the required return on the stock first.

Using CAPM we have:

Here:    

Using the dividend discount model:

  

12. Valuation based on comparable firms Multiple

Average of 5 comparable companies

Applied to GDC

Price-to-earnings

$2,646m/$280m = 9.45

VE = $168m × 9.45 = $1,587.60m

Price-to-book

$2,646m/$2,100m = 1.26

VE = $1,288 × 1.26 = $1,622.88m

EV-to-EBITDA

$3,584m/$580m = 6.18

EV = $390m × 6.18 = $2,410.20m VE = $2,410.20m – $856m = $1,554.20m

Price-to-cash flow

$2,646m/$180m = 14.70

VE = $102 × 14.70 = $1,499.40m

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Price-to-sales

$2,646 /$6,615m = 0.40

VE = $4,079× 0.40 = $1,631.60m

The estimated equity value of GDC ranges from a minimum of $1,499.40 million to a maximum of $1,631.60 million. The value range is not unusual.

Chapter 11 Answers to Review Problems Finance for Executives – 7th Edition

1. Structure and characteristics of financial markets a.

Direct financing refers to raising capital directly from ultimate savers (households with a cash surplus) whereas indirect financing refers to raising capital from financial intermediaries (such as banks and pension funds) in which ultimate savers have invested their savings.

b.

Primary markets refer to markets where securities are sold to investors for the first time whereas secondary markets are markets where the securities that have already been issued are bought and sold. Note that primary markets provide fresh capital to the issuing firm whereas secondary markets do not involve the firm.

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c.

Organized markets are regulated markets where only companies that can meet stringent conditions can list their shares whereas over-the-counter markets have less stringent listing and reporting requirements.

d.

Domestic securities are securities issued by firms in their local markets whereas international securities are issued in the international markets, markets that are outside the direct control and jurisdiction of the issuer‘s country of origin.

e.

Domestic securities are securities issued by firms in their local markets whereas foreign securities are securities issued by firms in the domestic markets of other countries.

f.

In a private placement securities are sold to qualified investors and are not listed or traded in the financial markets whereas in a public offering securities are sold to financial market participants who can trade them without restrictions.

g.

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In a rights offering, shares are issued exclusively to the firm‘s existing shareholders whereas in a general cash offering they are sold to any interested buyer. h.

In an underwritten issue the investment bank buys the securities from the issuer and then sells them to the public at its own risk (the bank acts as a dealer in this case) whereas in a best-efforts distribution, the investment bank does not buy the securities from the issuer; it only sells them on behalf of the issuer (the bank acts as a broker in this case). i.

The originating house is the investment bank that has initiated the issue whereas the selling group consists of a number of banks which are brought in to help distribute portions of the shares that have been allocated to them by the originating house or lead manager. j.

A seasoned issue refers to the issue of securities by a firm that has already issued similar securities in the past whereas a secondary distribution refers to the sale to the public of a large block of securities held by an investor who acquired them earlier directly from the firm. The former provides fresh capital to the issuing firm while the latter does not involve the firm.

2. Estimating the need for external funds a.

The external funds requirements can be calculated as: [ [

] ]

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[ [ b.

] ]

If the dividends were not paid, then: [ [

] ]

3. Rights issue a.

The number of rights MEC will grant must be equal to the number of MEC‘s shares outstanding, that is, 50 million rights.

b.

The number of rights (N) required to buy one new share is five: N  Number of rights 

Number of outs tan ding shares 50 million  5 Number of new shares 10 million

c.

The price will drop to $25 to reflect the fact that the share has gone ex-rights, that is, it entitles the holder to buy new shares at $20. The ex-rights price is (see equation 11.2):

Ex  rights price 

N  Rights  on price  Subsriptio n price 5  $26  $20 $150    $25 N 1 6 6

where the rights-on price is the share price prior to the rights issue announcement ($26).

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d.

The value of one right is simply $1, the difference between the rights-on price ($26) and the exrights price ($25). It can also be calculated directly with the formula in footnote 12: Value of one right 

Rights  0n price  Subscripti on price $26  $20 $6    $1 N 1 6 6

4. Leasing versus borrowing The relevant cash flows and the computation of the net present value of lease versus buy are presented in a spreadsheet format.

A

B

C

D

E

F

1

Now

2

0

1

2

3 Lease payments

$6,500

$6,500

$6,500

$6,500

40%

40%

40%

40%

$3,900

$3,900

$3,900

$3,900

6 Depreciation expenses

$6,000

$6,000

$6,000

$6,000

7 Loss of tax savings on depreciation

$2,400

$2,400

$2,400

$2,400

4 Tax rate 5 After-tax lease payments

Forecast at the end of year 3

4

40%

$3,000

8 Scrap value Cash saved from not buying 9 the truck

$24,000

10 Total differential cash flow

$20,100

11 Cost of debt

6.00%

12 NPV of leasing versus buy

$1,017

$6,300

$6,300

$6,300

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$5,400

• Data in rows 3, 4, 6, 8, 9 and 11 is data.

• Formula in cell B5 is =B3*(1 B4). Then copy cell B5 to next cells in row 5.

• Formula in cell C7 is =B6*B4. Then copy cell C7 to next cells in row 7.

• Formula in cell B10 is =B9+B8+B7+B5. Then copy cell B10 to next cells in row 10.

• Formula in cell B12 is =B10+NPV(B11,C10:G10).

a.

Discounting the total differential cash flows at the after-tax cost of debt of 6% yields a negative net present value, or net advantage of leasing, of –$1,017.

Conclusion: Leasing is more expensive than borrowing. OS Distributors should buy the truck and borrow to finance the purchase instead of leasing. b.

OS Distributors will be indifferent between buying or leasing if the net advantage of leasing (NAL) is zero, that is, if the present value at 6% of the differential cash flows from Year 1 to Year 4 is equal to $20,100 (the difference between the cash saved from not buying the truck and the after tax lease payment now, cell B9) : $20,100 = Present value (–$6,300 for 3 years) + Present value (cash flow in Year 4) The first term on the right side of the equation is equal to –$16,840. Thus, the present value of the cash flow in Year 4 is $3,260 ($20,100 – $16,840): $3,260 

Cash flow in year 4 Cash flow in year 4  (1  0.06) 4 1.2625

and the cash flow in Year 4 is $4,116 ($3,260 × 1.2625). This figure includes the $2,400 tax savings on depreciation (see Year 4 in table above). Deducting $2,400 from $4,116 gives an after-tax scrap value of $1,716. The pretax scrap value is thus $2,860 ($1,716/60%).

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5. Leasing Using a spreadsheet, the following table shows the after-tax cash flows to Thorenberg Inc. and to Foster Leasing Corporation and the net advantage to leasing to Thorenberg Inc.

A

B

1

C

D

Now 0

3 Purchase price

$100,000

7 After-tax lease payment

5

2

3

4

$20,000

$20,000

$20,000

$20,000

$25,000

$25,000

$25,000

$25,000

$25,000

36%

36%

36%

36%

36%

$16,000

$16,000

$16,000

$16,000

$16,000

$7,200

$7,200

$7,200

$7,200

$7,200

$23,200

$23,200

$23,200

$23,200

$7,200

Loss of tax savings on 8 depreciation 9 Differential cash flow

G

1

4 Depreciation expenses

6 Tax rate

F

Forecast at the end of year

2 Cash flows to Thorenberg

5 Lease payment

E

$84,000

10 Interest rate

8.00%

11 After-tax cost of debt

5.12%

12 Net advantage to leasing

$3,647

• Data in cells B3 and B11, in rows 5 and 6 is data.

• Formula in cell C4 is =SLN($B$3,0,5) when 5 is the number of years the machine is depreciated.

Then copy cell C4 to next cells in row 4.

• Formula in cell C7 is =B5*(1 B6). Then copy cell C7 to next cells in row 7.

• Formula in cell C8 is =C4*C6. Then copy cell C8 to next cells in row 8.

• Formula in cell B9 is = B7 B8+B3. Then copy cell B9 to next cells in row 9.

• The formula in cell B11 is =B10*(1 B6).

• The formula in cell B12 is =B9+NPV(B11,C9:G9).

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$20,000

36%

Now Cash flows to Foster 13 Purchase price

0

Forecast at the end of year 1

2

3

4

5

$7,200

$7,200

$7,200

$7,200

$7,200

$100,000

Tax savings on 14 depreciation 15 After-tax lease receipts

$16,000

$16,000

$16,000

$16,000

$16,000

16 Cash flow to Foster

$84,000

$23,200

$23,200

$23,200

$23,200

$7,200

• The value in cell B13 is the same as in cell B3. The values in rows 14 and 15 are the same as in rows 7 and 8.

• The formula in cell B16 is =B14+B15 B13. Then copy formula in cell B16 to next cells in row 16.

a.

The net advantage to leasing is negative for Thorenberg Inc.: –$3,646. Thus, the firm should buy rather than lease the equipment.

b.

The cash flows to the lessor (Foster) are just the opposite of those to the lessee (Thorenberg).

This makes sense since the cash transaction involves only two parties; the cash flows to and from each other must cancel out. c.

Leasing cannot take place if the cash flows to the lessee and the lessor are exactly the opposite and if their borrowing rate is the same. The leasing will take place only if any of these two conditions is not met. That would happen if:  The two firms are subject to different effective tax rates  The transactions costs are lower when leasing rather than buying  The borrowing rates of the two parties are different because their credit risk is different For use with Finance for Executives: Managing for Value Creation 7th edition

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6. Convertible preferred

a.

The conversion ratio is 2 (two common stocks for each preferred).

b.

The conversion price is $40 ($80/2).

c.

The conversion premium is 25 percent, that is, ($40

$32)/$32.

d.

The conversion value is $64 ($32×2).

e.

The yield of the equivalent straight preferred stock serving a $2.72 dividend is 3.4 percent ($2.72/$80) and its value would thus be $70.59 ($2.40/3.4%).

f.

The value of the option to convert is equal to the value of the convertible preferred minus its value if it were not convertible, that is, $9.41 ($80

$70.59).

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7. Timeline of dividend distributions a. Since the investor bought the stock on the ex-dividend date, he will not receive the dividend as the stock has to be bought before the ex-dividend date to be eligible for the dividend. b. Since the company registered the investor who purchased the stock on the ex-dividend date as the holder of record on 5th October, the same would be the holder of records date. c. The stock falls by the value of dividend, i.e. $1.25, on the ex-dividend date as the buyer on this or a later date will not receive dividends. d. The stock price would not actually fall by the amount of dividend on the ex-dividend date as it needs to factor in the tax on dividends. The actual fall will be the Amount of dividend (1 – Tax rate).

8. Deferred dividend payment a.

In one year AWC will (1) pay a higher special dividend equal to $260 million ($250 million × 1.04), which is $2.60 per share and (2) pay its regular $1 dividend per share ($100 million/100 million shares). The share price in one year will be $10 ($100 million/10%). The share price today is the discounted value of $2.60 at 4 percent for one year and $11 ($1 + $10) at 10 percent for one year. Note that the special dividend is discounted at 4 percent because this is the appropriate rate that corresponds to the risk of that cash flow:

b.

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It is the same share price as in the case of an immediate dividend payment ($12.50). This is exactly what we should expect in a perfect market where dividend policy does not affect share prices.

9. Cash retention and corporate taxes a.

AWC will receive a perpetual annual interest income of $250 million multiplied by the bond‘s coupon rate (r). The present value of this perpetual interest income at the rate ‗r‘ is $250 million (PV = $250m×r/r =$250m) and the share price is thus:

(

)

It is the same share price as in the case of an immediate dividend payment ($12.50). This is exactly what we should expect in a perfect market where dividend policy does not affect share prices.

b.

AWC will receive a perpetual aftertax annual interest income of $250 million multiplied by the bond‘s aftertax coupon rate. The present value of this perpetual interest income is $175 million (PV = $250m × r × (1 30%)/r = $175m) and the share price is thus (the assumption is thus the regular cash flow of $100 million is not taxed):

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(

)

The share price has dropped from $12.50 to $11.75 to reflect the tax payment which is worth $0.75 per share ($250 × 30%/100).

10. Investment decision versus dividend payment a.

*

+

NPV is negative because the

project‘s expected return (8%) is the lower than shareholders‘ expected return (10%).

b.

*

+

NPV is zero because the project‘s

expected return (10%) is the same as shareholders‘ expected return (10%).

c.

*

+

NPV is positive because the

project‘s expected return (12%) is the higher than shareholders‘ expected return (10%).

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11. Investment decision versus share buyback a.

(

)

b.

c.

The investment should not be undertaken because its NPV is negative. Note that NPV per share is $0.40, which is the difference between the price without the investment and the price with the investment.

d.

Yes, because the buyback will leave the share price at $10. With the $100m of cash, TRC will buy 10m shares ($100m/$10). After the buyback there will be 40m shares left (50m –10m) and the share price will be: (

)

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12. Payout policies of a growing firm a.

[

]

[

]

b. [

]

Wealth-per-share is thus $4 + $21 = $25, which is the same as before the dividend payment. c.

With the $40m of cash, SAC can buy 1.6m shares ($40m/$25). After the buyback there will be 8.4m shares left (10m – 1.6m) and the share price will be:

[

]

Shareholder‘s wealth per share remains the same. d.

[

]

Shareholders‘ wealth per share = $7.50 + $17.50 = $25 e.

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[

]

Shareholders‘ wealth per share = $7.50 + $17.50 = $25

Chapter 12

Answers to Review Problems Finance for Executives – 7th Edition

1. Historical returns a.

If one accepts that stocks are riskier than corporate bonds, which are riskier than government bonds, which in turn are riskier than Treasury bills, then stock returns should be higher than For use with Finance for Executives: Managing for Value Creation 7th edition

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corporate bond returns which should be higher than government bond returns which in turn should be higher than Treasury bills. But the annual data in the table do not appear to support a naïve understanding of theory. Looking at the table, we see that:



In 2000, 2001, 2002, 2005, 2008, 2011 and 2014 the returns on stocks were lower than the returns on corporate bonds (7 out of 20 years).



In 1997, 1998, 2000, 2002, 2005, 2007, 2008, 2011, 2014 and 2015 the returns on corporate bonds were lower than the returns on government bonds (10 out of 20 years).



In 1999, 2001, 2006, 2009, 2013 and 2015, the returns on government bonds were lower than the returns on treasury bills (6 out of 20 years).

These observations lead one to recognize that realized annual returns are not a reasonable proxy for the market expected returns. However, averages for longer periods of time support the theory more satisfactorily such as those observed over the 1926–2016 period at the bottom of the table.

b.

Riskier assets have higher volatility (their annual realized returns display wider fluctuations as shown in the table).

c.

The market risk premium for each of the periods observed can be found in the table below.

Market Risk Premium versus Government Bonds

Market Risk Premium versus Treasury Bills

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Time Period 1997

17.5%

28.1%

1998

15.5

23.7

1999

30.0

16.3

2000

30.6

15.0

2001

15.6

15.7

2002

39.9

23.8

2003

27.2

27.7

2004

2.4

9.7

2005

2.9

1.9

2006

14.6

11.0

2007

4.4

0.8

2008

62.9

38.6

2009

41.6

26.6

2010

5.0

15.0

2011

26.1

2.1

2012

12.7

15.9

2013

45.2

32.4

2014

11.0

13.7

2015

2.1

1.4

2016

10.2

11.8

Annual arithmetic averages

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1997 2016

1.6%

6.8%

1926 2016

6.0%

8.6%

We can see that the risk premiums for individual years are highly volatile. In some years the realized risk premiums are negative but the average of the realized risk premiums shown at the bottom of the table are positive. Looking at these averages, it seems that risk premiums have been declining over the past 10–20 years, but we cannot conclude that this phenomenon will persists in the future.

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2. Risk and return a.

The statement is unreliable but could turn out to be correct because the future is unknown. Future market returns are affected by several factors such as the growth of the economy, level of interest rates and inflation, and market sentiment, to name a few. Even if the same set of conditions were to be repeated, there is no reason to expect that future stock market returns will be consistent with those generated during the previous 10 years.

b.

Investors will hold bonds or stocks depending on their tolerance to risk, their need to receive a steady income, their time horizon, and their current consumption requirement (see chapter 3).

Investors with a short time horizon (those retired) may prefer bonds because they are likely to provide a more steady income than stocks, or be more easily liquidated at low risk of loss.

c.

This is incorrect as shown from the table of returns in question 1. The value of a bond will fall when interest rates rise (see chapter 10). If a government bond is sold when interest rates have risen, the investor would suffer a realized loss.

3. The cost of equity and the cost of debt a.

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The statement is incorrect. It ignores growth prospects for the company stock. According to the dividend discount model with constant growth expectations (see equation 12.5), the return expected by the company shareholders, kE, is:

kE 

DIV1 g P0

where DIV1 is the dividend next year, P0 is the current share price, and g is the expected growth rate. The Chief Operating Officer implicitly assumes in his comment that the firm does not have any growth expectation and thus underestimates the company‘s cost of equity capital.

b.

The statement is incorrect. The company‘s true cost of debt is the cost of debt if the firm borrows now, not its past, historical cost of debt. Furthermore, the interest expenses represent the cost of financial liabilities such as debt to banks or bonds. Liabilities of any company include these debts but also other liabilities such as accounts payable to suppliers, employees, and tax authorities. Thus, the $5 million of interest expenses should be applied only to financial liabilities and not all the liabilities to get an approximate cost of debt (but again, this approximate number would not be reliable because the true cost of debt is the interest rate the firm would pay today if it decided to borrow new money).

4. The cost of debt The current market price of the bond is $1,100 (110 percent of $1,000 par value). Using a spreadsheet as it is shown in the text to solve equation 12.1, we get kD = 6.76 percent.

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A

B

1 Number of periods

C

D

E

F

G

12

2 3 Coupon payment

$80

4 5 Market price

$1,100

6 Principal 7 repayment

$1,000

8 9 Yield to maturity

6.76%

10 The formula in cell B9 is: =RATE(B1,B3, 11 B5,B7).

12

5. The cost of equity According to the dividend discount model with constant growth expectations (see equation 12.5) the return expected by the company shareholders, kE, is:

kE 

DIV1 g P0

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where DIV1 = $2.10 is the dividend expected for next year [$2.00 × (1 + 0.05) = $2.10, where 0.05 or 5 percent is the expected growth rate of dividends], P0 = $50 is the current share price, and g = 0.05 is the expected dividends‘ growth rate. Thus:

kE 

$2.10  0.05  0.0420  0.0500  0.0920  9.20% $50

According to the Capital Asset Pricing Model (i.e., equation 12.11):

kE = RF + (RM – RF) × βOnogo

where RF = 4 percent is the risk-free rate, RM – RF = 5 percent is the market risk premium, and βOgono = 1.08 is Ogono‘s equity beta coefficient. Thus:

kE = 4% + (5% × 1.08) = 9.40%

The average of the two values for kE, 9.3%, should be the best estimate of the cost of equity for Onogo Inc.

6. Estimating the weighted average cost of capital Cost of equity based on expected return can be calculated as:

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Pre-tax cost of debt equals the yield to maturity of the debt = 4.5% After-tax cost of debt = 4.5% (1 – 0.30) = 3.15% (

)

(

)

7. Practical application of the Capital Asset Pricing Model This question is about some of the practical problems encountered in applying the Capital Asset Pricing Model (CAPM). Of the variables in the model, RF (the risk-free rate) is directly observable and  (the firm‘s equity beta) can be estimated by regressing the returns of a particular security, or securities belonging to the same industrial sector, on the returns of a market index as shown in the chapter. It is the expected average return on the market, RM, that creates the measurement problem. RM is usually estimated as the average historical return on some broad index, typically the S&P 500 for US stocks. Should we use a long-term or a shortterm estimation period? To illustrate, in Review Problem 1, the table reports that the 1926–2016 average nominal return on the market was 12% and the average return on government bonds 6.0%, which yields a market risk premium of 6%. But if we take a shorter period from 1997 and 2016, the average return on the S&P 500 index is 9.4%, and the return on government bonds 7.8%, yielding a market risk premium of 1.6%. Other time periods will yield different market risk premiums. Taking a more recent, shorter period to compute the average may capture current investors‘ attitude toward risk but this approach may reflect a particular mix of characteristics that may not be repeated in the future. It is preferable to use averages drawn from longer periods of time. Another debate is over whether the S&P 500 is an appropriate index in a world of multinational companies operating in a global economy. The issue has not been solved and probably won‘t be.

Why have some investment banks been using very low market risk premiums? The lower the market risk premium, the lower the cost of capital that is used to discount expected future cash flows, which generates higher company valuations. A cynic might suspect the banks have an incentive to generate higher valuations which will in turn generate higher fees. Clearly, the sellers of a company in a merger or an initial public offering would benefit from higher valuations at the detriment of buyers.

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8. Calculating the weighted average cost of capital a.

According to equation 12.13, Tale‘s cost of capital, or weighted average cost of capital (WACC), is:

WACC = kD (1 – TC)

D P E + kE + kP EDP EDP EDP

where kD = 6 percent is the cost of debt, TC = 35% is the tax rate,

D = 40% is the EDP

E = 50% is the proportion EDP P of equity financing, kP = 4.5% is the cost of preferred equity financing, and = 10% is EDP the proportion of preferred financing. Based on these figures, we get: proportion of debt financing, kE = 10% is the cost of equity,

WACC = [6% × (1 – 0.35) × 40%] + [10% × 50%] + [4.5% × 10%] = 7.01%

b.

The director confuses the cost of debt before tax with its cost after tax. The relevant cost of debt in calculating the WACC is obviously the cost after tax, which is 3.90 percent [6% × (1 – 0.35)].

The relevant cost of debt is thus cheaper than the cost of preferred equity financing (4.5 percent).

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Since the relevant cost of debt is cheaper than the cost equity (3.90 percent versus 10 percent), should Tale Inc. use more debt financing? No, because the more the firm uses debt, the higher the interest rate it will have to pay the new debt holders and the higher the rate of return expected by the equity holders since both suppliers of capital will face more and more risk as the debt equity ratio increases. At the end, when the only remaining source of financing is debt, the debt holders will, de facto, become equity holders and expect a rate of return equal to the cost of equity. See Chapter 13.

9. Estimating the cost of capital of a firm The relevant cost of capital for CAT is its weighted average cost of capital, or WACC, as given in equation 12.12 extended to a third source of capital—short-term debt:

WACC = kD (1 – TC)

D S E + kE + kS (1 – TC) EDS EDS EDS

D = 40% is the targeted EDS E proportion of long-term debt financing, kE is the cost of equity, = 55% is the targeted EDS S proportion of equity financing, ks = 3.5% is the cost of short-term debt, and = 5% is EDS the targeted proportion of short-term debt financing. where kD is the cost of long-term debt, TC = 35% is the tax rate,

To compute the cost of the long-term debt, we use a spreadsheet as it is shown in the text to solve equation 12.1. We get kD = 7.82%.

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A

B

1 Number of periods

C

D

E

F

G

10

2 3 Coupon payment

$90 (9 percent of $1,000)

4 5 Market price

$1,080 (108 percent of $1,000)

6 7 Principal repayment

$1,000

8 9 Yield to maturity

7.82%

10 11 The formula in cell B9 is: =RATE(B1,B3, B5,B7).

12

According to the Capital Asset Pricing Model, (see equation 12.11):

kE = RF + (RM – RF) × βCAT

where RF = 5.2 percent is the risk-free rate, RM – RF = 5 percent is the market risk premium, and βCAT = 1.03 is CAT‘s equity beta coefficient. Thus,:

kE = 5.2% + (5% × 1.03) = 10.35% For use with Finance for Executives: Managing for Value Creation 7th edition

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The weighted average cost of capital (WACC) measured at market rates for each component, using the target capital structure ratio, and a 35 percent corporate tax rate, is computed as follows:

WACC = [7.82%(1 – 0.35)40%] + [10.35%55%] + [3.5%(1 – 0.35)5%] = 7.84%

10. Yield spreads During periods of growth or stability, corporate or non-governmental bonds offer higher return and since the risk is lower for corporate bonds, investors buy them to achieve a higher yield. As investors buy these bonds and their demand increases, they offer less and less return. This reduces the spread.

When recession or similar conditions strike, the demand for treasury bonds increases as they are a safe heaven. This leads to a decreased return paid on treasury bonds. Another effect is the demand of corporate bonds decreasing which leads to the corporate issuers increasing the return to entice investors. These two actions increase the spread.

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11. Estimation of the cost of capital of a division To estimate the equipment division‘s weighted average cost of capital, you need to estimate its after-tax cost of debt and its relevant financing ratios as well as its appropriate cost of equity according to the Capital Asset Pricing Model using the data on proxy firms. Apply the following procedure: Step 1: Estimate the division‘s after-tax cost of debt.

We assume that the division‘s after-tax cost of debt, kD (1 – TC), where kD is the pretax cost of debt and TC is the corporate tax rate, is the same as that of the firm: kD (1 – TC ) = 7%(1 – 0.40) = 4.2% Step 2: Estimate the division‘s cost of equity based on data from proxy firms.

According to the Capital Asset Pricing Model (see equation 12.11), we have: kE = RF + (RM – RF) × βdivision

where RF = 5.2 percent is the risk-free rate, RM – RF = 5 percent is the market risk premium, and βdivision is the equipment division‘s equity beta coefficient. This equity beta can be estimated from the data on proxy firms by applying the following three-step procedure: Step 2.1: Estimate the asset betas of the proxy firms using equation 12.7.

asset 

equity  Debt  1 Equity   

For proxy A:  asset 

0.70  0.35 11.00

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For proxy B: asset 

1.00  0.56 1 0.80

asset 

1.02  0.60 1 0.70

For proxy C:

Step 2.2: Estimate the equipment division‘s asset beta as the average of the proxies‘ asset betas

asset 

0.35  0.56  0.60  0.50 3

Step 2.3: Estimate the equipment division‘s equity beta by relevering the division‘s estimated asset beta of 0.50 at the division‘s target debt-to-equity ratio of 1.20, using equation 12.6.

 Debt  βequity = βasset = 1   Equity 

= 0.50 × [1 + 1.20] = 1.10 Step 2.4: Estimate the division‘s cost of equity using its estimated equity beta of 1.10 and the Capital Asset Pricing Model. kE = 5.2% + (5% × 1.10) = 10.7% Step 3: Calculate the division‘s weighted average cost of capital using the division‘s target debtto-equity ratio of 1.20, which is equivalent to a debt-to-total financing ratio of 54.55% (Note: .

WACC = (4.2% × 45.45%) + (10.7% × 54.55%) = 7.75% For use with Finance for Executives: Managing for Value Creation 7th edition

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12.Estimation of cost of capital for a spinoff a.

The CEO wants to have an estimate of the value of a division that is to be sold before beginning discussions with the company‘s investment bankers. The issue is the appropriate discount rate to use in the valuation of the division‘s expected cash flows—the company WACC or a WACC that reflects the business and financial risk of the division to be sold?

To calculate the division‘s WACC, both the cost of debt and equity need to be estimated. If we accept that the sample‘s average debt-to-equity ratio as well as the average cost of their debt would be appropriate for the division, and if we assume that the pure-play airline companies have roughly the same size, we get the following values for the division based on the numbers for the pure-plays given in the table:

Cost of debt (kD) =

7.25%

Debt-to-equity ratio =

1.91.

Note that a debt-to-equity ratio of 1.91 would be equivalent to D/(E + D) of 65.64% because . Let‘s round this number to 66%. This gives an equity ratio of 34%.

Next, in order to compute an appropriate equity beta for the division from the betas of the sample of other airlines, we need to take into account the differences in their capital structure. We thus need to estimate the unlevered or asset beta of each division at their corresponding D/E ratio and take their average as a proxy for the division‘s asset beta. To do this, we use equation 12.7: For use with Finance for Executives: Managing for Value Creation 7th edition

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β asset 

β equity  D 1 E 

where D/E is the debt-to-equity ratio for each airline at market value. This formula gives A = 0.53, B = 0.33, C = 0.57, D = 0.54, and E = 0.35. If we can assume that the average of these asset betas provides a reasonable proxy for the asset beta of the division, we get:

Asset, Division 

0.53  0.33  0.57  0.54  0.35  0.464 5

Next, we need to estimate the equity beta for the division, taking into account its debt-to-equity ratio of 1.91. For this, equation 12.6 can be used:

 D β Equity, Division β Asset, Division 1   0.464  1  1.91  1.35  E

The cost of equity of the division, given by the Capital Asset Pricing Model (equation 12.11), is thus:

kE = RF + (RM – RF) × βEquity, Division

where RF = 5 percent is the risk-free rate, RM – RF = 5 percent is the market risk premium, and βEquity Division = 1.35. We get:

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kE = 5% + (5%  1.35) = 11.75%

and the division cost of capital is:

WACCDivision = [7.25%  (1 – 0.30)  66%] + [11.75%  34%] = 7.34%

b.

If the company‘s WACC of 6.40% had been used to discount the division‘s cash flow instead of the estimated divisional WACC of 7.34%, this would have resulted in an overvaluation (because a lower discount rate generates a higher value) and, possibly complicated the management‘s discussion with the investment bankers.

Chapter 13 Answers to Review Problems Finance for Executives – 7th Edition

1. Earnings per share analysis a.

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The following tables show the calculations of Chloroline‘s EPS and return on investment as a function of the firm‘s EBIT, without debt and with debt.

Current Capital Structure: No Debt and Two Million Shares Outstanding

Earnings before interest and tax (EBIT) Less interest expenses Equals earnings before tax Less tax (40% of earnings before tax) Equals net earnings Divided by the number of shares Equals earnings per share (EPS) Divided by share price Equals return on investment

Recession $5.0 million $0 $5.0 million $2.0 million $3 million 2 million $1.5 $50 3.0%

Expected $15.0 million $0 $15.0 million $6.0 million $9.0 million 2 million $4.5 $50 9.0%

Expansion $20.0 million $0 $20.0 million $8.0 million $12.0 million 2 million $6 $50 12.0%

Proposed Capital Structure: Borrow $50 million at 8% and use the cash to repurchase 1 million shares at $50 per share Recession Expected Expansion Earnings before interest and tax (EBIT) $5.0 million $15.0 million $20.0 million Less interest expenses on debt ($4.0 million) ($4.0 million) ($4.0 million) Equals earnings before tax $1.0 million $11.0 million $16.0 million Less tax (40% of earnings before tax) $0.4 million $4.4 million $6.4 million Equals net earnings $0.6 million $6.6 million $9.6 million Divided by the number of shares 1 million 1 million 1 million Equals earnings per share (EPS) $0.6 $6.6 $9.6 Divided by share price $50 $50 $50 Equals return on investment 1.2% 13.2% 19.2%

b.

The analysis shows that a substitution of debt for equity will increase Chloroline‘s EPS and return on investment in the expected and expansion scenarios, but will decrease EPS and return on investment in the recession scenario. These results, however, are insufficient to make a recommendation on whether the firm should recapitalize for the following reasons: 1. They do not show the impact of the recapitalization on the market value of Chloroline and its share price.

2. They depend upon the accounting conventions that are used to calculate EBIT. 3. They do not account for the financial distress costs that debt financing generates.

2.

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This statement is false. An increase in debt financing has two consequences: (1) an increase in risk for both shareholders and debt holders and (2) an increase in the firm‘s expected earnings before interest. Each effect cancels each other, leaving the value of the firm unchanged.

However, since shareholders are taking more risk, the return expected from their equity investment in the firm will rise to reflect the higher risk.

3.

Homemade leverage

a.

Currently, Alberton does not have any debt outstanding and it does pay any tax. Therefore, its earnings after tax are equal to its earnings before interest and tax, which is $4 million. Since the payout ratio is 100%, the amount of dividends paid to Alberton‘s shareholders is $4 million. As an owner of 140,000 shares out of 1 million shares outstanding, Mr. Robert receives $560,000 (14% of $4 million) every year. b.

Under the proposed capital structure, the number of shares outstanding will be reduced since the proceeds of the debt issue will be used to buy back shares.

Currently 1. Number of shares outstanding

1 million

2. Share price

$60

3. Market value of Alberton‘s assets (line 1 × line 2)

$60 million

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1. Debt-to-assets ratio

30 %

2. Amount of debt issued (line 4  line 3)

$18 million

3. Number of shares repurchased (line 5/line 2)

300,000

4. Number of shares outstanding (line 1 – line 6)

700,000

5. Earnings before interest and tax (EBIT)

$4 million

6. Interest rate

10%

7. Interest charges (line 9  line 5)

$1.8 million

8. Distributable earnings (line 8 – line 10)

$2.2 million

9. Number of shares owned by Mr. Robert

140,000

10. Cash to be received by Mr. Robert (line 11  line 12)/line 7)

$440,000

c.

Mr. Robert will receive less cash under the new capital structure than under the current one ($440,000 versus $560,000). This is because the interest rate on the debt, 10%, is higher than Alberton‘s return on assets, 6.67% ($4 million of EBIT divided by $60 million of assets).

Mr. Robert can keep receiving $560,000 from his investment in Alberton if he does the following: 



Tender a percentage of its shares equal to the percentage of shares that Alberton will buy back, that is 30% (line 6/line 1), or 42,000 shares (30% of 140,000 shares). Mr. Robert will then have 98,000 shares of Alberton (140,000 shares less 42,000 shares) plus $2.52 million in cash.

Subscribe to Alberton‘s debt issue up to $2.52 million. From then on, Mr. Robert will receive dividends and interest payments from Alberton, for a total of $560,000 every year, the same amount he gets under the current capital structure:

1. Number of shares outstanding 2. Number of shares owned by Mr. Robert 3. Distributable earnings (see line 8 above)

700,000 98,000 $2.2 million

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Amount of dividend to be received by Mr. Robert (line 3  line 2)/line 1) Amount of debt subscribed by Mr. Robert Interest rate Amount of interest to be received by Mr. Robert (line 6  line 5) Total amount of cash to be received by Mr. Robert (line 4 + line 7)

4.

5.

6.

7.

8.

4.

$308,000 $2.52 million 10% $252,000 $560,000

Cost of debt versus cost of equity

The argument is irrelevant. Using more debt relative to equity makes the firm riskier for both shareholders and bondholders, thus increasing the return expected by them from investing in the firm. Both the cost of debt and the cost of equity increase with more debt financing, especially the latter since shareholders are residual claimants of the firm‘s cash flows.

According to the capital asset pricing model, a higher debt-to-equity ratio increases the equity beta coefficient, and as a result, the equity risk premium required by the equity holders (see Appendix 13.1).

5. Changes in capital structure and the cost of capital a.

In the absence of debt, the cost of equity of Starline is equal to the return from its assets because the shareholders are the only claimants to the cash flows generated by these assets. Thus, Starline‘s return on assets is 14%. This is also Starline‘s WACC in the absence of debt. As the debt-to-equity ratio goes up from zero to 100%, Starline‘s shareholders will bear more and more (financial) risk. Equation 13.7 shows how the cost of equity is related to the leverage ratio:

k LE  rA  ( rA  k D ) (1  TC ) where: k EL = rA = kD = Tc = D/E =

D E

cost of equity return on assets = 14% cost of debt = 8% corporate tax rate = 40% debt-to-equity ratio

k LE  .14  (.14  .08) (1  .40)

D E

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k LE  .14  .036

D E

From equation 13.8, we have:

WACC  k LE

E D  k D (1  Tc ) ED ED

D  k LE  k D (1  Tc ) E D D 1 1 E E 1

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D/E

0

25%

50%

75%

100%

kD k EL WACC

0.08 0.14 0.14

0.08 0.149 0.129

0.08 0.158 0.121

0.08 0.167 0.116

0.08 0.176 0.112

b.

k LE

WACC

kd

c.

According to the above analysis, you would be tempted to recommend that Starline increase its indebtedness as much as possible because the higher the level of debt, the lower the weighted average cost of capital and the higher the value of the firm. However, the analysis ignores the impact of financial distress costs on the WACC and on the value of the firm when debt is increased.

Conclusion: You should not recommend an increase in debt on the basis of this analysis alone.

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6.

The cost of equity, the weighted average cost of capital, and financial leverage

a.

From equation 13.2:

k LE  rA  ( rA  k D )

D E

where: k EL

= cost of equity

rA

= expected return on the firm’s assets

kD

= cost of debt

D/E = debt-to-equity ratio

At the current target capital structure of 80% equity and 20% debt (D/E=.25):

k LE = 12% + (12% – 8%)  0.25 = 13%

Since the return on assets does not depend upon the way the assets are financed, the equation is still applicable if the target capital structure changes to 50% equity, 50% debt (D/E = 1). Then, we have:

k LE = 12% + (12%

8%)  1 = 16%

Albarval‘s return on assets accrues to both its shareholders and debt holders in proportion to their respective investments in the firm. Since a firm‘s weighted average cost of capital (WACC) is equal to the sum of the shareholders‘ and bondholders‘ expected returns in proportion to their respective investments in the firm, it must be equal to the expected return on the firm‘s assets.

Thus, Albarval‘s WACC is 12%. As the return on assets does not depend upon the way the assets are financed, the change in the target capital structure to 50% equity, 50% debt (D/E = 1) does For use with Finance for Executives: Managing for Value Creation 7th edition

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not affect the firm‘s WACC that will still be 12% under the new capital structure. This can be checked easily by computing the Albarval‘s WACC under both target capital structures.

b.

From equation 13.7:

k LE  rA  ( rA  k D )(1  Tc )

D E

where: Tc = corporate tax rate

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When the target debt-to-equity ratio is 0.25, the cost of equity is:

k LE = 12% + (12% – 8%)  (1 – 0.40)  0.25 = 12.6%

And, from equation 13.8, the weighted average cost of capital is:

WACC  k LE

E D  k D (1  Tc ) ED DE

WACC = 12.6% × 0.80 + 8% × (1 – 0.40) × 0.20 = 11.04%

When the target debt ratio is 1:

k LE = 12% + (12% – 8%)  (1 – 0.40)  1 = 14.4% and WACC = 14.4%  0.50 + 8%  (1 – 0.40)  0.50 = 9.6%

Although the return on assets is still not affected by changes in the capital structure, the weighted average cost of capital is because the interest payments are tax deductible. The 8% interest rate required by Albarval‘s debt holders changes to 4.8% [8%  (1 – 0.40)] when the corporate tax rate is 40%. Albarval‘s WACC decreases from 11.04% to 9.6% when the debt ratio increases from 0.25 to 1 because the extra return expected by the shareholders from the interest tax shield and the lower after-tax cost of debt more than offset the higher financial risk generated by a higher level of debt.

7. Changes in cost of equity due to leverage

We need to adjust the cost of equity to the change in the leverage and the tax rate.

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Now the equity cost for increased leverage would be:

8. The value of the interest tax shield

a.

The annual tax savings, or interest tax shield (ITS), is:

ITS = Tax rate  Interest rate  Amount of debt

ITS = 0.35  0.08  $25,000,000 = $700,000

If the debt is permanent, the present value of the interest tax shield is equal to the present value of a perpetual annuity of $700,000 at 8%:

PV(ITS)permanent =

ITS $700,000 = $8,750,000  Interest rate .08

Note that the value of the tax shield would represent 8.75% of the market value of the firm, since the firm has currently no debt and its market value is $100,000,000.

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If the debt matures in five years, the present value of the interest tax shield is equal to the present value of a five-year annuity of $700,000 at 8%: PV(ITS)5 years =

$700,000 $700,000 $700,000 $700,000 $700,000     = $2,794,897 1  .08 (1  .08) 2 (1  .08)3 (1  .08) 4 (1  .08)5

b.

If the interest rate increases immediately after the debt is issued:

PV(ITS)permanent =

$700,000 = $7,777,778 .09

and (ITS)5 years =

$700,000 $700,000 $700,000 $700,000 $700,000 = $2,722,756     1  .09 (1  .09)2 (1  .09)3 (1  .09)4 (1  .09)5

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9. Cost of capital and interest tax shield

a. The cost of equity can be calculated as the return on equity. This is equal to net income/equity value.

Hence the cost of equity = $2.5/$20 = 12.50% b. We need to calculate the present value of the interest tax shield. The interest payments would be: $5 million 10% = $0.50 million.

Tax shield = $0.50 million 30% = $0.15 million PV of the shield = $0.15 million/0.10 = $1.50 million This increase in equity will be added now and the value of the equity is now $20 million + $1.50 million = $21.50 million.

The value of debt is now $5 million.

The total value of the company is $26.50 million. c. Initial stock price = $20 million/2 million = $10.00 Stock price after taking on debt = $21.50 million/2 million = $10.75

10. Industry influence on the capital structure

The probability that an electric utility goes bankrupt is quite small because (1) it is usually a local monopoly and (2) most of its valuable assets are tangible ones. It should exhibit the highest debt ratio among the three firms. At the opposite, a biotechnology firm‘s most valuable assets are intangible and its operating margin is likely to be quite volatile. As a result it should have the lowest debt ratio. An auto parts firm is more (less) likely to go bankrupt compared to a utility (biotechnology) firm because it has relatively less (more) tangible assets and more (less) volatile operating margins.

11. Board of directors and management

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It is in the interest of the managers to maintain a low debt-to-equity ratio when the board of directors exercise little power on them. By keeping financial leverage low, they reduce the probability of the firm to face financial distress and the probability to be personally affected by these costs, such as more oversight by the financial markets, lower personal revenues, low morale among employees, etc.

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12. Agency costs

Shareholders expropriate wealth from bondholders when they induce management to (1) make investments which are riskier than anticipated by bondholders, (2) increase debt at a higher level than anticipated by bondholders, and (3) increase dividends or repurchase shares beyond what is anticipated by bondholders. Note that bondholders can reduce the wealth expropriation by imposing strict covenants to the debt issue.

Chapter 14 Answers to Review Problems Finance for Executives – 7th Edition

1. Valuation issues a.

When the yield on government securities rises, equity investors require a higher return to hold shares. This reduces share prices and decreases (not increases) price-earnings ratios. b.

For typical cash-flow streams, it is the present value of the cash flows expected beyond the 5- to 10-year forecasting period that dominates: it usually accounts for more than 50% of a company‘s estimated DCF value. c.

In a leveraged buyout, debt financing provides more than valuable tax savings. It is also a device to monitor management (more debt means more pressure on management to generate cash to service debt and, thus, less wasted cash). And because management usually holds a relatively For use with Finance for Executives: Managing for Value Creation 7th edition

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small amount of equity, debt financing is a way to provide them with a higher percentage of the firm‘s total equity (more debt financing means less equity financing and, thus, a higher fraction of equity in the hand of management).

2. Some issues in mergers and acquisitions a.

It can create value through synergistic revenue enhancement (post-merger revenues exceeding the sum of the revenues of the pre-merged firms). b.

Value can be created in a merger even in the absence of synergies if the management of the target firm can be improved. This could occur irrespective of synergistic cost reductions or synergistic revenue enhancements.

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c.

Growth in earnings per share does not necessarily create value. Value will be created only if the merger has a positive net present value. d.

There is no evidence that acquiring firms create value by uncovering undervalued target firms. If they did, the share price of target firms would not drop to their pre-merger level when the mergers are cancelled.

3. Leveraged buyout Value creation   

Lower taxes from additional annual depreciation expenses resulting from the revaluation of fixed assets Lower taxes from additional interest expenses More dedicated managers being able to generate higher cash flows from assets

Value destruction  

Higher cost of equity capital Increased probability of not being able to service debt

4. Mergers and price-to-earnings ratios a.

The maximum price that Maltonese should pay for the acquisition of Targeton is $60 million.

This is the value of Targeton standing alone—$45 million (1.5 million shares at $30 each)—plus $15 million, which is the value creation expected from the merger. At any higher price, the net present value of the acquisition would be negative. At $60 million, the net present value of the acquisition is zero for Maltonese and all the gains of the merger ($15 million) will go to Targeton‘s shareholders. This represents $40 per share outstanding. b.

The following table shows how the P/E ratio of the merged firm can be estimated.

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1.

2.

3.

4.

5.

6.

Maltonese Inc.

Targeton Corp.

$60 5 million $300 million 10 $30 million $6

$30 1.5 million $45 million 6 $7.5 million $5

Share price Number of shares outstanding Market value of equity (line 1  line 2) P/E ratio Earnings after tax (line 3/line 4) Earnings per share (line 5/line 2)

Merged firm 7. Earnings after tax (from line 5) 8. Market value of equity (from line 3 + gains from merger) 9. Number of shares outstanding

10. Earnings per share (line 7/line 9) 11. Share price (line 8/line 9) 12. P/E ratio (line 11/line 10)

$30 million + $7.5 million = $37.5 million $300 million + $45 million + $15 million = $360 million 5 million of outstanding Maltonese shares + 0.75 (1.5/2) million Maltonese shares to issue = 5.75 million shares $6.52 $62.61 9.6

5. Mergers and price-to-earnings ratios a.

The following table shows how the earnings per share, price-to earnings ratio, and share price of the merged firms can be calculated.

1. Share price 2. Number of shares outstanding 3. Market value of equity (line 1 × line 2) 4. P/E ratio 5. Earnings after tax (line 3/line 4) 6. Earnings per share (line 5/line 2)

Mergecandor Corp.

Tenderon Inc.

$30 2 million $60 million

$15 1 million $15 million

7.5 $8 million $4

5 $3 million $3

Merged firm 7. Earnings after tax (from line 5) 8. Market value of equity (from line 3)

$8 million + $3 million = $11 million $60 million + $15 million = $75 million

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9. Number of shares outstanding 10. Earnings per share (line 7/line 9) 11. P/E ratio (line 8/line 7) 12. Share price (line 10 × line 11)

2 million of outstanding Mergecandor shares + 0.5 (1/2) million Mergecandor shares to issue = 2.5 million shares $4.4 6.82 $30

Note that since the merger does not create any wealth gain, the net present value of the transaction is zero. Further, since the exchange ratio is exactly equal to the ratio of the two companies‘ share price, there must not be any wealth transfer between the shareholders of Mergecandor and those of Tenderon. This is confirmed by the calculated share price of the merged firm, which is exactly equal to $30, the pre-merger share price of Mergecandor. In other words, the merger would not make the shareholders of Mergecandor richer or poorer. This would also be the case for Tenderon shareholders, who would get a share of the merged firm valued at $30 when surrendering two shares of Tenderon at $15 each (2  $15 = $30). b.

If the P/E ratio of Mergecandor stays at 7.5 after the merger, we have the following: Merged firm 13. P/E ratio 14. Market value of equity (line 13  line 7) 15. Share price (line 14/line 9)

7.5 $82.5 million $33

At $33 a share instead of $30, there is a ―market‖ gain from the merger of $7.5 million ($33 – $30 = $3  2.5 million shares). A Mergecandor shareholder would gain $3 per share held ($33 – $30), or make a 10 percent ($3/$30) return form the merger. The gain would be the same for a Tenderon shareholder who would get a share of the merged firm valued at $33 in exchange of two Tenderon shares valued at $15 each, or $30 in total. In other words, the ―market‖ gain would be evenly split between the shareholders of the two firms.

6. Enterprise value-based equity valuation We need to calculate the EBITDA first which can be calculated as: Item

Value

Sales

$75,000,000

Cost of goods sold

($48,000,000)

Selling, general and administrative expenses

($7,500,000)

EBITDA

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The enterprise value multiple is 12 and hence the enterprise value would be: Total value of equity and debt = Enterprise value + Cash = $234,000,000 + $20,000,000 = $254,000,000 The value of equity = $254,000,000

$120,000,000 = $134,000,000

7. Comparative valuation Based on P/E ratio: EPS for the median company = $34 million/$10 million = $3.40 P/E ratio = $20/$3.40 = 5.88 Value of company = 5.88

$21 = $123.53 million

Based on P/B ratio, we have: BVPS for the median company = $100 million/10 million = $10 P/B ratio = $20/$10 = 2 Value of company based on book value = $70 million

2 = $140 million

Based on EV/EBITDA multiple: EV for the median company = ($20

10 million) + $175 million

$3 million = $372 million

EV/EBITDA multiple = $372 million/$70 million = 5.31 Using the same multiple for HBC, we have: Value of the company = ($52 million

5.31)

$150 million + $2 million = $128 million

8. Net present value of an acquisition a.

The amount of wealth created by the merger is the present value of the $1,000,000 savings on the administrative costs of the two firms. This is the present value of a constant cash flow of $1,000,000 at Motoran‘s cost of capital of 12.5 percent and its value is given by equation 14.6 where the constant growth rate g is set equal to zero: For use with Finance for Executives: Managing for Value Creation 7th edition

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Wealth created 

Expected annual cash flow savings $1,000,000   $8 million Cost of capital .125

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b.

If Motoran acquires Tortoran, it will get two things. First, the value of Tortoran standing alone ($20 million) plus $8 million of value created by the merger, for a total of $28 million. If the $25 million offer is accepted by Tortoran‘s shareholders, Motoran would pay $25 million for an investment which is worth $28 million. The net present value of the acquisition is thus $3 million ($28 million less $25 million).

9. Discounted cash-flow valuation The minimum price that David Murlow should ask for his firm is the present value of the cash flows expected from the assets of the firm standing alone. The value of the firm is the sum of the present value of the cash flows expected at the end of each of the next three years plus the present value of the terminal value at the end of the three-year period.

The free cash flows from the firm‘s assets (FCF) can be estimated with equation 14.3: FCF = EBIT(1 – Tc) + Depreciation expenses – WCR – Net capital expenditures where EBIT is earnings before interest and tax, TC is the corporate tax rate, and WCR is the change in working capital requirement. Since annual capital expenditures are expected to be equal to the annual depreciation expenses, the equation reduces to: FCF = EBIT(1 – TC) – WCR Using a spreadsheet similar to Exhibit 14.5 we can estimate the equity value of Murlow Company as follows:

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A

B

C

D E F END-OF-YEAR FORECAST

1 $ millions 2 3 Current Year 1 Year 2 Year 3 Year 4 4 5 Sales growth rate 6,00% 6,00% 6,00% 4,00% 6 Operating margin as percent of sales 20,00% 20,00% 20,00% 20,00% 7 WCR in percent of sales 18,0% 18,00% 18,00% 18,00% 18,00% 8 Sales $500,0 $530,0 $561,8 $595,5 $619,3 9 EBIT 106,0 112,4 119,1 123,9 10 EBIT × (1 – Tax rate of 40%) 63,6 67,4 71,5 74,3 11 WCR at year-end 90,0 95,4 101,1 107,2 111,5 12 less ΔWCR [change in (11)] -5,4 -5,7 -6,1 -4,3 13 14 equals free cash flow from assets $58,2 $61,7 $65,4 $70,0 15 16 Terminal valuevalue of assets end-of-year 3 $1 167 17 18 19 Beginning Year 1 20 21 WACC 10,00% 22 DCF value of assets $1 030 23 less book value of debt $0 24 equals DCF value of equity $1 030 25 26 Rows 5 to 7, 21 and 23, plus cell B8 are data.

27 The formula in cell C8 is: =B8*(1+C5). Then copy formula in cell C8 to cells D8, E8, and F8.

28 The formula in cell C9 is: =C6*C8. Then copy formula in cell C9 to cells D9, E9, and F9.

29 The formula in cell C10 is: =C9*(1-.4). Then copy formula in cell C10 to cells D10, E10, and F10.

30 The formula in cell B11 is: =B7*B8. Then copy formula in cell B11 to cells C11, D11, E11, and F11.

31 The formula in cell C12 is: =B11-C11. Then copy formula in cell C12 to cells D12, E12, and F12.

32 The formula in cell C14 is: =C10+C12. Then copy formula in cell C14 to cells D14, E14, and F14.

33 The formula in cell E16 is: =F14/(B21-F5).

34 The formula in cell B22 is: =NPV(B21,C14:E14)+E16/(1+B21)^3.

35 The formula in cell B24 is: =B22-B23.

36

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10. Discounted cash-flow valuation a.

Apply the following three-step method: Step 1: Provide a formula to estimate the free cash flows from assets (FCF) that Portal is expected to generate in the next five years.

From equation 14.3, we can write: FCF = EBIT(1 – Tax rate) + Depreciation – WCR – Net capital expenditures where EBIT is earnings before interest and tax, or pretax operating profit, and WCR is the change in working capital requirement. Because annual net capital expenditures will be equal to annual depreciation expenses, we have:

FCFPortal = EBIT(1 – Tax rate) – WCR Step 2: Estimate LMC’s weighted average cost of capital (WACC).

1.

2.

3.

4.

Cost of equity according to the Capital Asset Pricing Model = 5% + 1.05 × 5% = 10.25% Percentage of debt financing = 50% After-tax cost of debt = 6% × (1 – 0.40) = 3.6% Percentage of equity financing = 100% – 50% = 50%

WACC = 0.50 × 10.25% + 0.50 × 3.6% = 6.93%

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Step 3: Using a spreadsheet similar to Exhibit 14.5 estimate the DCF value of Portal’s equity from the forecasting assumptions: A

B

C

1 $ millions

D

E

F

G

END-OF-YEAR FORECAST

2 3

Current

Year 1

Year 2

Year 3

Year 4

Year 5

5 Sales growth rate

5.00%

5.00%

5.00%

5.00%

3.00%

Operating margin as percent of 6 sales

16.00% 17.00% 18.00%

19.00% 20.00%

7 WCR in percent of sales

18.0% 18.00% 18.00% 18.00%

18.00% 18.00%

8 Sales

$750.0

4

$787.5

$826.9

$868.2

$911.6

$939.0

9 EBIT

126.0

140.6

156.3

173.2

187.8

10 EBIT× (1 – Tax rate of 40%)

75.6

84.3

93.8

103.9

112.7

141.8

148.8

156.3

164.1

169.0

6.8

7.1

7.4

7.8

4.9

$68.9

$77.3

$86.3

$96.1

$107.8

11 WCR at year-end

135.0

12 less ΔWCR [change in (11)] 13 14 equals free cash flow from assets 15 16 Residual value end-of-year 4

$2,741.8

17 18 19 Beginning Year 1 20 For use with Finance for Executives: Managing for Value Creation 7th edition

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21 WACC

6.93%

22 DCF value of assets

$2,373

23 less book value of debt

$500

24 equals DCF value of equity

$1,873

25 Rows 5 to 7, and 23, plus cell B8are data.

26 27 The formula in cell C8 is: =B8*(1+C5). Then copy cell C8 to cells D8, E8, F8, and G8.

28 The formula in cell C9 is: =C6*C8. Then copy cell C9 to cells D9, E9, F9, and G9.

29 The formula in cell C10 is: =C9*(1 0.4). Then copy cell C10 to cells D10, E10, F10, and G10.

30 The formula in cell B11 is: = B7*B8. Then copy cell B11 to cells C11, D11, E11, F11, and G11.

31 The formula in cell C12 is: =B11 C11. Then copy cell C12 to cells D12, E12, F12, and G12.

32 The formula in cell C14 is: =C10+C12. Then copy cell C14to cells D14, E14, F14, and G14.

33 The formula in cell F16 is: =G14/(B21 G5).

34 The formula in cell B22 is: =NPV(B21,C14:F14)+F16/(1+B21)^4.

35 The formula in cell B24 is: =B22 B23.

36

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b.

To estimate the changes in equity value resulting from the suggested performance improvements, simply modify the relevant data in the spreadsheet used in part a. To find the estimated amount of value created, simply deduct $1,873 million, the DCF value of Portal‘s equity without improvements, that is, its value ―as is.‖

Expected Cash Flows from Assets ($ millions)

Action None Faster growth Higher operating margin Lower WCR/Sales ratio Lower cost of capital Sum of the four actions Combined actions 1

New DCF Value

Value Created

$68.9; $77.3; $86.3; $96.1 2,741.81 $68.5: $77.3; $86.8;$97.2; $3,193.71 $73.6; $82.2; $91.5;$101.6 $2,885.21 $84.6; $78.0; $87.2; $97.0;$2755.81 $68.9; $77.3; $86.3; $96.1;$2,968.41

$1,873 million

–

$2,220 million

$347 million

$ 2,000 million

$127 million

$1,901 million

$28 million

$2,074 million

$201 million

$89.1; $83.2; $93.1; $103.7 $3,704.91

$2,680 million

$703 million $807 million

Terminal value at Year-end 4

The sum of the changes in value resulting from each separate action ($703 million) is smaller than their cumulative effects ($807 million) because combining the various actions reinforces their individual impact. For example, a higher cash flow discounted at a lower cost of capital will generate a higher value than each one of the two changes taken separately.

11.

Alternatives to cash acquisition

a.

From equation 14.6, where the constant growth rate g is set equal to zero, the discounted cash flow (DCF) value of the $800,000 indefinitely annual increase to Osiris‘ cash flow from assets is:

DCFto Osiris 

Expected annual free cash flow increase $800,000   $10 million Cost of capital .08

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Since the market value of Polos prior to the acquisition is $30 million, its value to Osiris when accounting for the expected synergies is: Value of the acquisition to Osiris = Value of Polos standing alone + Value of synergies = $30 million + $10 million = $40 million b.

After the acquisition, the market value of Osiris would be: Osiris‘ valuepost acquisition = Osiris‘ valuestanding alone + Value of the acquisitionto Osiris = $50 million + $40 million = $90 million Under the exchange of shares alternative, the cost to Osiris would be 25 percent of its postacquisition value or $22.5 million. Under the cash purchase alternative, the cost would be $20 million. c.

Under the exchange of shares alternative, the NPV of the acquisition would be the value of the acquisition minus its cost or $17.5 million ($40 million less $22.5 million). Under the cash alternative, it would be $20 million ($40 million less $20 million).

For use with Finance for Executives: Managing for Value Creation 7th edition

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12.

Cash or stock offer?

a.

Mirandel‘s share price, PMirandel, is the present value of an annuity equal to the dividend expected for next year growing at a constant rate, g (5 percent), forever. Equation 14.6 shows that we can write: DIVnext year PMirandel  kg where k is Mirandel‘s cost of capital. From this relationship, we get: k

DIVnext year PMirandel

g

The following table shows how we can calculate Mirandel‘s cost of capital using this equation: 1.

2.

3.

4.

5.

6.

7.

8.

9.

Current dividend (per share) Expected dividend growth rate, g Dividend next year [line 1  (1 + line 2)] Earnings after tax Number of shares outstanding Earnings per share (line 4/line 5) P/E ratio PMirandel (line 7  line 6) Cost of capital [(line 3/line 8) + line 2]

$1.50 5% $1.575 $2 million 2 million $1 20 $20 12.9%

b.

If Mirandel acquires Tarantel, the dividend would grow by 8 percent instead of 5 percent.

Applying the price formula from above, we get:

PMirandel 

$1.50  (1  .08)  $33.06 .129  .08

This represents an increase of $13.06 per share ($33.06 – $20). Since Mirandel has 2 million shares outstanding, the value of Tarantel for Mirandel‘s shareholders is $26.12 million ($13.06  2 million). This $26.12 million is $3.62 million higher than the current market price of Tarantel‘s equity, which is $22.5 million (Earnings of $1.5m x P/E ratio of 15).

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c.

If Mirandel offers $50 in cash for each outstanding share of Tarantel, it will acquire Tarantel for $25 million ($50  0.5 million shares). The net present value of the acquisition would be $1.12 million ($26.12 million – $25 million). If it offers 756,000 of its shares in exchange of the outstanding stock of Tarantel, Mirandel would give Tarantel‘s shareholders 756,000  $33.06 = $24.99 million worth of the merged firm‘s stock. The net present value of the acquisition would be $1.126 million, which is not significantly different from the cash offer.

Whether Mirandel should make a cash or a stock exchange offer depends upon the following considerations: 1. If Mirandel‘s management believes that Mirandel‘s shares are currently overvalued, the stock exchange offer makes more sense than a cash offer.

2. If cash is offered to Tarantel‘s shareholders, they would receive a fixed price. If the merger is very successful, they would not benefit from the additional wealth created by the merger. However, if the merger is a failure, the losses would not be shared by Tarantel‘s shareholders, and shareholders of Mirandel would be worse off than in the case of a stock exchange.

3. In a cash offer, Tarantel‘s shareholders may have to pay capital gain taxes, while in a stock exchange the transaction is tax free.

Chapter 15 Answers to Review Problems Finance for Executives – 7th Edition

For use with Finance for Executives: Managing for Value Creation 7th edition

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1. Various types of risk

a.

Business risk results from the choice of nonfinancial assets the firm has made (the left side of the balance sheet), whereas financial risk results from the firm‘s decision to borrow (financial debt on the right side of the balance sheet).

b.

Diversifiable risk is the risk investors can eliminate by holding well-diversified portfolios of shares of companies, whereas undiversifiable risk is the risk investors cannot eliminate through diversification.

c.

Systematic risk is the same as undiversifiable risk. It is the only risk that matters to investors who hold the shares of a company. Unsystematic risk is the same as diversifiable risk.

d.

An insurable risk can be covered by buying an insurance contract (for example the risk of fire), whereas an uninsurable risk is a risk for which the firm cannot get an insurance coverage because insurance companies would be reluctant to insure the firm against this type of risk (for example, the risk of product defects, although today, insurance companies are offering coverage for many forms of risk).

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e.

Project risk originates at the level of the project itself, whereas corporate risks are risks not directly related to a particular project, such as the risk that a key senior manager would leave the firm.

f.

Foreign-exchange risk and currency risk are the same.

g.

Financial investment risk results from the firm‘s holding of financial assets whose value fluctuates, whereas financial risk results from the firm‘s borrowing.

h.

Credit risk is the risk that the firm‘s may not be able to cash the sales it has made to some of its clients who have received goods or services but have not yet paid for them. It is unrelated to the firm‘s financial risk.

i.

Liquidity risk is part of the firm‘s financial investment risk: it is the risk that the firm‘s may not be able to sell some of its financial assets at their fair value because of adverse market conditions, whereas refinancing risk occurs when the borrows and then finds itself unable to renew the loan.

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j.

Both these risks occur because the firm borrows: financing cost risk is the risk that a loan may have to be renewed at a higher interest rate, whereas refinancing risk is the risk that the loan may not be renewed irrespective of what the cost of borrowing is.

2. Levels of risk Since the risk is faced by the company, because of the evolving industry, it is a business risk.

Traditional internal combustion car manufacturers need to transition to electric cars as consumers have started to prefer them due to lower running and maintenance costs, environmental concerns, government subsidies in some cases, etc.

The move toward electric car manufacturing is a strategic decision which needs to be carefully planned and depends on quality, marketing, operational efficiencies, etc. Hence it is a strategic risk.

One of the primary reasons for success of an electric car is its performance and range. These largely depend on the technology used. In this case, it is majorly a technological risk.

3. Analyzing risk types

a. b. c. d. e. f. g.

It is a form of business process risk under operational risk.

Credit risk.

Currency risk is the main risk faced in this scenario.

Economic risk under macro risk umbrella.

Maturity mismatch which is a form of financing risk.

It‘s a form of operational risk and may include business process risk, property damage risk, among others.

This is an example of a credit risk because the currency risk has been hedged by the swap. The risk is the risk of the counterparty not honoring the contract.

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h.

This is an example of a price risk. Increase rates may cause the prices to fall.

4. Systematic risk

a.

A firm faces 4 broad types of risk: Business risk, financial risk, financial investment risk, and currency risk. Because the firm has no financial assets and all its activities are domestic, it only faces the first 2 types of risk.

b.

The firm‘s systematic risk (beta) of 1.20 captures both its systematic business risk and systematic financial risk, with the latter occurring because the firm borrows. To get the firm‘s systematic business risk, we have to measure beta assuming the firm has no debt. The formula that provides a firm‘s beta without debt (  U ) is given by equation 12.7 in Chapter 12. In can write:

U 

 1.20 1.20    0.60 Debt 1  1 2 1 Equity

We can infer from the above that systematic financial risk account for the difference, that is, 0.60. In percentage, this represents 50% of total systematic risk (0.60/1.20).

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Some of the major issues a firm risk policy should address are:

1. Making sure that there is a process in place to identify and control risk, and that the process to decide whether to reject or accept a risk is well established – this can be the responsibility of a risk management committee headed by a senior executive 2. Making sure that decision-makers make value-creating investment decisions that take into account all the risks the firm is exposed to – this can be achieved by better coordination between the firm‘s strategic committee and its risk management committee 3. Making sure that corporate risks are taken into account (the risks that are not directly related to specific projects) 4. Making sure that managers have are incentivized to act in the best interest of the firm‘s owners.

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6. Measuring risk exposure

a.

€50m  €625. The table below 11%  3% summarizes the impact of the three sources of risk on the firm‘s enterprise value. The reduction in EV is the difference between €625m and the value in the second column. MVR is equal to the reduction in EV multiplied by the probability of occurrence.

The value of the firm‘s assets (its enterprise value) is EV 

Source

Reduction

Probability

EV of risk

Cost of capital down to 10.5% Growth rate

MVR

MVR EV

in EV

of occurrence

€588.24m

€36.76m

10%

€3.68m

0.59%

€500.00m

€125.00m

60%

€75.00m

12.00%

€562.50m

€62.50m

40%

€25.00m

4.00%

down to 1% Cash flow down to €45m

b.

The first risk listed in the table is low; the second is high; and the third is moderate.

7. Inventory value and the risk of obsolescence

HDM is exposed to two particular types of business risk. The risk of a decline in the price of For use with Finance for Executives: Managing for Value Creation 7th edition

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inventory is that the cost of HDM‘s computers will be higher than that of competitors that purchase components at a later date. To protect against this risk, the firm should buy components just before assembling its computers in order to minimize inventory holdings. The risk that machines become obsolete is a technological risk: competitors that acquire the latest model will assemble computers that are less costly than those assembled by HDM. One way to protect itself against this type of risk is for HDM to outsource its manufacturing (assuming this is possible), or leasing the machine.

Chapter 16 Answers to Review Problems Finance for Executives – 7th Edition

1. Pricing forward contracts a. Using equation 16.1: The value of the contract is zero. b.

and the value of the forward contact is

c. F0 = $50 x (1+0.03-0.02)1 = $50.5 and the value of the forward contact is zero.

2. Hedging interest-rate risk with futures a.

The company should sell the futures because if the interest rates rise, the value of futures will fall and the company can earn profit. If the rates fall, the company can get the loan at a lower rate. Overall, this reduces the gain as a result in the fall in rates but hedges against the rise in rates for the loan.

b. To hedge $150 million, BWV needs to buy: For use with Finance for Executives: Managing for Value Creation 7th edition

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c.

The current price can be calculated using the cash flow discounting:

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d. To issue $150 million worth of bond, the company will receive:

e. Price of contract at 3.75%:

Since the price has fallen, there is a gain on sold futures contracts. The total gain is: ($1,014.01 $1,006.97) 150,000 = $1,055,611.10 f. For the hedge to be perfect, the gain from the shorted futures should cancel out the loss from the issue.

Loss from the issue = $150,000,000

$147,957,563.98 = $2,042,436.02

Net position = $1,055,611.10

$2,042,436.02 = $986,824.92

g. Gain per contract = $1,014.01 accuracy)

$1,006.97 = $7.037407 (not rounding for increased

To hedge $2,042,436.02 loss from the issue, we need: $2,042,436.02/$7.037407 = 290,225.64 contracts or 290,226 contracts

3. Forward contracts: alternative pricing formulas To see this, consider the case of a stock that pays no dividends and whose expected value is E(ST). What is its present value (S0)? It is E(ST) discounted to the present at the risk-adjusted rate kS, that is, S0 =

and thus E(ST) = S0(1+k)T. Putting this into equation 16.3 yields equation

16.1 in the case where the dividend yield is zero.

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4. Hedging with Eurodollar futures a.

Sell ten December 3-month Eurodollar futures contracts

b.

Dec 10 LIBOR Cost of borrowing $1 million for 3 months Profit (loss) on the futures contract Actual borrowing cost Actual borrowing rate

2.50% $1million 0.025 3/12 = $6,250 $1million (0.025 – 0.03 ) 3/12 = ($1,250) $6,250 + $1,250 = $7,500 =($7,500/$1,000,000) 12/3 = 3 percent

3.00% $1million 0.03 3/12 = $7,500 $1million (0.03 – 0.03 ) 3/12 =$0 $7,500 + $0 =$7,500 =($5,000/$1,000,000) 12/3 = 3 percent

3.50% $1million 0.035 3/12 = $8,750 $1million (0.035 – 0.03 ) 3/12 = $1,250 $8,750 – $1,250 =$7,500 =($5,000/$1,000,000) 12/3 = 3 percent

The effective interest rate is locked at the current LIBOR futures implied rate (3 percent).

5. Hedging with stock index futures a. Short. Number of contracts to sell: ($1.5 million)/($250 × 3,000)) = 2 contracts b. 1.5 × ($1.5 million)/($250 × 3,000) = 3 contracts c.. d. and e.

S&P index in 3 months

2,900 3,000

S&P futures price now Profit (loss) on the 3 futures contracts S&P index return Expected portfolio return using CAPM Expected portfolio value in 3 months Expected net value of the hedge portfolio

3

(3,000 2,900) = $75,000

3.000 3,000 250

(2,900 – 2,975)/2,975 = –0.025 0.01 + 1.5 [–0.025 –0.01] = –0.0462 $1.5 million (1 – 0.0462) = $1,418,250 $1,418,250 + $75,000 = $1,493,250

3

(3,000 – 3,000) = $0

3.100 2,975 250

(3,000 – 2,975)/2,975 = 0.008 0.01 + 1.5 [0.008 – 0.01] = –0.007 $1,500,000 ( 1 – 0.007) = $1,489,500 $1,489,500 + $0 = $1,489,500

3

© 2022 Cengage Learning EMEA

250

(3,100 – 2,975)/2,975 = 0.042 0.01 + 1.5 [0.042 – 0.01] = 0.058 $1.5 million (1 + 0.058) = $1,587,000 =$1,587,000 – $75,000 = $1,512,000

For use with Finance for Executives: Managing for Value Creation 7th edition

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(3,000 – 3,100) = ($75,000)

6. Option premium for copper a. C[S0 = $6,000; X = $6,000; T = 0.25; RF = 5%; σS = 25.01%] = $336 b. C[S0 = $6,000; X = $5,900; T = 0.25; RF = 5%; σS = 25.01%] = $389.51 The call premium is higher because the cost of one ton of copper to WTM would be lower if the option is exercised ($5,900 vs $6,000). c. P[S0 = $6,000; X = $6,000; T = 0.25; RF = 5%; σS = 25.01%] = $261.49

7. Put-call parity relationship a. According to the put-call parity relationship: Put‘s price = $5 + $50e-0.04x.25

$50.5 = $5 +$49.5

$50.5 = $4

b. Now buy the call and sell short both the put and the stock for: $5 + $4.3 + $51 = $50.3 and invest the $50.3 at the risk free rate of 3 percent for 3 months.

In 3 months‘ time:  If WHQ stock price S is greater than $50, exercise the call and you collect: $50 +S – S +$50.3e0.04x0.25 = $0.08  If WHQ stock price S is less than $50, the put is exercised and you collect: $50 +S – S +$50.3e0.04x0.25 = $0.08 The net gain is: $0.08.

8. Valuing employee stock options a. Using the Black-Scholes formula we get: For use with Finance for Executives: Managing for Value Creation 7th edition

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The cost of the option issue to PQS is b. There should not be any drop in the PQS share price as the dilution effect has already been anticipated by the stock market when the options were issued.

9. Mergers and the value of the firm's equity and debt a.

CAFC [VAFC = $100m; X = $70m; T = 10; RF = 6%; Bond Value (AFC) = $100m = 10; RF = 6%;

= 30%] = $66.07 million

$66.07m = $33.93m CCMC [VCMC = $100m; X = $60m; T

= 40%] = $73.80 million

Bond Value (CMC) = $100m b. Yield Zero (AFC) = (

)

Yield Zero (CMC) = (

)

$73.80m = $26.20m

c.

and

d. CMerged [VMerged = $200m; X = $130m; T = 10; RF = 6%;

√

= 25%] = $132.70m

Bond Value (Merged) = $200m – $132.70m = $67.30m Value of combined equity dropped by = $132.70 – ($66.07m + $73.80m) =

$7.17m

Value of combined debt rose by = $67.30m – ($33.93m + $26.20m) = +$7.17m The merger has benefited the bondholders to the expense of the shareholders.

10. Option strategies a. The investor can buy a call option on the same stock. As the price of the stock rises, so will the price of the call. She may sell the call option before the expiry to settle the gain For use with Finance for Executives: Managing for Value Creation 7th edition

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as the difference between the selling and buying price. Additionally, she can borrow on margin and buy the stock at the expiry, sell the stock, and pay back the loan. b. Since the investor has already bought a call option to gain from the rise in price, she can purchase a put option to guard against the fall in the price. The call and put should ideally be for the same strike price, and expiration on the same stock. The price of this strategy is the total cost of the options. This strategy is called long straddles.

c. She can sell a call option at a higher strike price and use the funds to buy a put at a strike near the current price of the stock. This is called a collar. The drawback is that the gain is limited to the strike of the call sold.

11. Options and the valuation of a start-up firm a. PFC should not open a restaurant now because this project‘s NPV is negative: NPV (one restaurant now) =

$1.2m + $1.0m = $200,000

b. The value (C) of the call option that justify the $2.3m must satisfy the following equation: Adjusted Present Value = $2,300,000 = C = $2.5m = *

(

$200,000 + C, from which we get

)

+ where n is

the number of restaurant that should be opened in one year. For n equal to 11, the call is worth $2,673,779 which is the number of stores for which C is the closest to at least $2.5m.

12. Option and joint ventures a. PAFE [PV = €245m; X = €230m; T = 1; RF = 4%;

= 25%] = €13m

b. Yes ( €5m + €13m = €8m)

Chapter 17 For use with Finance for Executives: Managing for Value Creation 7th edition

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Answers to Review Problems Finance for Executives – 7th Edition

1. Currency pairs The pairs in the first vertical row can be calculated as reciprocals of the pairs in the first horizontal row.

Thereafter, any pair can be calculated as the multiple of the first horizontal and the first vertical.

USD

EUR 1.2070

USD

GBP

Yen

CHF

1.3884

0.0092

1.0925

1.1503

0.0076

0.9051

0.0066

0.7869

EUR

0.8285

GBP

0.7203

0.8693

Yen

108.6957

131.1957

150.9130

CHF

0.9153

1.1048

1.2708

118.7500 0.0084

2. Exposure This problem illustrates one of the dilemmas facing multinational companies. It is basically about changes in the valuation of a foreign subsidiary‘s assets and liabilities, how to report them in the consolidated accounts of the group, and ultimately whether they can have an impact on share prices. With the all current method (FASB52), presented in Appendix 17.1, all assets and liabilities of the subsidiary are translated at the rate prevailing on the date of the balance sheet.

This means, other things equal, that if the subsidiary‘s currency depreciates, the value of its equity will fall, thus producing a loss. Under FASB52, such a loss would be taken directly to an For use with Finance for Executives: Managing for Value Creation 7th edition

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equity account in the consolidated accounts. At the same time, the dollar value of the earnings in the subsidiary will probably be lower than they would have been without a change in the currency. This will happen whether or not any income has been repatriated. The share price may be affected in the short term—hence the concern of management, especially in the U.S., about hedging potential losses such as described in the problem.

Is hedging a potential loss with a forward contract a wise decision? The idea of the hedge is to make a gain on the forward contract that would offset all or part of the loss in value. If the peso did fall 20% to peso 60 per USD, the value of the subsidiary‘s equity would fall to $41.67 million (peso 2,500 million divided by peso/USD 60) producing a USD 8.33 million loss.

Assuming a full hedge, pesos would be sold forward at peso/USD 53, and the contract would show a gain of USD 5.5 million [peso 2,500 million divided by peso/USD 60 less peso 2,500 million divided by peso/USD 53)]. This will produce a net loss of USD 2.83 million (USD 8.33 million less USD 5.5 million). If the scenario was changed, and the peso strengthened to, say, peso/USD 45, the net loss would still be the same—the subsidiary‘s equity would gain, but the forward contract would produce a loss. The basic problem is that an unrealized ―paper‖ gain or loss of equity is being offset by a realized cash-flow loss or gain from the forward contract. By hedging this balance sheet position, the company would be locking in the same pretax loss. The firm‘s management needs to ask itself this question.

Another point to consider is the overall economic impact of a depreciation in the subsidiary‘s currency. If most or all of the subsidiary output is exported, the cheaper peso should mean more sales and, consequently, higher profits. So if in the immediate future, a depreciation of the peso would lead to a drop in reported USD income, earnings should rise subsequently. The overall impact on share prices may not be negative if the stock market anticipates that the increase in earnings more than compensates the drop in the USD value of the peso.

3. Hedging imports a. The company faces the risk of USD appreciating against the euro. This will lead to less dollars being remitted for the specified amount of euros.

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b. GTC should enter a contract to buy USD from euros in three months‘ time. This could be done by entering a forward contract with another party at the given rate (USD 1.2043/Euro) to sell $120 million euros. c. Since the dollars per euro receivable are lesser now, there is a gain on the original position as the original position will yield more dollars. GTC should enter into another contract to sell USD for euros at the current rate (1.2027) to solidify the gain. The difference in the two contracts will be the gain for the company.

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4. Hedging imports with forwards, futures, and options MPC can either do nothing or hedge its position using one of the following hedging techniques: (1) forward contracts, (2) futures contracts, or (3) options. Each of these cases is examined below.

1. Hedging with forward contracts Buy JPY 250 million at the forward rate of JPY/USD 106.42 for delivery on September 8 (90 days later). On September 8, the cost of the computer equipment will be:

JPY 250,000,000 = USD 2,349,182 JPY/USD 106 .42 2. Hedging with currency futures contracts Buy 20 September yen futures on June 10 at USD 0.0095 per yen; sell 20 September yen futures on September 8. The price at which MPC would sell the futures on September 8 is not known on June 10 since their expiration date is on September 17. Furthermore, MPC would have to buy 250 million yen in the spot market on September 8 in order to pay its supplier. As a result, the net dollar cost of the computer equipment would not be known on June 10.

For illustration purposes, let us assume that on September 8 the spot rate is JPY/USD 0.0095 and the September yen futures rate is USD 0.0097. The profit on the futures transaction is the sale of 20 futures on September 8 less the purchase of 20 futures on June 10: JPY12,500,000 × 20 × [USD/JPY 0.0097 – USD/JPY 0.0095] = USD 50,000 The cost of buying JPY250 million at the spot rate on September 8 is: JPY 250,000,000 × USD/JPY 0.0095 = USD 2,375,000 The net cost of the computer equipment is: USD 2,375,000 – USD 50,000 = USD 2,325,000

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3. Hedging with options Buy JPY250 million OTC call options on June 10 with a strike price of USD 0.00021 per yen. The cost of the option is: JPY 250,000,000 × USD/JPY 0.00021 = USD 52,500 Case 1: On September 8, the spot exchange rate is higher than the strike price of JPY/USD 108. MPC will exercise its right to buy yen at the spot rate and pay:

JPY 250,000,000 = USD 2,314,815 JPY/USD 108 The net cost of the computer equipment would be: USD 2,314,815 + USD 52,500 = USD 2,367,315 Case 2: On September 8, the spot exchange rate is lower than the strike price of JPY/USD 108. MPC would not exercise its option. The dollar cost of the equipment, although not known on June 10, would be lower than USD 2,367,315.

What should MPC do? Unless (1) MPC has another yen exposure that is the opposite of the one created by the purchase of the computer equipment, or (2) the size of the exposure (JPY250 million) is not significant when compared to MPC cash revenues, we would not recommend that it leave its position open (not hedging). Unless MPC creditworthiness is so low that it cannot find another party (bank) to be the counterparty in a forward transaction, we would recommend the forward hedge over the futures hedge. Unless MPC believes strongly that the yen will depreciate between June 10 and September 8, we would recommend the forward hedge over the option hedge.

5. Currency risk management The problem here is that there are two sources of uncertainty: the exposure, which is dependent on a successful bid, and the future exchange rate. The company needs to find the appropriate instrument for hedging a contingent risk.

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In the past, the firm is successful, on average, in 67% of the bids that they submit. This means that if they use forward contracts—either 30-day or 90-day maturities—to hedge these exposures, one-third of the time they would end up with an open forward contract that could produce either a gain or loss depending on the spot rate at which they would close it out. In essence, they would have a €2,500,000 open position one-third of the time. The hedge would be to sell forward the amount of the exposure. If the bid were not successful, they would have to buy euros on the spot market to close out the forward contract. To illustrate the risk, if the euro were to appreciate by 5%, they would have to buy spot euros at around USD/EUR 0.93. This would produce a loss on the forward contract of USD 111,250 [€2,500,000  (USD/EUR 0.8855 – USD/EUR 0.9300)]. Of course, if the euro were to continue to weaken against the U.S. dollar, the open forward contracts would produce gains. On the other hand, for those bids that were accepted, the net gain or loss from the hedge would be negligible at the current spot and forward rates since the forward discount is minimal.

If Charles were to use an option hedge, he would buy 30-day put options that would expire to coincide with the announcement of the bid’s success. At current option prices, these would cost USD 23,750 per hedge in premiums (€2.5 million  USD 0.0095 per euro). One third of the time, the option would not be needed—when the bid was not successful. In these cases, the most that could be lost would be the amount of the premium, which, at USD 23,750, is considerably less than the potential loss from the open forward position. If they were to systematically fully hedge each bid with a put option, this would mean a monthly cost of around USD 25,000 for the hedging program. Successful bids would then be hedged with forward contracts designed to mature when the invoices were paid.

A more satisfactory hedge could be a compound option (an option to buy an option) but this alternative was not given in the problem. In any event, the option hedges would result in a less volatile earnings stream.

6. Parity relations a.

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Purchasing power parity says that changes in the exchange rate between two countries‘ currencies are determined by the difference in the expected inflation rates between the two countries.

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b.

According to the international Fisher effect, the difference in interest rates between two countries is equal to the difference in the expected inflation rates between the two countries. c.

Interest rate parity says that changes in the exchange rate between two countries‘ currencies are determined by the difference in interest rates between the two countries. d.

Forward rates are good predictors of future spot rates.

7. Interest-rate parity relation a.

The return on one USD deposit is:

USD 1.00 × (1 + 0.03) = USD 1.03

b.

The return in USD on a dollar-covered euro lending is:

 1  USD 1.00 ×   (1  0.0315 )  1.248  = USD 1.03 1.25  For use with Finance for Executives: Managing for Value Creation 7th edition

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c.

If you borrow USD 1.00, you will have to repay US D1.03 in one-year time. The return you will get from using this USD 1.00 to buy spot euros, placing them at the euro interest rate, and selling the return forward would be USD 1.03. The two amounts are equal, so it would not be worthwhile to engage in arbitrage trading. Interest parity holds.

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8. The purchasing power parity relation a.

A

B

1 Initial capital

USD10,000,000

2 Spot rate $/£

1.60

3 Spot rate £/$

0.625

4 6-month forward rate

1.65

5 Annual interest rate in the U.S.

3%

6 Annual interest rate in the United Kingdom (U.K.)

1%

7 Initial capital in British Pound

£6,250,000

8 Investment value in the next 6 months

investment in the U.S.

USD10,150,000

9 Investment value in the next 6 months

investment in the U.K.

USD10,364,063

Cells B1 to B6 are data.

Formula in cell B7 is =B1*B3.

Formula in cell B8 is =B1*(1+B5*6/12).

Formula in cell B9 is =B7*(1+B6*6/12)*B4.

The finance manager should invest the money in the United Kingdom.

b.

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From equation 17.1

(

)

( )

The expected spot rate in one year = 1.70*(1+4%)/(1+2%) = $1.98/£.

The forward rate can be derived from the expected spot rate as shown by equation 17.10

(

)

Therefore, the one-year forward rate is expected to be $1.98/£.

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9. Arbitrage activity a.

The arbitrage would be as follows:

Now:

1. Buy USD 2,247,797 (¥250 million at the spot rate of ¥/USD 111.22).

2. Invest these dollars in a 90-day dollar time deposit at 3.125% p.a. The interest to be received from this investment will be USD 17,561 (USD 2,247,797.03125/4).

3. Sell USD 2,265,358 (USD 2,247,797 of principal plus the USD 17,561 of interest) forward at the 90-day forward rate.

At the end of 90 days, unwind the arbitrage and receive ¥251,771,888 from the forward contract (USD 2,265,358  ¥/USD 111.14).

Since the risk from a fall in the value of the dollar has been eliminated by the forward contract, we can calculate the arbitrage profit against the riskless alternative investment of the yen time deposit. That would have yielded ¥251,347,500 principal and interest at the end of 90 days [¥250 million  (1 + 0.02156/4)]. The arbitrage profit would be ¥424,388 (¥251,771,888 less ¥251,347,500).

b.

The forward rate can be derived from the interest rate parity relation (IRP). In Appendix 16.2, we show that this relationship implies the following: For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

Fh0/ f 1  rh  S0h / f 1  rf or

Fh0/ f  S0h / f

1  rh 1  rf

where:

Fh0/ f

= the 90-day forward exchange rate (¥/USD 111.14)

S0h / f

= the spot exchange rate (¥/USD 111.22)

rh

= the 90-day dollar interest rate (3.125%)

rf

= the 90-day yen interest rate (2.156%)

If the dollar interest rate were to suddenly increase by 25 bp (and assuming no change to the spot rate or the yen interest rate), the forward rate should immediately rise to ¥110.88:

0.02156 4 ¥/USD 111.22  = ¥/USD 110.88 0.03125  0.0025 1 4 1

Whether this would be a good forecast of the future spot yen exchange rate in 90 days is a good question. Empirical evidence seems to show that the forward rate is an unbiased predictor of the future spot rate, that is, over a period of time, the error will be approximately zero.

Conclusion: The new forward may or may not predict the future spot. A higher dollar interest For use with Finance for Executives: Managing for Value Creation 7th edition

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rate, according to the international Fisher effect, should strengthen the dollar rather than weaken it. There are other forces affecting exchange rates such as capital flows that often can have much more impact on rates than changes in the interest rate.

10. International capital budgeting (1) The net present value calculation follows exactly the same approach as the one used for Chapter 17‘s Zap Scan project in Switzerland (Exhibit 17.3). The cost of capital is 12 % (5% US government rate plus 7% risk premium).

See spreadsheet next page

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A

B

1

C

Now

2 3

Expected cash flows in millions of euros (EUR)

4

Cash flow

5

Cash flow from liquidation

D

E

F

G

Forecast at the end of the year

0

1

2

3

4

5

€125

€30

€30

€30

€30

€30 €30

6

Total cash flow

€125

€30

€30

€30

€30

€60

7

Expected USD/EUR spot rate using PPP (equation 17.1)

8

Euro-zone expected inflation rate

3.0%

3.0%

3.0%

3.0%

3.0%

9

United States expected inflation rate

4.0%

4.0%

4.0%

4.0%

4.0%

10

Current spot rate EUR/USD

0.8000

11

Current spot rate USD/EUR

1.2500

12

Expected future spot rate USD/EUR

1.2500

1.2621

1.2744

1.2868

1.2993

1.3119

13

Expected cash flows with inflation in millions of euros (EUR)

€125

€30.9

€30.9

€30.9

€30.9

€61.8

14

Expected cash flows in millions of U.S. dollars (USD)

$156.3

$39.0

$39.4

$39.8

$40.1

$81.1

15

Cost of capital

12.0%

16

Net present value

$9.782 million

Rows 4, 5, 8, 9, and in cells B10 and B15 are data.

The formula in cell B6 is: =B4+B5. Then copy formula in cell B6 to next cells in row 6.

The formula in cell B11 is: =1/B10.

The formula in cell C12 is: =B12*(1+C11)/(1+C10). Then copy formula in cell C12 to next cells in row 12.

The formula in cell B13 is =B6. The formula in cell C13 is =C6*(1+C8). Then copy formula in cell C13 to next cells in row 13.

The formula in cell B14 is = B13*B12. Then copy formula in cell B14 to next cells in row 14.

The formula in cell B16 is =B14+NPV(B15;C14:G14).

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11. International capital budgeting (2)

a.

The minimum price that the owners of Chateau Cheval Noir should ask for the vineyard is the present value of the cash flows expected from the assets of the vineyard. This is the sum of the present value of the cash flows expected from the vineyard at the end of each of the next five years plus the present value of the terminal value at the end of the five-year period.

The free cash flows from the firm‘s assets (FCF) can be estimated as follows (see equation 14.3 in Chapter 14): FCF = EBIT(1 – Tc) + Depreciation expenses – WCR – Net capital expenditures where EBIT is earnings before interest and tax, TC is the corporate tax rate, and WCR is the change in working capital requirement. Since annual capital expenditures are expected to be equal to the annual depreciation expenses, the equation reduces to: FCF = EBIT(1 – TC) – WCR The following spreadsheet shows how the net present value of the project is estimated.

A

B

1

C

Now 0

2

D

E

F

G

H

Forecast at the end of the year 1

2

3

4

5

6

3

Expected inflation rate in Australia

5.0%

5.0%

5.0%

5.0%

5.0%

5.0%

4

Australian corporate tax rate

30.0%

30.0%

30.0%

30.0%

30.0%

30.0%

5

Working capital requirement (WCR) as percent of sales

10.0%

10.0%

10.0%

10.0%

10.0%

10.0%

10.0%

6

Sales

$16.0

$16.8

$17.6

$18.5

$19.4

$20.4

$21.4

7

Earnings before interest and tax (EBIT)

14.0

14.7

15.4

16.2

17.0

17.9

18.8

For use with Finance for Executives: Managing for Value Creation 7th edition

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8

Tax rate

9

EBIT × (1 – Tax rate of 30%)

10

WCR/Sales

11

WCR at year-end

12

Change in WCR

13

Expected cash flow from vineyard in AUD

14

Residual value Year-end 5 in AUD

15

Cost of capital in Australian dollars

12.0%

16

Vineyard value in Australian dollars

$146 million

17

Expected inflation rate in Euro-zone

18

Current spot rate AUD/EUR

1.750

19

Current spot rate EUR/AUD

0.571

20

30%

30%

30%

30%

30%

30%

30%

10.3

10.8

11.3

11.9

12.5

13.1

10%

10%

10%

10%

10%

10%

10%

1.6

1.7

1.8

1.9

1.9

2.0

2.1

0.1

0.1

0.1

0.1

0.1

0.1

$10.2

$10.7

$11.3

$11.8

$12.4

$13.0

$186.2

Expected future spot rate EUR/AUD

0.571

2.0%

2.0%

2.0%

2.0%

2.0%

2.0%

0.555

0.539

0.524

0.509

0.494

0.480

€5.7

€5.8

€5.9

€6.0

€6.1

€6.3

21

Expected cash flows in millions of euros

22

Residual value Year-end 5 in euros

23

Cost of capital in euros

10.0%

24

Vineyard value in euros

€70.8 million

€78.2

• Rows 3, 4, 5, 8, 10, plus cells B15, B18 and B23 are data.

• The formula in cell C6 is =B6*(1+C3). Then copy formula in cell C6 to next cells in row 6.

• The formula in cell C7 is =B7*(1+C3). Then copy formula in cell C6 to next cells in row 7.

• The formula in cell C9 is =C7*(1 C8). Then copy formula in cell C9 to next cells in row 9.

For use with Finance for Executives: Managing for Value Creation 7th edition

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• The formula in cell B11 is =B10*B6. Then copy formula in cell B11 to next cells in row 11.

• The formula in cell C9 is = (C8 B8). Then copy formula in cell C9 to next cells in row 9.

• The formula in cell C12 is =C11 B11. Then copy formula in cell C12 to next cells in row 12.

• The formula in cell C13 is =C9 C12. Then copy formula in cell C13 to next cells in row 13.

• The formula in cell G14 is =H13/(B15 H3).

• The formula in cell B16 is =NPV(B15,C13:G13)+G14/(1+B15)^5.

• The formula in cell C20 is =B20*(1+C17)/(1+C3). Then copy formula in cell 20 to next cells in row 20.

• The formula in cell C21 is =C13*C20. Then copy cell C21 to next cells in row 21.

• The formula in cell G22 is =H21/(B23 H17).

• The formula in cell B24is =NPV(B23,C21:G21)+G2(1+B23)^5.

b.

Why the higher discount rate for Australian dollar cash flows? One argument could be that this represents the only diversification of the investors and that any favorable portfolio effects this might bring them would be offset by the possibility of unforeseen costs incurred overseeing the management of a winery on the other side of the globe. Other arguments could be that PPP does not hold and the Australian dollar depreciates faster than has been estimated in the analysis, or that the inflation rate differential widens. Finally, in Australia discount rates have been traditionally higher than in the Euro-zone because of the relative scarcity of capital.

12. International capital budgeting (3)

a.

Project in China

A

B

C

D

E

F

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G

1

Now

Forecast at the end of the year

0

1

2

3

4

5

¥14.00

¥3.00

¥3.00

¥5.00

¥6.00

¥6.00

4 Inflation rate in China

4%

4%

4%

4%

4%

5 Inflation rate in the U.S.

4%

4%

4%

4%

4%

2 Cash flows from China plant

3 (millions of Yuan)

6 Spot rate CNY/USD

6.82

7 Spot rate USD/CNY

0.147

8 Expected spot rate USD/CNY

0.147

0.147

0.147

0.147

0.147

0.147

9 (millions of USD)

$2.05

$0.44

$0.44

$0.73

$0.88

$0.88

10 Cost of capital

10%

11 NPV (millions of USD)

$0.41

Cash flows from China plant

• Rows 2, 4, 5 6 and cell B10 are data.

• The formula in cell B7 is = 1/B6.

• The formula in cell C8 is =B8*(1+C5)/(1+C4). Then copy cell C7 to next cells in row 7.

• The formula in cell B9 is =B3*B8. Then copy cell B9 to next cells in row 9.

• The formula in cell B11 is =B9+NPV(B10;C9:G89).

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Project in Indonesia

A

B

1

C

D

E

F

G

Forecast at the end of the year

Now 0

1

2

3

4

5

Rp20,00 0

Rp5,000

Rp5,000

Rp6,000

Rp7,000

Rp7,000

4 Inflation rate in Indonesia

6%

6%

6%

6%

6%

5 Inflation rate in the U.S.

4%

4%

4%

4%

4%

2 Cash flows from Indonesia

3 plant (millions of Rupiah)

6 Spot rate IDR/USD

9,699.78

7 Spot rate USD/IDR

0.0001031

Expected spot rate 8 USD/IDR

0.0001031 0.0001011 0.0000992 0.0000974 0.0000955 0.0000937

Cash flows from Indonesia

9 plant (millions of USD)

$2.06

10 Cost of capital

10%

11 NPV (millions of USD)

$0.11

$0.51

$0.50

$0.58

$0.67

• Rows 3, 4, 5 plus cells B6 and B10 are data.

• The formula in cell B7 is = 1/B6.

• The formula in cell C8 is =B8*(1+C5)/(1+C4). Then copy cell C8 to next cells in row 8.

• The formula in cell B9 is =B3*B8. Then copy cell B9 to next cells in row 9.

• The formula in cell B11 is =B9+NPV(B10,C9:G9).

The US company would choose the project in China because its NPV is higher.

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$0.66

b.

If the NPV of two projects are positive and equal, the US company could consider the project which provides more diversification to its investment portfolio and the country with more political stability.

Chapter 18 Answers to Review Problems Finance for Executives – 7th Edition

1. Understanding market value added and economic value added a.

The firm with the highest market value added, which is not necessarily the one with the highest market value, is the one that has created the most value for its shareholders. b.

Positive MVA means that the present value of the future stream of EVAs is positive. This does not necessarily imply that current ROIC exceeds the firm‘s WACC. c.

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Growth will increase a firm‘s MVA only if expected ROICs exceed the firm‘s WACC. If this is not the case, growth will destroy value. d.

Not necessarily so. Positive MVA means that the present value of the future stream of EVAs is positive, not necessarily this year. e.

Higher ROIC is only half the story. ROIC must exceed the WACC in order to create value. A business will still create value if its ROIC falls, as long as ROIC remains above the WACC.

2. Value drivers The following tree shows the value drivers and their relationship to value creation measured by EVA. Drivers related to the management of operations 1.

2.

3.

4.

Self-sustainable growth Sales growth Operating margin Amount of working capital requirement

Strategic value drivers 1.

2.

3.

4.

Ability to raise equity Tax management Amount of cash and fixed assets Financial structure

For use with Finance for Executives: Managing for Value Creation 7th edition

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SELF-SUSTAINABLE GROWTH ABILITY TO RAISE EQUITY SALES GROWTH OPERATING MARGIN

EFFECTIVE TAX

AFTER-TAX OPERATING MARGIN

minus CASH

EVA

WORKING CAPITAL NET FIXED ASSETS INVESTED CAPITAL AFTER-TAX COST OF DEBT PROPORTION OF DEBT

CHARGE FOR CAPITAL EMPLOYED

WEIGHTED AVERAGE COST OF CAPITAL

COST OF EQUITY PROPORTION OF EQUITY

For use with Finance for Executives: Managing for Value Creation 7th edition

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3. Adjusting accounting data to estimate a firm’s economic value added a.

Invested capital December 31, Year 1

$ millions Cash Accounts receivable Inventories Prepaid expenses Accounts payable Accrued expenses

December 31, Year 0

$239 500 416 58 264 437 Working capital requirement1 Net fixed assets Total invested capital

$ 37 668 547 159 346 681

$ 273 827 $1,339

$ 347 1,279 $1,663

Working capital requirement = Accounts receivable + Inventories + Prepaid expenses – Accounts payable – Accrued expenses 1

Net operating profit after tax (NOPAT) in Year 0

$ millions

Year 0

Earnings before interest and tax (EBIT)

$244 35%1

Tax rate Net operating profit after tax (NOPAT)

1

[$244  (1 – 0.35)] $159

Tax expenses are equal to 35% of the earnings before tax ($64 = 0.35  $182).

For use with Finance for Executives: Managing for Value Creation 7th edition

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b.

Invested Capital December 31, Year 1

December 31, Year 0

$159

$1,339

$1,663

Restructuring charges, Year 0

28

–

28

Goodwill amortization

14

98

93

Accumulated bad debt allowance

–

26

30

Non-operating loss, Year 1

–

35

35

$201

$1,498

$1,849

$ millions

NOPAT

Unadjusted

Adjusted

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c.

EVA = NOPAT – [WACC  Average adjusted invested capital]

= $201 million – 0.10  [($1.498 million + $1.849 million)/2] = $33.65 million

4. Economic value added analysis a.

Pretax economic value added (EVA) based on initial invested capital: EVA = Pretax operating profit – (Pretax cost of capital × Invested capital) = $170 million – (15% × $1,000 million) = $170 million – $150 million = $20 million

Pretax economic value added (EVA) based on expected return on invested capital (ROIC): Pretax ROIC = $170 million/$1,000 million = 17% EVA = (Pretax ROIC – Pretax cost of capital) × Invested capital = (17% – 15%) × $1,000 million = 2% × $1,000 million = $20 million b.

1. Reducing operating expenses by $10 million would raise EVA by $10 million: EVA = [$170 million + $10 million] – $150 million = $30 million 2. Reducing invested capital by $60 million would raise EVA by $9 million: EVA = $170 million – 15% × ($1,000 million – $60 million) For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

= $170 million – $141 million = $29 million 3. Lowering pretax cost of capital to 14% would raise EVA by $10 million: a. EVA = $170 million – 14% × $1,000 million = $170 million – $140 million = $30 million

For use with Finance for Executives: Managing for Value Creation 7th edition

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4. Selling assets (at book value) for $100 million will reduce capital employed to $900 million and cut pretax operating profit by $10 million, thus raising EVA by $5 million (note that these assets have an expected ROIC of 10% which is lower than the WACC of 15%): EVA = $160 million – (15% × $900 million) = $160 million – $135 million = $25 million

5. Buying assets for $100 million will raise capital employed to $1,100 million and add $20 million in pretax operating profit, thus raising EVA by $5 million (note that these assets have an expected ROIC of 20% which is higher than the WACC of 15%): EVA = $190 million – (15% × $1,100) = $190 million – $165 million = $25 million

5. The relationship between a firm’s market value, its market value and its economic value added

added,

a.

EQUATION 18.1 DEFINES MARKET VALUE ADDED (MVA) AS THE DIFFERENCE BETWEEN THE MARKET VALUE OF CAPITAL AND THE AMOUNT OF CAPITAL EMPLOYED, WHICH IS ALSO EQUAL TO THE AMOUNT OF INVESTED CAPITAL. THUS: MVA = MARKET VALUE OF CAPITAL – INVESTED CAPITAL SINCE MVA IS ALSO EQUAL TO THE PRESENT VALUE OF THE FIRM’S EXPECTED FUTURE ECONOMIC VALUE ADDED (EVA), WE CAN WRITE: MVA = Market value of capital – Invested capital = PV of expected future EVAs

or For use with Finance for Executives: Managing for Value Creation 7th edition

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Market value of capital = PV of expected future EVAs + Invested capital

b.

We show in the chapter that the present value of a project‘s expected future EVAs is equal to (1) the change in the firm‘s MVA if the project is undertaken and (2) the net present value of a project. In Chapter 6, we showed that the net present value of a project is equal to the change in the market value of the firm‘s equity after the project is announced. Thus, to get the change in the firm‘s MVA and market value following the adoption of the project, we just have to compute the present value of the expected future EVAs of the project.

From equation 18.6 and the data given in the question, we can write: Project EVA = (Return on invested capital – WACC)  Invested capital = (0.014

0.08)  $50 million = 0.06  $50 million = $3 million

Discounting these $3 million for 4 years at a cost of capital of 8%, we get: PV of future expected EVAs 

$3 million $3 million $3 million $3 million    1  .08 (1  .08) 2 (1  .08) 3 (1  .08) 4

= $9.94 million Following the announcement of the project, we should expect that the market value of Value Inc. and its market value added to increase by $9.94 million.

6. Calculating EVA and MVA a.

For use with Finance for Executives: Managing for Value Creation 7th edition

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(

NOPAT = EBIT (1

Tax rate) = $10 million

Invested capital = $20 million million

(

)

)

(1

35%) = $6.5 million.

$30 million (equity addition)

$35 million (debt) = $85

= $2.250 million

b.

To calculate the MVA we need to discount the EVA for all the years.

For use with Finance for Executives: Managing for Value Creation 7th edition

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EVA Beginning

Growth Rate

1

$2.25

0.1

$2.48 0.952381

$2.36

2

$2.48

0.1

$2.72 0.907029

$2.47

3

$2.72

0.1

$2.99 0.863838

$2.59

4

$2.99

0.05

$3.11 0.822702

$2.56

$310.96 0.822702

$255.83

Year

4 (Terminal value)

EVA Ending

DF@5%

Present Value

Terminal value $310.96 MVA

$265.81

7. The effect of the management of the operating cycle on the firm’s economic value added

Working capital requirement (WCR) =

[Accounts receivable + Inventories + Prepaid expenses] – [Accounts payable + Accrued expenses]

a.

December 31, Year 1:

WCR = $2,730 + $2,800 + $0 – $1,400 – $200 = $3,930 For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

December 31, Year 2

WCR = $3,100 + $3,200 + $0 – $1,600 – $260 = $4,440

December 31, Year 3

WCR = $4,200 + $4,300 + $0 – $2,050 – $350 = $6,100

For use with Finance for Executives: Managing for Value Creation 7th edition

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b.

Managerial balance sheets

$ thousands

December 31, Year 1

December 31, Year 2

December 31, Year 3

$ 600 3,930 1,200 $5,730

$ 350 4,440 1,300 $6,090

$ 300 6,100 1,450 $7,850

$ 300 5,430

$ 500 5,590

$1,900 5,950

Invested capitalInvested Capital Cash Working capital requirement (WCR) Net fixed assets Total invested capital Capital employed Short-term debt Long-term financing Long-term debt Owners‘ equity Total capital employed

$1,300 4,130

$1,200 4,390 $5,730

$1,100 4,850 $6,090

$7,850

c.

Sentec would have created value in a given year, if during that year, its economic value added (EVA) was positive and destroyed value if its EVA was negative.

$ thousands

Year 1

Year 2

Year 3

1. Earnings before interest and tax (EBIT)

$650

$900

$1,350

2. Tax rate1

40.7%

40.3%

39.4%

3. Net operating profit after tax (NOPAT) [line 1  (1 – line 2)]

$385

$537

$818

For use with Finance for Executives: Managing for Value Creation 7th edition

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11%

11%

11%

$5,730

$6,090

$7,850

6. Charge for capital (line 4  line 5)

$630

$670

$864

7. EVA (line 3 – line 6)

–$245

–$133

–$46

4. Weighted average cost of capital 5. Invested capital

1

Income tax exp enses Earnings before tax

d.

Sentec has destroyed value in each of the three years. Value was destroyed because either/and the operating margin was too low, or the firm was using too much capital to generate its current level of operating margin (given the cost of capital of 11%).

THE NEXT QUESTION IS INTENDED TO IDENTIFY WHICH OF THE TWO CAUSED VALUE DESTRUCTION. e.

IN YEAR 3, SENTEC’S OPERATING MARGIN WAS EQUAL TO 4.3% ($1,350/$31,600), COMPARED TO 3.3 % FOR THE INDUSTRY AS A WHOLE. IF SENTEC DESTROYED VALUE IN YEAR 3, IT WAS CERTAINLY NOT DUE TO AN INSUFFICIENT OPERATING MARGIN SINCE IT WAS 30% HIGHER THAN THE INDUSTRY AVERAGE. THEREFORE, VALUE DESTRUCTION DURING THAT YEAR MUST HAVE COME FROM A HIGH CHARGE FOR CAPITAL, EITHER FROM A HIGH COST OF CAPITAL OR FROM TOO MUCH CAPITAL INVESTED IN THE BUSINESS, PARTICULARLY IN ITS OPERATING CYCLE. ON THE BASIS OF THE AVERAGE INDUSTRY PERFORMANCE REGARDING WORKING CAPITAL REQUIREMENT, WE CAN CONSTRUCT A PRO FORMA MANAGERIAL BALANCE SHEET AND ESTIMATE HOW MUCH LESS CAPITAL SENTEC COULD HAVE USED, AND CONSEQUENTLY, HOW MUCH LESS (MORE) VALUE WOULD HAVE BEEN DESTROYED (CREATED).

Pro forma working capital requirement (WCR) 12/31/Year 3

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Accounts receivable12/31/Year 3 =

Net sales Year 3  30 days 365



$31,600  30 days  $2,597 365



$25,100  $3,138 8

Accounts payable12/31/Year 3 =

Purchases Year 3 Cost of goods sold Year 3  Change in inventorie s Year 3  33 days   33 days 365 365

=

$25,100  ($3,138  $3,200)  33 days  $2,264 365

Working capital requirement = Accounts receivable + Inventories + Prepaid expenses – Accounts payable – Accrued expenses

= $2,597+ $3,138 +$0 – $2,264 – $350 = $3,121

Pro forma net fixed assets Same as before= $1,450 Pro forma long-term financing = pro forma owners’ equity + pro forma long-term debt Same as before =$5,950 For use with Finance for Executives: Managing for Value Creation 7th edition

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Pro forma short-term debt Note that the amount of long-term financing ($5,950) would have been higher than the investment in fixed assets and in the operating cycle ($1,450 + $3,121= $4,571). Sentec Inc. would not have needed any short-term debt, and have $1,379 million ($5,950 – $4,571) in cash.

Pro forma managerial balance sheet December 31, Year 3

$ thousands Invested capitalInvested Capital Cash Working capital requirement (WCR) Net fixed assets Total invested capital Capital employed Short-term debt Long-term financing Long-term debt Owners‘ equity Total capital employed

$1,379 3,121 1,450 $5,950

$

0 5,950

$1,100 4,850 $5,950

If Sentec had managed its operating cycle like the average firm in the industry in Year 3, its invested capital would have been equal to $5.950 million instead of $7.850 million. As a result, its economic value added would have been positive and equal to $164 million, as shown in the following table: Pro forma Year 3

$ thousands

1. Earnings before interest and tax (EBIT)

$1,350

2. Tax rate1

39.4%

3. Net operating profit after tax (NOPAT) [line 1  (1 – line 2)]

$818

4. Weighted average cost of capital

11%

For use with Finance for Executives: Managing for Value Creation 7th edition

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$5,950

5. Invested capital 6. Charge for capital (line 4  line 5)

$654

7. EVA (line 3 – line 6)

$164

1

Income tax exp enses Earnings before tax

Note that a better management of the operating cycle in Year 3 would have created $164,000 of value instead of destroying $46,000 of it, changing Sentec from a value destroying company into a value creating one.

8. Return on invested capital versus economic value added-based bonus systems a.

Currently, Fiona‘s division generates a 100% return on invested capital ($1,000,000 of NOPAT divided by $1,000,000 of invested capital). If the new project is launched, the division return on invested capital would drop to 75% ($1,500,000 of NOPAT divided by $2,000,000 of invested capital). Clearly, Fiona would not be enthusiastic about this new project. b.

Currently, Fiona‘s division generates an annual economic value added of $800,000 ($1,000,000 of NOPAT minus a charge for capital equal to 20% of $1,000,000 or $200,000). If the new project is adopted, the division‘s EVA would grow to $1,100,000 ($1,500,000 of NOPAT minus a charge for capital equal to 20% of $2,000,000 or $400,000). Clearly, Fiona would jump at the chance to have the project in her division. c.

The important difference between return on invested capital and economic value added is that the former is a percentage number while the second is a dollar value. Economic value added increases despite the fact that return on invested capital decreases as long as the net operating profit after tax is higher than the charge for capital. Since this is a necessary condition to create For use with Finance for Executives: Managing for Value Creation 7th edition

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value, economic value added based bonus systems are preferable to those based on return on invested capital.

9. Economic value added-based bonus system a.

Formula (1):

Cumulative bonus = 0.02  ($16 million + $20 million + $24 million)

= 0.02  $60 million = $1.2 million Formula (2):

Cumulative bonus = 0.01  $60 million + 0.075  ($24 million – $16 million)

= $0.6 million + $0.6 million = $1.2 million

b.

Formula (1):

Cumulative bonus = 0.02  (–$24 million – $20 million – $16 million)

For use with Finance for Executives: Managing for Value Creation 7th edition

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= 0.02  –$60 million = $0 (since the formula gives a negative bonus)

Formula (2):

Cumulative bonus = 0.01  –$60 million + 0.075  [–$16 million – (–$24 million)]

= $0 + $0.6 million = $.6 million

c.

Astra should choose formula (2) since it provides a strong incentive to manage for value creation, while formula (1) gives none. Note, however, that formula (2) would generate higher management compensation when the improvement is the result of market or industry factors that management does not control.

10. Economic value added, market value added, and net present value a., b., and c.

See spreadsheet next page

For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

A B C D E F 1 Now Year-end 1 Year-end 2 Year-end 3 Year-end 4 2 1. Investment data 3 Initial investment -$200,000 4 After-tax receipt from sale of equipment $0 5 Working capital requirement $40,000 $40,000 $40,000 $40,000 $0 6 Cans sold 100,000 100,000 100,000 100,000 7 Sale price/can $4 $4 $4 $4 8 Rental cost $50,000 $50,000 $50,000 $50,000 9 Variable cost/can $2 $2 $2 $2 10 Depreciation expenses $50,000 $50,000 $50,000 $50,000 11 Corporate tax rate 40% 40% 40% 40% 12 Cost of capital 10% 13 2. Expected net operating profit after tax (NOPAT) 14 Sales $400,000 $400,000 $400,000 $400,000 15 Variable costs $200,000 $200,000 $200,000 $200,000 16 Expected operating profit $100,000 $100,000 $100,000 $100,000 17 Taxes on operating profit -$40,000 -$40,000 -$40,000 -$40,000 18 Net profit after tax (NOPAT) $60,000 $60,000 $60,000 $60,000 19 3. Expected cash flow from the investment and net present value (NPV) 20 Change in working capital requirement -$40,000 0 0 0 40,000 21 Expected cash flow from the investment -$240,000 $110,000 $110,000 $110,000 $150,000 22 Net present value $136,006 23 4. Economic value added (EVA) and market value added (MVA) 24 Accumulated depreciation of the equipment $50,000 $100,000 $150,000 $200,000 25 Net book value of the equipment $200,000 $150,000 $100,000 $50,000 $0 26 Invested capital $240,000 $190,000 $140,000 $90,000 $0 27 Capital charge $24,000 $19,000 $14,000 $9,000 28 EVA $36,000 $41,000 $46,000 $51,000 29 MVA $136,006 30 31 Rows 3 to 12 are data.

32 The formula in cell C14 is: =C6*C7. Then copy formula in cell C14 to cells D14, E14, and F14.

33 The formula in cell C15 is: =C9*C6. Then copy formula in cell C15 to cells D15, E15, and F15.

34 The formula in cell C16 is: =C14-C8-C15-C10. Then copy formula in cell C16 to cells D16, E16, and F16.

35 The formula in cell C17 is: =C11*C16. Then copy formula in cell C17 to cells D17, E17, and F17.

36 The formula in cell C18 is: =C16-C17. Then copy formula in cell C18 to cells D18, E18, and F18.

37 The formula in cell B20 is: =-B5. The formula in cell C20 is: =-(C5-B5). Then copy formula in cell C20 to cells D20, E20, and F20.

38 The formula in cell B21 is: =B3+B4+B20+B18+B10. Then copy formula in cell B21 to cells C21, D21, E21, and F21.

39 The formula in cell B22 is: =B21+NPV(B12,C21:F21).

40 The formula in cell C24 is: =C10. The formula in cell D24 is: C24+D10. Then copy formula in cell D24 to cells E24 and F24.

41 The formula in cell B25 is: =-$B$3-B24. Then copy formula in cell B25 to cells C25, D25, E25, and F25.

42 The formula in cell B26 is: =B25+B5. Then copy formula in cell B25 to cells C25, D25, E25, and F25.

43 The formula in cell C27 is: =$B$12*B26. Then copy formula in cell C27 to cells D27, E27, and F27.

44 The formula in cell C28 is: =C18-C27. Then copy formula in cell C28 to cells D28, E28, and F28.

45 The formula in cell B29 is: =NPV(B12,C28:F28).

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d. Note that the calculated project‘s MVA ($136,006) is equal to its calculated NPV ($136,006). This will always be the case if, in computing the project‘s NPV, the change in working capital during the first year of the project is accounted for at the beginning of the year instead of the end of the year.

11. Comparison of investment analysis based on cash flows and economic value added The project‘s cost of capital is:

Percent of project debt financed × kD (1 – TC) + Percent of project equity financed × kE

where kD = 6% is the cost of debt, TC = 30% is the corporate tax rate, and kE = 12% is the cost of equity. Thus, the project‘s cost of capital is:

0.60 × 6% × (1 – 0.30) + 0.40 × 12% = 7.32%

Project valuation:

See spreadsheet next page

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A B C D 1 Now Year-end 1 Year-end 2 2 1. Investment data 3 Initial investment -$300,000 4 After-tax receipt from sale of equipment 5 Sales $1,000,000 $2,000,000 6 Operating expenses/sales 90% 90% 7 Working capital requirement/sales next year 10% 10% 10% 8 Depreciation expenses $100,000 $100,000 9 Corporate tax rate 30% 30% 10 Cost of capital 7.32% 11 2. Expected net operating profit after tax (NOPAT) 12 Depreciation expense $100,000 $100,000 13 Operating expenses $1,000,000 $1,900,000 14 Expected operating profit $0 $100,000 15 Taxes on operating profit $0 $30,000 16 Net profit after tax (NOPAT) $0 $70,000 17 3. Expected cash flow from the investment and net present value (NPV) 18 Working capital requirement $100,000 $200,000 $180,000 19 Change in working capital requirement -$100,000 -$100,000 $20,000 20 Expected cash flow from the investment -$400,000 $0 $190,000 21 Net present value $36,795 22 Internal rate of return 11.0% 23 4. Economic value added (EVA) and market value added (MVA) 24 Accumulated depreciation of the equipment $100,000 $200,000 25 Net book value of the equipment $300,000 $200,000 $100,000 26 Invested capital $400,000 $400,000 $280,000 27 Capital charge $29,280 $29,280 28 EVA -$29,280 $40,720 29 MVA $36,795 30 31 Rows 3 to 10 are data.

32 The formula in cell C12 is: =SLN(-$B$3,E4,3). Then copy formula in cell C12 to cells D12 and E12.

33 The formula in cell C13 is: =C6*C5+C12. Then copy formula in cell C13 to cells D13 and E13.

34 The formula in cell C14 is: =C5-C13. Then copy formula in cell C14 to cells D14 and E14.

35 The formula in cell C15 is: =C9*C14. Then copy formula in cell C15 to cells D15 and E15.

36 The formula in cell C16 is: =C14-C15. Then copy formula in cell C16 to cells D16 and E16.

37 The formula in cell B18 is: = B7*C5. Then copy formula in cell B18 to cells C18, D18, and E18.

E Year-end 3

$0 $1,800,000 90% $100,000 30%

$100,000 $1,720,000 $80,000 $24,000 $56,000 $0 $180,000 $336,000

$300,000 $0 $0 $20,496 $35,504

The formula in cell B19 is: =-B18. The formula in cell C19 is: =-(C18-B18). Then copy formula in cell C19 to cells D19 and

38 E19.

39 The formula in cell B20 is: =B3+B19+B16+B12. Then copy formula in cell B20 to cells C20, D20, and E20.

40 The formula in cell B21 is: =B20+NPV(B10,C20:E20).

41 The formula in cell B22 is: =IRR(B20:E20).

42 The formula in cell C24 is: =C12. The formula in cell D24 is: =C24+D12. Then copy formula in cell D24 to cell E24.

43 The formula in cell B25 is: =-$B$3-B24. Then copy formula in cell B25 to cells C25, D25, and E25.

44 The formula in cell B26 is: =B25+B18. Then copy formula in cell B26 to cells C26, D26, and E26.

45 The formula in cell C27 is: =$B$10*B26. Then copy formula in cell C27 to cells D27 and E27.

46 The formula in cell C28 is: =C16-C27. Then copy formula in cell C28 to cells D28 and E28.

47 The formula in cell B29 is: =NPV(B10,C28:E28).

For use with Finance for Executives: Managing for Value Creation 7th edition 48

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For use with Finance for Executives: Managing for Value Creation 7th edition

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a.

The net present value of the cash flows from this project at a WACC of 7.32% is equal to $36,795. The project‘s internal rate of return is equal to 11%. Because the project‘s NPV is positive and its IRR exceeds the WACC, the project is a value-creating proposition and should be undertaken. b.

The project‘s market value added (MVA) is equal to the present value of its stream of EVAs at a WACC of 7.32%. It is equal to $36,795, the same as the project‘s NPV. Because the project‘s MVA is positive, the project is a value-creating proposition and should be undertaken even though its first-year EVA is negative. What matters is the present value of the entire future stream of expected EVAs, not the sign of a single-year EVA. c.

When estimating EVA, invested capital must be measured at the beginning of the period and the stream of EVAs must be discounted at the same cost of capital as the cash flows (that is, at the WACC).

12. Financial strategy matrix Division

Print Media

Digital Media

WACC

2.00%

5.00%

1.00%

1.00%

ROE = SGR

6.60%

5.10%

6.00%

6.00%

1.60%

6.90%

1.00%

1.00%

ROIC B

Sales growth

SGR

Magazine Entertainment

a.

The magazine division has a cash deficit and destroys value. Digital media has a cash deficit and creates value. The entertainment division has a cash surplus and creates value. The print media division has a cash surplus and destroys value.

For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA

b.

Magazine division should either restructure or be sold off to reduce value destruction. Since digital media creates value, it should be injected with new funds to further increase the value.

The entertainment division should use the cash surplus to grow even faster, buy back shares or increase dividends. The cash from print media should be distributed elsewhere and some should be used to improve profitability. The capital structure for the division should be reviewed. If everything fails, sell off the division.

For use with Finance for Executives: Managing for Value Creation 7th edition

by Gabriel Hawawini and Claude Viallet, ISBN 9781473778917 © 2022 Cengage Learning EMEA