All Minicases with Excel Solutions Principles of Corporate Finance 14th Edition by Richard Brealey,

All Minicase Cases with Excel Solutions for Principles of Corporate Finance 14th Edition by Richard Brealey, Stewart Myers, Franklin Allen and Alex Edmans

REEBY SPORTS Minicase solution, Chapter 4 Principles of Corporate Finance, 14th Edition R. A. Brealey, S. C. Myers and F. Allen What is Reeby Sports worth per share? We will value the company using George Reeby's forecasts.

The spreadsheet accompanying this solution sets out a forecast in the same general format as Table 4.5. Historical results from 2014 to 2019 are also shown.

Earnings per share (EPS) equals return on equity (ROE) times starting book value per share (BVPS). EPS is divided between dividends and retained earnings, depending on the dividend payout ratio. BVPS grows as retained earnings are reinvested.

The keys to Reeby Sports’ future value and growth are profitability (ROE) and the reinvestment of retained earnings. Retained earnings are determined by dividend payout. The spreadsheet sets ROE at 15% for the six years from 2021 to 2025. If Reeby Sports will lose its competitive edge by 2025, then it cannot continue earning more than its 10% cost of capital. Therefore ROE is reduced to 10% starting in 2026.1 The payout ratio is set at .30 from 2021 onwards. Notice that the long-term growth rate, which settles in after 2026, is ROE × ( 1 – dividend payout ratio) = .10 × (1 .30) = .07.

The spreadsheet allows you to vary ROE and the dividend payout ratio separately for 2021-2025 and for 2026-2027.2 But let’s start with the initial input values. To calculate share value, we have to estimate a horizon value at H = 2025 and add its PV to the PV of dividends from 2020 to 2025. Using the constant-growth DCF formula, 1

A more sophisticated spreadsheet could distinguish ROE on existing assets from ROE on new capital investment. For example, ROE on new investment could drop all the way to 10% in 2023, but ROE for existing assets could decline gradually.

2 You can vary these inputs, but be careful not to enter ROEs and dividend payout ratios that generate longterm growth rates close to or above the cost of capital. As the growth rate approaches the cost of capital, the DCF formula explodes. If the growth rate exceeds the cost of capital, the DCF formula says stock price is negative, which is impossible. The spreadsheet reports “Formula not applicable” in this case. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

0.71 PVH = = 23.72 .10 - .07 The PV of dividends from 2020 to 2025 is $3.43 at the start of 2020, so share value is:3 PV = 3.43 +

23.72 = $16.82 (1.1)6

The spreadsheet also calculates the PV of dividends through 2027 and the horizon value at 2027. Notice that the PV at the start of 2020 remains at $16.82. This makes sense, since the value of a firm should not depend on the investment horizon chosen to calculate PV. (If you calculate a value that does depend on the horizon, you have made a mistake.)

We have reduced ROE to the 10% cost of capital after 2025, assuming that Reeby Sports will have exhausted valuable growth opportunities by that date. With PVGO = 0, PV = EPS/r. 4 So we could discard the constant-growth DCF formula and just divide EPS in 2026 by the cost of capital:

2.37 PVH = = $23.72 .10 This PV is identical to the PV from the constant-growth DCF formula. It doesn’t matter how fast a company grows after the horizon date H if it only earns its cost of capital.

How much of Reeby Sports’ value is due to PVGO? You can check by setting ROE = .10 for 2021 and all later years. You should get PV = $13.82. Thus PVGO = 16.82 – 13.82 = $3.00 per share for investments made in 2020 onward.

George Reeby has also identified a "comparable," Molly Sports. We could use its P/E ratio of 13.1 to calculate horizon value in 2025 and PV at the start of 2020. Using the original inputs for ROE, EPS in 2026 is 2.37.5

3

This DCF calculation assumes that the first dividend will be received after one year, at the end of 2020.

Normally dividends are paid quarterly, so it would be more realistic to assume receipt at the middle of the year. This “mid-year convention” would move all cash flows 6 months closer and therefore increase PV by 1.1.5. (In finance, “mid-year convention” does not mean June in Las Vegas.)

4 See Section 4.5.

5 Notice that the P/E ratio applies to the next year’s forecasted earnings. Sometimes “trailing P/Es” are used instead. Trailing P/Es are based on earnings over the previous year. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

PVH  13.1  2.37  $31.05 PV  3.43 

31.05  $20.96 (1.10)6

We could also use Molly’s P/E ratio to calculate Reeby Sports’ PV at the start of 2020 directly from 2020 EPS: PV = 13.1  2.03 = $26.59 Both values based on Molly’s P/E are higher than our DCF calculations. Is Molly significantly more profitable than Reeby Sports, or does our spreadsheet understate Reeby Sports’ prospects?

What if Reeby Sports could continue to earn ROE = .15 for two extra years, until 2027? You can check by changing ROE for 2026-2027 from .10 to .15. (The ROE for 2028 and 2029 is hard-wired at .10.) You should get NPV of $18.04, somewhat higher than our original DCF calculations, but not enough for Reeby Sports to match Molly’s P/E. You may wish to experiment to find inputs that generate P/E = 13 for Reeby Sports at the start of 2020. Do you think these inputs are reasonable?

March 1, 2019 VEGETRON’S CFO CALLS AGAIN Minicase solution, Chapter 5 Principles of Corporate Finance, 14th Ed. R. A. Brealey, S. C. Myers and F. Allen

The high-temperature process produces $110,000 per year for 5 years. The lowtemperature process produces $85,000 per year for 7 years. Each costs $400,000. The NPVs (at 9%) and IRRs are:

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NPV

IRR

High-temperature

+$28,000

11.7%

Low-temperature

+$28,000

11%

The NPVs are identical. The high-temperature process has a slightly higher IRR because of its quicker payback.

The CFO returns 30 minutes later: CFO: What did you find out?

You: It’s a dead heat. The two projects are equally valuable. NPV is +$28,000 for each.

The high-temperature process has a slightly higher DCF rate of return, but that’s typical of quick-payback projects. It doesn’t mean that the high-temperature process generates more value for the firm and its stockholders.

CFO: And the book rates of returns are irrelevant?

You: Yes. There’s not a single year when the book rate of return matches the true, DCF rate of return. Average book returns – for example the ratio of average income to average book investment – don’t measure the true rate of return. Book rates of return don’t help at all in making good capital investment decisions.

CFO: Let’s stick with the low-temperature process. I’m not 100% confident that the high-temperature process will work.

NEW ECONOMY TRANSPORT (A) Minicase solution, Chapter 6 Principles of Corporate Finance, 14th Edition R. A. Brealey, S. C. Myers and F. Allen This is straightforward capital investment decision, with a few real-life complications. For example, some cash flows are stated in real terms, some in nominal terms. We will use a real discount rate for the real cash flows, a nominal rate for the nominal flows. The alternative is to convert all cash flows to real terms (discounting at a real rate) or all to nominal (discounting at a nominal rate).

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Assumptions The spreadsheet for this minicase uses the following assumptions (others could be equally valid): 1. NETCO must decide immediately (t = 0).

2. Marginal tax rate is 21%.

3. Forecasted revenues and operating costs are constant in real dollars.

4. Sale price for the Vital Spark and parts is $200,000. Sale will trigger tax on the difference between sale price and book value, that is .21(200,000 – 140,000) = $12,600. After-tax proceeds are $200,000 – 12,600 = $187,400.

5. Investments can be depreciated immediately, i.e. at t = 0.

6. Full operations would resume at t = 1, and cash flows are discounted from midyear, that is, t = 1.5, 2.5, … .

7. The nominal opportunity cost of capital for NETCO is 11%. Using the assumed long-term inflation rate of 2.5%, the real opportunity cost of capital for NETCO is: 1.11  1  .0829, about 8.3% 1.025

The spreadsheet for New Economy Transport (A) calculates PVs for each investment and cash flow category and adds everything up to NPV. NPV is +$774,000 for the basic overhaul (REHAB) and even better with the new engine and control system (+$1,207,000 for REHAB PLUS). The REHAB PLUS option is clearly attractive.

NEW ECONOMY TRANSPORT (B) Minicase solution, Chapter 6 Principles of Corporate Finance, 14th Edition R. A. Brealey, S. C. Myers and F. Allen

We start with the assumptions and PV calculations in New Economy Transport (A). We could calculate the NPV of the new vessel in the same format. But the new vessel lasts for 20 years, 8 years longer than the rehabilitated Vital Spark. Thus we calculate equivalent annual cash flows. That is, we calculate the equivalent annual costs of the net investments required for the Vital Spark (with and without the new engine and control system) and for the new vessel. The equivalent annual costs are subtracted from net operating revenue. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

The spreadsheet for New Economy Transport (B) summarizes the calculations.

The net investments are: 1. Overhaul of the Vital Spark (REHAB): The investment of $820,000 is offset by the depreciation tax shield ($172,200) and the after-tax proceeds from sale as is (an opportunity cost of $187,400). The net investment is $460,400.

2. Overhaul with new engine (REHAB PLUS): Investment increases to $1,420,000, but the depreciation tax shield also increases. The net investment is $934,400.

3. New vessel: The PV of the $3,000,000 investment is only $2,851,351, because half of the payment is deferred to t = 1. The PV of training costs is also treated as an investment. In addition, NETCO can run the Vital Spark for one more year, generating after-tax revenues of $910,000 and a salvage value of $140,000 at t = 1. Thus the net investment in the new vessel (PV) is $1,263,779.

The net investments are converted into equivalent annual costs, that is, real annuities starting at t = 1.5 and continuing to t = 12.5 for the Vital Spark and to t = 20.5 for the new vessel. The equivalent annual costs per dollar of net investment are shown at the bottom of the spreadsheet.

The total equivalent annual cash flow for each option equals revenues – operating costs – equivalent annual cost of net investment. Overhaul of the Vital Spark generates a positive annual flow, as expected, since overhaul is positive-NPV. But the new vessel generates a larger equivalent annual cash flow of about +$349,000. Thus the Vital Spark is headed for retirement at t = 1.

February 20, 2019

JOHN AND MARSHA ON PORTFOLIO SELECTION Minicase solution, Chapter 8 Principles of Corporate Finance, 14th Edition R. A. Brealey, S. C. Myers and F. Allen

Recall that stock i’s beta is just the ratio of its covariance with the market (σim) to the market variance σm2, where σm2 = .162 = .0256. For Pioneer Gypsum, β = .65 = σim/.0256. Solving this equation gives a covariance of σim = .01664. The covariance also equals the correlation coefficient ρ times the product of the stock’s and market’s standard

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deviations σi and σm. For Pioneer, σim = ρσiσm = .01664 = ρ×.32×.16, which implies ρ = .325.

Here is the 2×2 covariance matrix for the market and Pioneer.

S&P 500

Pioneer

S&P 500

Pioneer

.0256

.01664

.01664

.1024

Now calculate the portfolio return rP, portfolio standard deviation σP and the Sharpe ratio for different fractions invested in the market and Pioneer. For example, suppose that the market gets 99% of investment and Pioneer 1%.

rP = .99×.125 + .01×.11 = .12485 σP2 = .992×.0256 + 2×.99×.01×.01664 + .012×.1024 = .0254 σP = √.0254 = .1595 Sharpe ratio = (rP – rf)/σP = (.12485 - .05)/.1595 = .4694 It turns out that the Sharpe ratio is maximized by putting about 95% in the market and 5% in Pioneer.

S&P 500

Pioneer

Sharpe ratio

1.0

0

.4688

.99

.01

.4694

.98

.02

.4698

.97

.03

.4701

.96

.04

.4702

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.95

.05

.4702

.94

.06

.4699

We can follow the same procedures for Global Mining. Global’s covariance is .03123 and its correlation with the market is .813. The 2×2 covariance matrix is:

S&P 500

Global

S&P 500

Global

.0256

.03123

.03123

.0576

Global’s return is not attractive: with a beta of 1.22, it should offer an expected rate of return of .05 + 1.22×.075 = .1415, over 14%. But John’s estimate is only 12.9%.

Therefore he should sell Global. In fact he should eliminate it from his portfolio.

Suppose that John’s starting portfolio matches the market and includes 0.75% in Global. Then he should sell all the Global shares and put the proceeds back into the overall market. The resulting portfolio weights are 100.75% in the market and -0.75% in Global. That is, the portfolio should “underweight” Global by -0.75% in order to reduce holdings of Global to zero. The underweight increases the Sharpe ratio from .4688 to .4693:

S&P 500

Global

Sharpe ratio

.99

.01

.4680

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1.0

0

.4688

1.005

-.005

.4691

1.0075

-.0075

.4693

The Sharpe ratio gets still better if the portfolio weight for Global is reduced below -.75%. A weight below -.75% means selling short. In order to sell short, John would have to borrow Global shares, sell them (with an obligation to repurchase and return the shares later) and invest the sale proceeds in the market. But we doubt that John is allowed to sell short from the portfolio he manages. We discuss short selling in Chapter 20.

THE JONES FAMILY, INCORPORATED Minicase Solution Principles of Corporate Finance, 14th Edition R. A. Brealey, S. C. Myers and F. Allen

If the wildcat well is a success, it should produce 75×365 = 27,375 barrels per year. Suppose production starts after one year. The net cash flow per barrel, after pipeline and shipping costs and including one year’s inflation at 2.5%, is (100 – 20) ×1.025 = $82. Total cash flow is C1 = 27,375×82 = $2,245,000 (we will round to the nearest $1000). Production will decline by 5% per year, but prices are projected to grow at 2.5% per year. The net growth rate is (1.025×.95) – 1 = –.026 or –2.6%.

Johnny used the CAPM to get a discount rate. The interest rate is 6%, the market risk premium is 7% and the beta is .8. Thus: (

)

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The cash flows from the oil well are a 15-year annuity declining at 2.6% per year.6 Johnny decided to use the short-cut formula in Table 2.2. The short cut starts with the formula for a growing (in this case declining) perpetuity, but subtracts the PV of another declining perpetuity. Let T = the date of the last cash flow from the declining annuity:

(

)

( (

) )

[

(

) ]

The second term inside the brackets subtracts the present value of an annuity starting in year 16 and discounts it back to the present. Note that the cash flow for year 16 is C1 × (1 - .026)15.

Of course there was a 30 per cent chance of a dry hole, so Johnny multiplied his PV of $13,757,000 by 1 - .3 = .7 and subtracted the $5 million investment.

NPV = .7  13,757,000 – 5,000,000 = + $4,630,000 What about the operating leverage that so concerned Johnny’s father? Operating leverage is caused by fixed costs, in this base by the pipeline and shipping costs. These costs start at 20 × 1.025 = $20.50 per barrel in year 1 and are expected to grow at 2.5% per year. The calculation above folds them into net cash flows and discounts them at 11.6%, as if they were just as risky as the revenues. If they are really fixed, they should be discounted at a lower rate, for example at the 7% long-term borrowing rate for Jones Family Oil, Inc.

6

This assumes that the well produces one lump-sum cash flow per year at dates 1, 2, … , 15. This timing may not be right. If the cash flows are spread evenly over each year, and the well starts production at date 1, then it would be better to assume receipt at dates 1.5, 2.5, … , 15.5 (the mid-year convention). In this case you could discount the present values by an extra half year to account for the six-month delays. Or you could switch over to continuous compounding.

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Johnny decided to see how the PV of the fixed costs would change when discounted at 7 vs. 11.6%. The PV per barrel at 11.6%, which was included in the PV calculated above, is:   1  .026 15  20.5 PV  1      $125.6 .116  (.026)   1.116  

The PV at 7% increases to:   1  .026 15  20.5 PV  1      $161.4 .07  (.026)   1.07  

Thus recognizing operating leverage could decrease overall PV by (161.4 – 125.6) × 27,375 = $980,000 and decrease NPV to 13,757,000 – 980,000 = $12,777,000.7 The wildcat well’s NPV is still positive, however, because .7 × 12,777,000 = $8,944,000 is still greater than the $5 million outlay.

It seems that Marsha’s oil well is an excellent investment. In fact it remains a good investment (ignoring any adjustment for operating leverage) even if production lasts only 6 years. You can check this by recalculating the declining annuity formula with T = 6, multiplying by the 0.7 probability of finding oil and subtracting the investment of $5 million. The resulting NPV is still positive.

WALDO COUNTY Minicase solution, Chapter 10 Principles of Corporate Finance, 14th Ed. R. A. Brealey, S. C. Myers and F. Allen

7

This holds the 11.6% discount rate for revenues constant. If that rate was right for net cash flows (revenues less fixed costs), it is too high for revenues alone. Operating leverage adds risk to net cash flows, not to revenue. A lower discount rate for revenues would increase NPV and make the Marsha’s investment still more attractive. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

The attached Excel spreadsheet was prepared by George Chavez for the proposed Downeast Tourist Mall. The spreadsheet will carry out the various sensitivity and breakeven analyses suggested in the minicase.

Enter changes in the inflation rate and forecast errors for rental revenues and share of retail sales in the spreadsheet’s left-hand panel. To see the effect of a year’s delay in startup, enter 0 if no delay and 1 is start up is delayed one year. Changes in the timing and amount of construction costs should be entered directly in the cash flow table.

All cash flows except depreciation are forecasted in real terms. Note that depreciation is not subtracted in calculating operating cash flow. Depreciation tax shields are valued separately by discounting at the nominal rate. We isolated these tax shields to see the effect of changes in inflation. Inflation affects the PV of depreciation tax shields, which are fixed in nominal terms. The other cash flows are given in real terms and discounted at (1.09/1.02) – 1 = .0686.

The project’s terminal value is $30 million, the value of the land in year 18, or in year 19 if construction and startup are delayed.

If all goes as planned, the project’s NPV is + $36.6 million, but cash flows could turn out worse or better than projected. For example, a 20 per cent shortfall in rentals and share of retail sales cuts NPV to - $1.1 million.

ECSY-COLA IN INGLISTAN Minicase solution, Chapter 11 Principles of Corporate Finance, 14th Edition R. A. Brealey, S.C. Myers and F. Allen

Libby Flannery prepared the attached spreadsheet to analyze the NPV of EcsyCola’s proposed investment in Inglistan. With the inputs suggested in the mini-case, NPV was very slightly negative on a $20 million outlay.

Libby was conscious of the spreadsheet’s simplifying assumptions. First, the project cash flows were projected as a perpetuity. The project, if successful, would generate cash returns for a long time, but not forever. On the other hand, the 25% © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

nominal discount rate handed down from Ecsy-Cola’s headquarters seemed unreasonably high – there was clearly a built-in fudge factor.8 She decided to check her results with a more reasonable discount rate, say 15%.

Libby used her spreadsheet to conduct a sensitivity analysis, assuming for simplicity that the optimistic and pessimistic probabilities were each 25%:

Steady-State Sales

Probability

$ millions

NPV at

NPV at

25%, $ millions

15%, $ millions

Optimistic

80

.25

+ 14.8

+ 42.9

Most Likely

50

.50

- 0.1

+ 15.7

Pessimistic

20

.25

- 14.9

- 11.6

If Libby waited a year, and discovered that potential sales were only 20 million liters per year, Ecsy-Cola would not invest. Then the downside NPV, assuming a 25% discount rate, would be zero, not −$14.9 million. The payoff to waiting would be: Expected NPV, invest in year 1 = .25  14.8 + .50  (−0.1) + .25  0 = + $3.65 million

At a 15% discount rate, the expected NPV from investing in year 1 would be +$18.6 million. These calculations suggested a “wait and see” strategy.

The problem with that strategy was potential competition. If steady-state sales turned out higher than now expected – 80 million liters per year, for example – then Sparky-Cola, or some other competitor, would surely enter. Therefore the high cash flows for the optimistic case were not sustainable in the long run, and the optimistic-case NPVs, while no doubt positive, were less than her spreadsheet suggested. Competition would limit the upside NPVs. Libby realized that investing right away, and establishing the Ecsy-Cola brand in Inglistan before her competitors could act, gave her best chance of generating a significant positive NPV. In the optimistic scenario, competition would come sooner or 8

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later, but Ecsy-Cola would have a head start and probably the largest market share. If Ecsy-Cola was just breaking even (earning its cost of capital), competitors would have no incentive to enter.

Libby had to weigh the competitive advantages of investing immediately against the possibility of a costly mistake. Therefore she refocused her analysis on establishing the minimum potential size of the market. If NPV at that minimum was at least zero, or perhaps an acceptably small negative number, she resolved to invest right away.

March 1, 2019

CLAXTON DRYWALL COMES TO THE RESCUE Minicase Solution, Chapter 17 Principles of Corporate Finance, 14th ed.

R. A. Brealey, S. C. Myers and F. Allen 1. Find the discount rate that makes the present value of 19 $950,000 payments equal to $9,050,000. It is 8.11%.

2. The 7% mortgage rate is better than the 8.11% rate in the lease. Of course the lease is like a 90% mortgage: it provides an extra $1,050,000 of up-front financing for the $10 million investment. So the law firm might prefer the lease if it were short of cash and a bank would charge a high interest rate on $1,050,000 of additional borrowing. But the minicase says that the law firm does have ample cash flow. Thus the mortgage is better.

3. Suppose a recession knocks the market value of the office building from $10 million down to $9 million. With all-equity financing, the rate of return to equity is –10%. With the mortgage, the net equity value drops from $2 million to about $1 million ($9 million less the $8 million mortgage).9 The return is approximately –50%. With the lease, equity value drops from $9,050,000 to about zero. The return is approximately –100%.

We say “about” because a small fraction of the mortgage will be paid off after one year. The same qualification applies to lease financing, because the present value of remaining lease payments will be a little less than $9 million after the lease payment is made in year one.

9

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4. No. The law firm will make these investments regardless of how the office building is financed.

BRUCE HONIBALL’S INVENTION Minicase solution, Chapter 21 Principles of Corporate Finance, 14th Edition R. A. Brealey, S. C. Myers and F. Allen

MEMORANDUM January 28, 2018 To: Bruce Honiball From: Sheila Liu Re: Gibb River Bank Equity-Linked Deposits

Bruce, thank you for your memo. I think equity-linked deposits are a good idea, but they may be hard to sell in today’s low interest-rate environment.

Spotting the option. Think of it this way. Whatever happens to Australian share prices, depositors under your scheme get back their initial investment of $A100 at the end of the year. If share prices rise by y%, they also receive a bonus of .5y  $A100. For example, if prices rise by 10%, the bonus is .5  .10  $A100 = $A5. If share prices fall, depositors do not receive any bonus. Thus

Share prices fall

Share prices rise by y%

Repayment of deposit

$A100

$A100

Bonus

zero

.5y  $A100

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The key questions are: Is this a good deal for Gibb Bank depositors? If it is, can we afford to offer it to them? We can answer these questions by considering an alternative investment strategy that generates the same results.

Valuing the option. Suppose an investor buys a 1-year call option on the market index with an exercise price equal to its current level. Let’s call the current level of the index 100. The payoff on this call option is:

Share prices fall Payoff on call

Share prices rise by y% y  $A100

zero

In other words, the bonus payment on the equity-linked deposit is exactly half the payoff on an option to buy the market index at its current level of 100.

Now it is easy to see how to value the equity-linked deposit. Value is equal to the present value of $A100 received at the end of the year plus half the present value of a call option. To value the payment of $A100, we simply discount at the current interest rate.

(The equity-linked deposits would deliver part of the stock market’s upside, but would pay no interest. Therefore we have to discount.) The Australian short-term Treasury rate is about 1.5%,, so the value of the promised payment is 100/1.015 = $A98.52.10 Valuing the call option could be harder. Fortunately, Black and Scholes have devised a formula that does the trick.11 We need the following inputs:

Current level of index

100

Index minus next year’s dividends

95.6

Exercise price of call option

100

Interest rate

1.5%

Time to maturity

1 year

Volatility of index

16.4%

We don’t know what the short-term Australian Treasury rate will be when you tackle this minicase. Look it up on the web and redo the calculations below.

11 To replicate Sheila’s calculations, follow the procedures given at pp. 573-577.

10

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I assumed a 4.4% dividend yield and subtracted next year’s dividends from the index level, which I take as 100 for the following illustrations. Subtracting dividends is important because depositors in the equity-linked account will not get them, even if the market goes up.12 I estimated the volatility of the Australian equity index by calculating the standard deviation of market returns over the past 20 years.13 You can put in your own figure if you feel that market volatility is likely to change.

Using my inputs, the Black-Scholes formula says the call option is worth $A4.99.

Remember that the value of an equity-linked deposit is equal to the present value of the promise of $A100 plus half the value of a call option. Therefore the value of the deposit is 98.52 + .54.99 = $A101.02. If this estimate is right, we would be taking in $A100 from depositors and offering them in exchange an investment worth $A101.02. In other words, each $A100 of deposits would have a NPV for us of +100 – 101.02 = −$A1.02.

Administrative costs would push NPV even further into negative territory.

The problem here is that the interest rate is so low. Depositors are not giving up much in exchange of half of the market upside. Could we charge an annual fee for access to equity-linked deposits? Promise a smaller fraction of the upside? Of course the equity-linked deposits would also attract new customers that we could sell other banking services to.

How could we reduce risk? That depends on how we invest the depositors’ money. Australian government debt could provide a safe 1.5% return, but would not protect us if share prices take off and oblige us to pay out large bonuses to depositors.

Suppose instead that we invest $98.52 at 1.5%. We would then be sure that we could pay back the initial deposit of $A100. At the same time, for each $A100 of deposits we could buy .5 call options on the market index.14 That would guarantee that we could also pay any bonus. We would then have a completely hedged, risk-free position.

12

See pp. 581-582.

Using the Excel function STDEV, the standard deviation of the last 20 market returns in Table 21.3 is 16.4%. Sheila and Bruce will have to think hard about the future standard deviation of the market. They may wish to check implied volatilities from call options on the Australian market index.

14 Sheila should have added a qualification at this point. If Gibb Bank buys a call to hedge the equity-linked deposits, it will get dividends, unlike the depositors. Its call would be more valuable than the depositors’. Hedging would not require .5 calls, but .5×95.6 = .478 calls.

13

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What if equity-linked deposits sell like hot cakes and it becomes difficult or expensive to buy sufficient call options on the index? There is another way to hedge our risks. Black and Scholes showed that a call option can be replicated by a mixture of delta shares and borrowing. In my example, delta works out at .4595 and the amount borrowed is $A38.94. So to replicate one call, the bank would need to invest .4595  $A95.60 in the market index and borrow $A38.94.15 The net cost of replicating one call would be .4595  95.60 – 38.94 = $A4.99. Of course, to replicate .5 calls, the bank would need to invest and borrow half as much. So, if necessary, we can hedge the equity-linked deposits by borrowing to buy the market.16 As time passes and share prices change, we would need to adjust the amounts that the bank borrows and invests in the market index.

Bear Market Deposits. I have also looked briefly at your idea of bear market deposits. Again it is useful to break the payoffs into a fixed payment and a bonus.

Suppose we stick with your suggestion to pay a bonus of $A5 for each 10% fall in the index. Then the payoffs from a bear market deposit are as follows:

Share prices fall by y%

Share prices rise

Repayment of deposit

$A100

$A100

Bonus

.5y  $A100

zero

Consider a 1-year put option on the market index with an exercise price equal to its current level ($A100). The payoff on this put option is:

Payoff on put

Share prices fall by y%

Share prices rise

y  $A100

zero

15

The amount borrowed is N(d2) times the PV of the exercise price, .395 × 98.52 = 38.94. Gibb Bank could borrow the money by simply investing less in its portfolio of 1-year Australian Treasury securities and repurchasing the securities after one year. Banks usually hold large portfolios of government securities.

16 Sheila is assuming that delta has been estimated correctly. But if the Australian market turns out to be more or less variable than in the past, delta will not be .4595, and Sheila’s strategy will not replicate the call option exactly. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

In other words, the bonus payment on the bear market deposit is exactly .5 times the payoff on an option to sell the market index at its current level of 100.

I have also calculated the value of this downside bonus. Using exactly the same inputs, I get a value for the put option of $A7.91.17 So the value of a bear market deposit is: PV(fixed payment) +

PV(bonus)

98.52 + .57.91 = $A102.48 The NPV here is −$A2.48, still not a good deal for us.

We could get rid of all the risk of offering such a deposit by investing the money in a mixture of a 1-year Australian Treasuries and a fraction of a put option. We can also replicate the put by investing in a mixture of Treasuries and the market. Since delta in this case is negative, that involves selling the market index. 18 Let me know if I can be of further help.

Sheila

17

Sheila used put-call parity (see pp. 548-550): Value of call + present value of exercise price = value of put + share price

Sheila calculated the value of a call as $A4.99. Share price is $A95.60, adjusted for lost dividends, and the present value of the exercise price is $A98.52. The value of a put is therefore 4.99 + 98.52 – 95.60 = $A7.91.

18 The delta for a put equals the delta for a matching call minus 1. In this case delta (put) = .4595 – 1 = – .5405. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

MEMORANDUM January 28, 2018

To:

Sheila Liu

From: Bruce Honiball Re: Gibb River Bank Equity-Linked Deposits

Sheila, thank you for your memo with your interesting calculations.

Unfortunately I have already mentioned equity-linked deposits to our CFO. She is enthusiastic.

The next step is to develop a paper that we can present at next month’s board meeting. Have a go at reworking your paper, leaving out all that higher mathematics and concentrating instead on the guts of the proposal. Get it all down in a couple pages that anyone can understand.

Thanks again,

Bruce

THE SHOCKING DEMISE OF MR. THORNDIKE Minicase solution, Chapter 24 Principles of Corporate Finance, 14th Edition R. A. Brealey, S. C. Myers and F. Allen After the corpse was removed, police inspectors came to dust the bedroom for fingerprints. Morse knew they would find nothing. He walked down the marble staircase of Rupert Thorndike’s mansion and into the paneled library. He sat at a table in front of the fireplace, scarcely noticing the painting over it, Monet’s portrait of the legendary John D. Thorndike at Giverny. He turned on his laptop computer.

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Thorndike Oil had three classes of securities outstanding: $250 million of debentures (face value), 30 million shares, and an issue of subordinated convertible notes.

Morse had to calculate the change in the value of each security now that Thorndike was gone, and given the now near-certain acquisition of Thorndike Oil by T. Spoone Dickens.

Table 1 reports Morse’s results. The notes summarize his reasoning.

With Table 1 in hand, it was easy to calculate the increases in value due to the murder and resulting acquisition. Debt increased by 39.5% of face value. Common stock increased by $1.00 per share, and each convertible note increased from 103.95% to 110% of face value (from $1039.50 to $1100 per bond). Morse summed the gains to Doris, John and Patsy (see Table 2). Then he reached for his cell phone and dialed Chief Inspector Spillane.

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Thorndike Oil

Table 1

Values of Thorndike Oil Securities Before and After the Murder

Before Debt

Equity

Convertible notes

After

$151.25 million,

$250 million

60.5% of face value

100% of face value

$270 million,

$300 million,

$9 per share

$10 per share

103.95% of

110% of

face value

face value

Notes

1. Debt, before: PV at 12% of the 5% coupon for 10 years, plus repayment of face value (100%) at year 10, is 60.5% of the $250 million face value, or $151.25 million.

Debt, after: essentially risk-free. The debt will be repaid in short order and should trade very close to face value. The gain in market value is 1 - .605 = .395, or 39.5% of face value.

2. Shares: Share price increases from $9.00 to $10.00.

3. Convertible notes: Conversion value before is 110 shares at $9 per share = $990 per $1,000 note. The bonds were trading at 5% over conversion value, or 1.05×990 = $1,039.50. Note holders will convert prior to the takeover, receiving 110×10 = $1,100. (If they don’t convert, they get only $1,000.) In other words, the notes increase by 110 – 103.95 = 6.05% of face value.

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Thorndike Oil

Table 2

Who Gained Most?

(Figures in millions)

Debt

Doris

John

Patsy

$1.58

0

0

$1.2

$0.5

$1.5

(1.00×1.2)

(1.00×.5)

(1.00×1.5)

0

$0.3025

$0.1815

(.0605×5)

(.0605×3)

___________

___________

_________

$2.78

$0.8025

$1.6815

(.395×4)

Stock

Convertible notes

Total

RENSSELAER ADVISORS Minicase solution, Chapter 26 Principles of Corporate Finance, 14 Edition R. A. Brealey, S. C. Myers and F. Allen February 20, 2019

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RENSSELAER ADVISORS

To: Mr. Hendrik van Wie, Chief Financial Officer, Madison Mills, Inc. From: Pieter Coeymans, Vice President, Rensselaer Advisors Subject: Investment strategy for Madison Mills pension assets Date: December 1, 2018

As you requested, Rensselaer Advisors (RA) proposes a conservative investment strategy for the $90 million in pension assets that Madison Mills (MM) has designated to cover benefits for its retired employees. The present value (PV) of these benefits is $89.4 million, so this part of MM’s pension plan is fully funded.

MM could purchase a portfolio of U.S. Treasury securities with payoffs exactly matching the payments [shown in Table 26.6]. However, RA proposes a simpler but still conservative strategy. RA manages Treasury portfolios with durations of 1, 7 and 15 years. RA proposes to invest $89.4 million as follows, retaining $600,000 in cash for immediate benefit payments:

Durations:

1 year

7 years

15 years

Investment (millions)

$20

$44.7

$24.7

.224

.50

.276

(Total = $89.4

million) Fraction of portfolio

Portfolio duration = .224×1 + .50×7 + .276×15 = 7.87 years

This portfolio duration exactly matches the duration of the benefits that MM is obligated to pay. Thus MM will be insulated from changes in the level of interest rates.

If rates rise from the current 5% level, the market value of MM’s pension assets will fall, but the PV of benefits will fall by the same amount. If rates fall, the market value of the pension assets will increase to offset the increase in PV of benefits. In addition, RA’s plan eliminates MM’s exposure to the volatility of common stocks or other risky assets. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Of course durations change as interest rates change and time passes. Therefore RA will track durations and rebalance the portfolio in order to keep durations matched and keep MM insulated from interest rate risk.

[The memo goes on to argue that RA’s experienced staff and quantitative modeling skills, combined with its “proprietary” duration-matching strategy, amply justify RA’s moderate management fee.]

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RENSSELAER ADVISORS

To: Mr. Hendrik van Wie, Chief Financial Officer, Madison Mills, Inc. From: Pieter Coeymans, Vice President, Rensselaer Advisors Subject: Updated investment strategy for Madison Mills pension assets Date: December 1, 2019 As you requested, Rensselaer Advisors (RA) has revaluated Madison Mill’s (MM’s) pension investment strategy in light of the dismal performance of the U.S. stock market over the last year. We understand that the market value of MM’s pension assets earmarked for retired employees’ benefits has fallen to $78 million. The evident risks of the stock market have reinforced RA’s confidence in its proprietary fixed-income strategy.

The attached table [Table 26.6a] recalculates the present value (PV) of benefits for retired employees at $90.4 million. Despite payment of benefits for 2018, this PV has increased because of the fall in interest rates from 5% to 4%. The duration of the benefits is now 7.98 years.

This part of MM’s pension plan is now underfunded ($78 million vs. $90.4 million), so MM will have to make several years of additional pension contributions to close the gap. RA’s duration-matching strategy can still insulate MM against changes in future interest rates, but it will be necessary to set the duration of pension assets 15.9% higher than the duration of benefits. (Note that the PV of benefits is 15.9% higher than the market value pension assets: 90.4/78 = 1.159.) Thus if interest rates change, the dollar change in the market value of pension assets will match the dollar change in the PV of benefits.

The duration of benefits is 7.98. The duration of pension assets must be 7.98×1.159 = 9.25. RA proposes the following portfolio:

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Durations:

1 year

7 years

15 years

Investment (millions)

$15

$29.8

$33.2

.192

.382

.426

(Total = $78

million) Fraction of portfolio

Portfolio duration = .192×1 + .382×7 + .426×15 = 9.25 years

MM can use additional required pension contributions to provide cash to pay benefits due immediately.

[The memo goes on to applaud Mr. van Wie for his forward-thinking decision to avoid the excessive volatility of the stock market and to commit to fixed-income strategies for pension investing.]

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Table 26-6a Madison Mills Pension Fund Projected Benefits for Retired Employees Updated to December 2019 with 4% interest rate Year

Date (t)

Payment

PV at 5%

PV × t

2020

1

9,009,500

8,662,981

8,662,981

2021

2

8,522,000

7,879,068

15,758,136

2022

3

8,434,500

7,498,240

22,494,719

2023

4

7,858,500

6,717,479

26,869,915

2024

5

7,794,000

6,406,100

32,030,499

2025

6

7,729,500

6,108,736

36,652,417

2026

7

7,639,500

5,805,392

40,637,745

2027

8

6,440,500

4,706,010

37,648,082

2028

9

6,330,000

4,447,374

40,026,366

2029

10

6,242,500

4,217,209

42,172,093

2030

11

6,205,000

4,030,650

44,337,146

2031

12

5,775,500

3,607,360

43,288,323

2032

13

5,600,700

3,363,635

43,727,259

2033

14

5,432,000

3,136,845

43,915,825

2034

15

5,140,000

2,854,060

42,810,893

2035

16

4,234,900

2,261,048

36,176,764

2036

17

4,123,000

2,116,638

35,982,844

2037

18

3,890,000

1,920,213

34,563,841

2038

19

3,500,600

1,661,533

31,569,132

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2039

20

3,400,500

1,551,944

31,038,876

2040

21

3,340,600

1,465,968

30,785,318 SUM = 721,149,176

PV:

90,418,482

Duration:

7.98

EXACTA, S. A. Minicase solution, Chapter 27 Principles of Corporate Finance, 14th edition R. A. Brealey, S. C. Myers and F. Allen Exacta now has export revenues in dollars of $320 million. Assuming an exchange rate of, say, 1.33 $/€ (.75 €/$), this revenue is worth €240 million. Suppose the dollar falls suddenly to 1.45 $/€ (.69 €/$). What is the loss to Exacta?

First, the value in euros of Exacta’s dollar accounts receivable (payments due on prior export sales) drops immediately. If accounts receivable equal two month’s sales, the loss is 320  2/12  (.75 – .69) = €3.2 million. This exposure would be easy to hedge by a forward sale of dollars for euros.

Second, the value in euros of Exacta’s future export revenues falls, because it cannot immediately raise its prices in dollars to compensate for the fall in the dollar. The annual exposure if the dollar falls to .69$/€ is therefore 320  (.75 – .69) = €19.2 million.

Exacta’s conservative CEO might decide to hedge all of next year's export revenues.

How will construction of the new U. S. plant affect these exposures? Two-thirds of the plant’s operating expenses will be in dollars, which provides a natural hedge.

Table 1 shows how Exacta is affected by a drop in the dollar from .75 to .69 €/$. Look first at the left-hand column (for .75 €/$). We start with dollar revenues from the new plant ($420 million). A profit of $52 million from the plant implies total costs of $368 million. Two-thirds of these costs are in dollars, so we subtract $245.3 million, leaving a net dollar cash flow of $174.7 million.19 This converts to €131 million. After subtracting Exacta’s cost in euros,20 it is left with €39 million.

Now look at column (A) in the table. At .69 €/$, the net dollar cash flow now converts to only €120.5 million, leaving Exacta with €28.5 million after its costs in euros 19

For simplicity we are forgetting about U. S. or French taxes.

One third of costs are incurred in euros. The costs are $368/3 = $122.7 in dollars or 122.7×.75 = €92 in euros.

20

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are paid. (We assume that Exacta’s costs in euros are not affected by the dollar’s decline.)

So its loss from the fall in the dollar is €39 – 28.5 = €10.5 million.21 Column (B) shows the annual proceeds to Exacta if all costs were in euros rather than dollars. (This would be a pure export business with $420 million in annual sales.) In this case Exacta gets only €13.8 million. Column (C) shows the result if all costs of the new U. S. plant are in dollars. In this case Exacta gets €35.9 million, its U.S. profits of $52 million times the exchange rate of .69 €/$. In this case Exacta would only have to worry about hedging the profits of the U. S. plant, not its sales revenues.

Now let’s go back to the base case in the left-hand column of Table 1. If Exacta decides to hedge the annual dollar cash flow produced by its U. S. plant, it will sell $174.7 million forward for euros. It may also decide to hedge any dollar accounts receivable accumulated by the U. S. plant.

Of course, selling forward one year’s net dollar revenues is somewhat arbitrary (why not 15 or 18 months?) and leaves Exacta exposed to subsequent changes in the exchange rate. Exacta might think about hedging the present value of the dollar cash flows generated by the plant,22 but calculating the sensitivity of this present value to changes in the euro-dollar exchange rate would not be easy. M. Pangloss would have to try to understand the long-run effects of an exchange-rate shift on the plant’s cash flow in dollars and euros. There is no reason to think that financing all of the plant’s construction cost with dollar borrowing would be the correct hedge for any exposure.

Once Exacta decides how much to hedge its dollar exposures, it can do so either by selling dollars forward or by borrowing dollars and immediately converting the proceeds of the borrowing into euros. The forward market is more liquid for short-term transactions, but for longer-term hedges it may be easier to borrow dollars and convert to euros.

21

It doesn’t matter whether Exacta bills its U. S. plant for these costs in dollars or euros.

There is no point in hedging the investment in the plant, because that investment will be sunk by the time the plant is operating.

22

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Table 1. Calculating Exacta S.A.’s Net Profits in Euros from its U.S. Plant At 1.33 $/€ (.75 €/$)

At 1.45 $/€ (.69 €/$)

Revenue

$420.0

(A) $420

(B) $420

(C) $420

Operating costs (in dollars)

$245.3

$245.3

__--__

$368

Net dollar cash flow

$174.7

$174.7

$ 420

$ 52

Value in euros

€ 131.0

€ 120.5

€ 289.8

€ 35.9

Exacta’s euro costs

€ 92.0

€ 92.0

€ 276.0

__--__

Net to Exacta

€ 39.0

€ 28.5

€ 13.8

€ 35.9

Column A shows the impacts of a declining dollar. Columns B and C are hypothetical cases. Column B assumes that all costs are in euros; Column C assumes that all costs are in dollars.

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