Ch 8: Capital budgeting Pick the best investment option (WACC 10%pa): A B +R100 +R1 500
NPV  Returns above/below WACC (Seems B is best [offers more]?) Initial investment R1 000 R20 000 (A’s return 10% [100/1000] > B’s of 7,5%) NPV index (A:1100/1000 and B:21500/20000) 1,1 1,075 (Enables comparison when investments differ) Project life (A’s return pa =5%<B’s 7,5%) 2 years 1 year Replacement chain] R576 R16 502 [A:100/(1,735x,1) B:1500/(,909x,1)(Compares project if terms differ) What is the effective return? IRR? IRR? Which pays back soonest? DPP? ? ? What is the risk of these options?
Which technique is best? All have merit!
Common shortcomings • All are financial in nature, ignoring possible qualitative advantages/disadvantages, • All do not disclose the source of funding, • All require reliable information to produce credible estimates, • Assessment criteria could obscure the larger strategic/tactical intentions of the enterprise (e.g. suffer lower returns to become independent from suppliers/gain a market monopoly) • All rate of return methods ignore project size
Internal Rate of Return (IRR) • IRR discounts project CFs to Nil or Cost Year
0
1
2
Cash Flows (10,000) t PV Factor 1/(1+r) 27,2% 1.0000 Present Values (10,000)
8,000 0.7863 6,290
6,000 0.6183 3,710
∑n(C/[1+r])t C=cash flows
IRR NPV
27.2% 0
10,000
NPV Profile How will NPV change with a change in discount rate? NPV Profile 5,000 4,000 3,000
NPV
IRR 2,000 1,000 0
0%
1,000 2,000
3%
6%
9%
12
%
15
%
18
%
21
%
24
%
27
%
30
%
33
%
36
%
39
%
Discount rate NPV
NPV or IRR? • If project has +NPV, its IRR>WACC – Both same answer • But, compare two mutually exclusive projects
0
Y ear P r o je c t A P r o je c t B
(1 0 ,0 0 0 ) (1 ,0 0 0 )
NPV Cost of Capital
Project A Project B
1 1 1 ,8 0 0 1 ,4 0 0
IR R
10% 11800/1,1=10727 1400/1,1 = 1 273
727 Best 273
Best
18% 40%
• Amount of project is not an issue if no cap. rationing. • If markets efficient finance can be raised at WACC.
Nonconventional project  multiple IRRs .
0
Y ear P ro ject I
1
(200) 14%
C ost of C ap ital
N P V 200+877769=92 IR R 200+725525= 0 IR R 200+27676= 0
(92) 38% 262%
2
1,000
(1,000)
/1,14=877
/1,142=(769)
/1,38=725
/1,142=(525)
/3,62=276
/3,622=(76)
N P V P r o f ile o f N o n  c o n v e n t io n a l P r o je c t 5 0 .0 0
44%
262% 440%
418%
396%
374%
352%
330%
308%
286%
264%
242%
220%
198%
176%
154%
132%
110%
88%
66%
44%
22%
0%

( 5 0 .0 0 )
NP V
( 1 0 0 .0 0 )
( 1 5 0 .0 0 )
( 2 0 0 .0 0 )
( 2 5 0 .0 0 )
200
Payback Period (PP) Method • Best projects have the shortest investment recovery period (from project cash flows discounted or not) • Management sets maximum required payback period
0
1
2
3
4
Project I Project J
(12,000) (12,000)
4,000 2,000
6,000 4,000
6,000 4,000
1,000 8,000
Payback I Payback J
2.33 , 3.25
Year
Years  undiscounted
Pros & Cons of Payback Period • Advantages –Simple to calculate and understand –Widely used in practice –Risk indicator (Sooner not later) • Disadvantages –Ignores cash flows after the payback –Ignores time value of money (PTO) –Bias against long term projects
Discounted Payback Period (DPP) â€˘ Discounted Payback = period to recover investment from PV of project cash flows Year Project I Project J Cost of Capital
0
1
2
3
4
(12,000) (12,000)
4,000 2,000
6,000 4,000
6,000 4,000
1,000 8,000
/1,153
/1,154
/1r =
15%
/1,15
/1,152
If we discount each year by multiplying the cash flow by 1/1+r)t , then the present values of each year's cash flows are as follows; Project I (12,000) 3,478 4,537 3,945 572 11,960 Cumulative Project J (12,000) 1,739 3,025 2,630 4,574 11,968 Cumulative The discounted payback of I is very close to 3 years and the discounted payback of J is very close to 4 years
Accounting Rate of Return (ARR) • ARR = Incremental NIAT/Average BV • ARR pa = ARR/Number of project years • Avg BV = Cost/2 (if residual value = 0) If res. value Avg BV = (CostRes.)/2 + Residual • Net income = NIATD (depreciation) • Advantages of ARR – Simple to calculate and understand (ROI) – Widely used in practice – Risk assessed against Required Return • Disadvantages of ARR – Ignores time value of money – Longer term projects may be shunned
Profitability Index (BenefitCost Ratio) • PI measures return relative to cost • PI = Present Value of future CFs/Cost – If PI > 1 = Accept the project (+NPV) – If PI < 1 = Reject the project (NPV)
• Use PI when capital is rationed – Maximise return relative to project cost
Economic Value Added (EVA) • • • •
EVA
Can EVA evaluate projects? EVA = NOPAT  (Investment x WACC) Project Value =Investment +PV of future EVAs PV of future EVAs = project’s NPV
Net Book Value WACC = 15% pa EBIT (1t) = NOPAT
0
1
2
3
4
1,100,000 880,000 660,000 440,000 220,000
5

56,800 163,300 163,300 163,300 163,300 Capital charge (Open Book value x WACC)15% 165,000 132,000 99,000 66,000 33,000 EVA 108,200 31,300 64,300 97,300 130,300 Tax = 29%
BV start of year (Dpn 20% pa SL)
PV of EVAs = NPV
92,272
1,1m /1,15
0,88m 0,66m 0,44m /1,153 Etc. /1,152
0,22m
Does EVA agree with NPV? • NPV after tax = PV of EVAs NPV 0 Cost 1,100,000 Cash flows Taxation 29% Net Cash Flows 1,100,000 Tax Wear & Tear 20%pa SL Net present value 92,272
1
2
3
4
5
300,000 450,000 450,000 23,200 66,700 66,700 276,800 383,300 383,300 220 000 220 000 etc.
450,000 66,700 383,300
450,000 66,700 383,300
Tax = (Cash flow  Depreciation) x tax rate
• What about ROA?
Year Net cash flow after tax & W&T BV start of year (Dpn 20% pa SL)
ROA (based on beginning of year book value)
1
2
3
0,0568m 0,1633m etc. 1,1m 0,88m 0,66m
5%
19%
25%
4
5
0,44m 0,22m
37%
74%
EVA Cash flows considerations • Estimation of future cash flows • After tax cash flows = consider tax issues • Beginningofproject cash flows – Cost of project = cash outflow – What about depreciation/wear and tear? – Sale/recouping existing equipment (Residual value and recoupment tax )? – Working capital requirements?
Tax Effects  Introduction Depreciation deduction Deduction from taxable income Tax Value Cost less tax deductions to date Effect on Cash Flow Net operating income x (1tax rate) Deduction x tax rate (Tax saving)
DEPRECIATION DEDUCTIONS AND CASH FLOW Cost of Plant Rm Depreciation Allowance Tax rate
120.0 20% 30% Don't Buy
Operating Income
Assume that the project does not result in an increase in cash flow in year 1.
Buy
Diff.
100
100
0
0
24
24
TAXABLE INCOME
100
76
24
CASH FLOW  Tax due
30
22.8
7.2
Depreciation deduction
Alternative Depreciation x tax rate
Depreciation
24
Tax rate
30%
Cash flow
7.2
Sale of equipment: Tax effects • HC>SP>Tax value = W&T Recoupment
Tax cash flow = (sp (up to cost)tv) x tax rate • Tax value > Sales Price = Scrapping allow.
Tax cash flow = (tvsp) x tax rate • Capital Gains Tax: SP>HC x 50% x tax rate
SA Tax Depreciation rates p.a. • Mnfg Equip. [s12C]  20% SL or 40% in Yr1 & 20% SL in Yrs 24 • Mnfg bdgs [s13]  5% SL • M/V & other assets [s11(e)]  20% SL • SARS issued recommended economic lives for various categories of assets • Cost of P&E supplied by connected person is limited to original cost to that person
Capital Gains Tax Capital Gains Tax on Disposal of Asset Machinery which cost R600000 on 1 October 1999, was sold for R900000 on 1 October 2002 Proceeds Cost Time apportionment
900,000 [1 October 1999] To 1/10/2001 300,000 0.6667
600,000 200,000 2/3yrs
Time apportionment base cost*
800,000
Capital Gain Or 1/3 of Cap profit of R300 000
100,000
Tax
29%
29,000
* The base cost could also be the market value at 1 October 2001 or 20% of the proceeds.
Recoupment & Capital Gains Tax • Assume F/A cost of R1m and TV of R0,6m. The selling price is R1,3m. Rm 1.3
Capital Gain Recoupm ent
1.0 0.6
Proceeds Cost Tax value
• Cash flow effects are: Tax effects Amount Inclusion rate Taxable Tax rate Tax Recoupment 400,000 100% 400,000 29% 116,000 Capital Gain 300,000 50% 150,000 29% 43,500 700,000 159,500
Relevant revenues & costs  some rules. • • • • • • • • •
•
Only include Incremental cash flows Use future aftertax cash flows Ignore Sunk costs Opportunity costs  foregone cash flows New product lines may have negative/positive effects on existing lines Evaluate all alternatives Ignore all Allocated costs Ignore Financing charges (avoid double counting). Working capital – Net incremental – Changes, not level – Separate accounting from cash flows Separation of financing and investment decision
Working Capital Income Statement
Expense
S A L ES CO S T O F S A LE S
10000000 4500000
O P E N IN G S TO C K P URCHA S E S C L O S IN G S TO C K G R O S S PR O F IT
0 6000000 1 5 0 0 0 0 0 5500000
Cash out flow
Working Capital In v e s tm e n t in w o rk in g c a p ita l c h a n g e s a c c o u n tin g e a rn in g s to c a s h flo w s
F r o m A c c o u n tin g 1
2
S a le s
1 2 ,0 0 0 .0 0
1 2 ,0 0 0 .0 0
C o s t o f S a le s O p e n in g in v e n to ry P u rc h a s e s C lo s in g in v e n to ry
8 ,0 0 0 .0 0 9 ,6 0 0 .0 0 1 ,6 0 0 .0 0
8 ,0 0 0 .0 0 1 ,6 0 0 .0 0 8 ,0 0 0 .0 0 1 ,6 0 0 .0 0
4 ,0 0 0 .0 0
4 ,0 0 0 .0 0
1 2 ,0 0 0 .0 0 8 ,0 0 0 .0 0
1 2 ,0 0 0 .0 0 8 ,0 0 0 .0 0
4 ,0 0 0 .0 0
4 ,0 0 0 .0 0
Y ear
0
G ro s s p ro fit T o C a s h flo w s S a le s C o s t o f s a le s In v e s tm e n t in in v e n to ry * In v e s tm e n t in d e b to rs #
1 ,6 0 0 .0 0 2 ,0 0 0 .0 0 3 ,6 0 0 .0 0
* T h e in v e s tm e n t in in v e n to ry is a s s u m e d to ta k e p la c e a t th e b e g in n in g o f th e p ro je c t. # T h e in v e s tm e n t in d e b to rs w ill o c c u r in th e firs t 6 0 d a y s b u t is a s s u m e d to ta k e p la c e a t th e b e g in n in g o f th e p ro je c t.
Inventory  Changes Sometimes future inventory levels are stated as a percentage of sales. The cash flows are represented as changes in the inventory levels.
Inventory as a percentage of Sales Sales Inventory Cash flow
R000s 10%
1
2
3
15,000
18,000
9,000
1,500
1,800
900
(1,500)
(300)
900
Post Audits • What are post audits? – Formal assessment and comparison of actual returns achieved for specific projects as compared to projected returns.
• Advantages – Lessons for management. Identify critical factors and ensures focus on achieving projected cash flows
• Disadvantages – Sponsors may find risks excessive and reduce investment – Difficulties in separating project cash flows from other business cash flows
Modified IRR(MIRR) • NPV  assumes reinvestment at WACC • IRR  assumes reinvestment at the IRR • MIRR  Reinvestment cash flows at WACC to end of project  Discount FV (End value) to Zero PV to find MIRR
Example: Normal IRR Year Project E Project F E F Cost of Capital
IRR IRR
0
1
2
100.00 100.00
20.00 80.00
20.00 50.00
3 Total 100.00 140.00 10.00 140.00
14.2% 26.0% But, assumes reinvestment at IRR 10.0%
If we compare IRRs than the second project is much more attractive and would be selected. However, comparing IRRs may overstate the return as the IRR method assumes reinvestment at the IRR. This may be an unreasonable assumption.
MIRR â€“ Reinvestments at WACC (10%) What happens if we assume that cashflows are reinvested at the cost of capital?
Reinvestment at Cost of Capital Project E
0
1
2
100.00
20.00
20.00
80.00
50.00
100.00 Project F
100.00
100.00 24.20 20(1,1)2 20(1,1) 22.00 FV @ WACC 146.20
100.00 Project E 146,2/1,1353 = PV R100 100.00 Project F 161,8/1,1743 =PV R100 100.00 E F
MIRR MIRR
3
0 0
13.5% Prev 14,2% 17.4% Prev 26% If we assume reinvestment at the cost of capital, then the relative return of the second project is reduced significantly. As this project has significant cash flows early on, changing the reinvestment assumption can make a large difference to the expected return.
10.00 96.80 55.00 FV @ WACC 161.80 0 0
146.20 161.80
Reinvests Gives actual returns return/incre ase in wealth At WACC Increase in wealth/net flow
Caters for timevalue of money Discounts at WACC
Accepts projects when
Discount cash flows In IRR (%)
Required period met IRR>RRR
Not No. Ignores consider flows after ed PP Actual return = At IRR IRR
ARR
Not at all No tax
ARR>RRR
Average return Ignored
CAPM
In Market Return>RRR Required return At market return (%) return
Technique
NPV
Payback period IRR
Positive NPV
Caters for different initial outlay
Caters for riskiness of project
Technique
Caters for project period
NPV
Use Value chain Use NPV Index
Payback period
Only to payback
Yes, to payback In soonest payback
IRR
Part of IRR
Part of IRR
ARR
In average return Part of ARR
Compare to RRR
CAPM
Part of actual return
In project Beta Use when bus. Risk is equal
Part of actual return
WACC must be adjusted
Compare to RRR
Class example – Tax effects Firm has a WACC of 15% pa and can replace an existing machine with an advanced model: Existing Advanced • Cash cost price (SL Dpn; W&T SL 3 yrs) R100 000 R150 000 Age of machine 3 years old New • Total estimated useful life 5 years 5 years • Residual value at present R 60 000 N/A (new) • Residual value in two years time R 20 000* R110 000 • Residual value in five years time N/A R 30 000 • Tax value deductible end of next year R 25 000 Gross revenues per annum R 60 000 R 90 000 Variable cost of revenues per annum R 30 000 R 40 000 Fixed production cost per annum R 20 000** R 16 000 • Additional working capital required to end N/A R 10 000 • * Same as estimated residual at acquisition • ** Excluding depreciation
• The full purchase price of the advanced machine and additional working capital will be borrowed at 10% pa and repaid in three annual instalments of R64 340 pa. • SARS has a one year taxation time lag and normal tax rate is 30%. Ignore VAT. All cash flows occur at the end of each year unless otherwise indicated. • REQUIRED: NPV over next 2 years of every available option.
Solution: NPV PV Existing machine Advance mach. • After tax WACC = 15% C/Flow NPV C/Flow NPV • Yr 0 Opport./Cost+WCap/Proceeds 1 60 000 60 000 160 000* 160 000 • Yr 2 Tax/Saved Recoup.(6025)30%,756110 500 7 939 • Yr 2 Tax on W&T 25x,3 &150/3x,3 ,7561 7 500 5 671 15 000 11 342 • Yr12 Profit p.a. (603020)=10 1,6257 20 000 16 257 • Yr12 Profit p.a.(904016**)=34 1,6257 68 000 55 274 • Yr2 Sale machines 20 & 110 ,7561 20 000 15 122 110 000 83 171 • Yr2 Recover incremental w/cap ,7561 10 000 7 561 • Yr23 Tax on profit 10 & 34x,3 1,4136 6 000 4 241 20 400 14 419 • Yr3 Tax saved W&T 150/3x,3 ,6575 15 000 9 863 • Yr3 Tax recoup.20x,3&(11050),3,6575 6 000 3 945 18 000 11 835 23 197
 19 043
* Cost of machine R150000 plus working capital R10 000 = R160 000 • • • •
Yr 0 Proceeds
PV
Discontinue C/Flow NPV
1
60 000 10 500
60 000 Yr 2 Tax/Saved Recoup.(6025)30% ,7561  7 939 52 061 NB: Compare lease and buy option cash flows at the after tax rate of debt
Ch 9  Further Cap. Bud. issues • Evaluate projects with unequal economic lives  Equivalent annual costs • Adjust for inflation in cap budgeting analyses • Rank/select projects under capital rationing • Include effects of tax losses in decisions • Determine optimal economic lives & replacement time • Strategic options in project evaluation • Methods used in practice  Theory and Practice
Projects with Unequal Econ. Lives â€˘ NPVs are not comparable Projects with Unequal Lives Cost of Capital
14%
0
1
2
3
4
5
6
Project X R000s
(5,200) 2,800 2,800
2,800 Unequal lives
Project Y R000s
(8,000) 2,500 2,500
2,500 2,500 2,500 2,500
Project X Project Y
1,301 1,722
NPV NPV
Over 3 years Over 6 years. Which one? What if X duplicated?
If there is an opportunity to reinvest in a similar project X in 3 years time, then; Project X R000s (5,200) 2,800 2,800 2,800 Reinvestment (5,200) 2,800 2,800 2,800 (5,200) 2,800 2,800 (2,400) 2,800 2,800 2,800 Project X
NPV
2,178 [If an opportunity exists to reinvest, select X.]
Projects with Unequal Lives • NPV of 2 x X was comparable with 1xY • Can also use Equivalent Annual NPV (Annuities) – NPV X 1301/∑1/1,143=1301/2,322 = 0,5603m – NPV Y  1722/∑1/1,146=1722/3,889 = 0,4428m • Not suitable for independent or nonrepeatable projects
Equivalent Annual Costs • How does one account for changes in technology? • Can risk be minimised by choosing smaller projects? • What are inflation and currency effects on the cost of new equipment?
• One can convert capital costs into Equivalent Annual costs,e.g.: X = Invest/∑1/1,143= 5,2m/2,322 = 2,239m Y = Invest/∑1/1,146 = 8m/3,889 = 2,057m • Further adjustments required for capital tax allowances (will reduce real cost of F/assets) PTO
Capital Budgeting and Inflation • Inflation effects may be material! Why?
• Disc rate21%=Rf8%+Risk6%+Inflation7% • Nom. rate =(1+Real rate)(1+Inflation rate)1 • If the expected inflation rate is 7% and the real rate is 4%, then the nominal (quoted) rate is: (1,04 x 1,07)1= 11,3%
Capital Budgeting no inflation adjust. NO ADJUSTMENT FOR INFLATION COST COST OF CAPITAL INFLATION REAL RETURN YEAR
60 m Dpn SL 3 years 16.6% 10.0% 6.0% 1
CASH FLOWS 14.00 Tax saving  Depr. R20x0,4 tax 8.00 NET 22.00 RATE 1/1,166 0.86 Present Value 18.87 PRESENT VALUE COST NPV Reject project
53.45 60.00 (6.55)
2 15.00 8.00 23.00 0.74 16.92
3 20.00 8.00 28.00 0.63 17.66
Future cash flows do not include price adjustments due to inflation. Yet the discount rate is a nominal rate.
Cap. Bud.: C/Flows inflation adjusted CASH FLOWS ADJUSTED FOR INFLATION COST COST OF CAPITAL INFLATION REAL RETURN YEAR
60 m Dpn SL 3 years 16.6% 10.0% Tax rate 6.0% 1
2
CASH FLOWSAdded 10% Infl.15.4014x1,1 Tax saving  Depr.R20x0,4 tax 8.00 NET 23.40 Discount rate 1/1,166 0.86 Present Value 20.07 PRESENT VALUE COST Accept project NPV
61.14 60.00 1.14
40%
18.1515x1,12 8.00 26.15 0.74 19.23
3 26.62 8.00 34.62 0.63 21.84
Cash flows adjusted for inflation by multiplying real cash flows by t (1+inflation rate) . The tax saving due to the depreciation allowance is based on historical cost, and so will not change.
CAPITAL RATIONING PROJECT
The Company should select Projects A,B,C, D and reject E. Yet the firm is only able to invest 9m due to capital rationing. Why? PTO!
IRR
Rm
Rm
Each
A B C D E
28% 21% 20% 18% 12%
Cum
5 4 5 3 5
5 9 14 17 22
Note: Projects have different investments, yet IRR caters for this element (NPV does not â†’ PI)
COST OF CAPITAL
15%
Why does Capital Rationing occur? • Hard/Tough Capital Rationing – Capital Markets. Does this mean capital markets are not efficient? Cash shortage/High interest rates/High Inflation
• Soft Capital Rationing – Use of capital limits to ensure subsidiaries prioritise investments. Capital limits ensures discipline in relation to investments by lower level management.
Capital Rationing Rules • Maximise the total NPV subject to the capital constraint. • Use the Profitability Index to rank projects if projects are divisible • Why? The PI measures the return relative to cost.
Profitability Index (BenefitCost Ratio) Evaluates projects with diff. investments • A project’s PI measures the return of a project relative to cost • PI = Present Value/Cost – If PI > 1 = Accept the project – If PI < 1 = Reject the project
Capital Rationing Assume capital constraint = Project 0 1
15 m 2 NPV
A B C
15 25 22
15 8 7
PI =(23,7+15)/15
30 4 6
Note. PI = (NPV+Cost)/Cost =(23,7+15)/15 = 2,58 12% Cost of Capital =
Combined NPV = As compared to A alone
31.4 23.7
PI
23.7 2.583 , 15.5 2.938 , 15.9 3.271 ,
Assessed Tax Losses Existing products earn R5mpa +New
Cash inflow is R5mpa
ASSESSED LOSSES Rm
Assume Assessed Loss = Other Product Lines If the Assessed Loss =
Rm
3.5 or
10.0
5.0 3.5
The tax loss should be set off against income from existing products. The effect on the new project is zero.
If Assessed Loss =
10.0
Year Cash Flows from new project Tax 30% x R5m from new project ? Tax 30% x R5m from existing products
1 5.0 
After tax cash flow
5.0
2 5.0 1.5 1.5 2.0
Assessed Tax Losses Answer to ?
The taxinyear 2, refers to the taxonthe cashflows of the newproject andthe tax that the firmis required to pay on the cash flows fromexisting products as the effect of utilising the loss inyear 1, is that the firmis not able to use the tax loss to save tax inyear 2 onthe existing products. If no tax loss, then the tax for the new project would be as follows; 1 Yr Cash flows 5.0 Tax 1.5 3.5 Total Tax for new project
2 5.0 1.5 3.5
3.0
This is the same as before but the timing of using the tax loss is different. There is value in being able to use the tax loss at an earlier stage.
Optimal Economic Lives • Abandonment Value & Continuing evaluation of projects – Compare a project’s economic value (PV of future cash flows) to its abandonment value
• Replacement timing – Use Equivalent Annual Cost (EAC) to determine the optimal time to replace assets
Replacement timing • Equivalent Annual Cost (EAC) – Asset should be replaced end of 4 years. WACC = 16% pa Equivale nt Annual Cos ts  Re place m e nt Tim ing 7,800
7,758
7,700
7,642
7,600
7,543 7,500
7,463
7,500 7,419 7,372
7,400
7,404 7,355 7,367
7,300 7,200 7,100 1
Yrs 1 2 3 4 5
2
EAC PV Factor 7,500 0.862 7,419 1.605 7,372 2.246 7,355 2.798 7,367 3.274
3
4
5
6
7
8
9
10
@16% 0 1 2 3 4 5 NPV 6,466 (20,000) 15,700 (outflows) and remaining inflows 11,909 (20,000) (2,300) 13,555 16,556 (20,000) (2,300) (2,645) 11,538 (increasing mtnce cost) 20,582 (20,000) (2,300) (2,645) (3,042) 9,624 24,122 (20,000) (2,300) (2,645) (3,042) (3,498) 7,787
Strategic (Real) Options • Real NPV = NPV + Value of Embedded options Examples
• • • • • • • • • • •
Flexibility of Process: Different input mixes to produce same output The Option to abandon the project  exit values The Option to Expand the project Temporary Closure Termination The ability to delay the project Leasing structures Research & Development availability Exploration to reduce uncertainty Sequencing of Investments Taxation benefits
Capital Budgeting: Theory vs Practice • • • • • •
Which methods are used in practice? Trends Risk Appraisal Firm Size Inflation, Tax & Postcompletion audits Relative performance of DCF firms
What information is required? E.G.: Capital Budgeting in the Hotel Industry • • •
• • •
Economic Overview [ demography, tourism, data of occupancy and room rates, hotel types] Site Evaluation [ size,nature of area, transport, distance to attractions/ draws, climate and location of competitors] Competitive market supply [review of local hotels, tourist boards, hotel tariffs, market reports, tour operators] – Total hotel supply [hotels, rooms, grade] – Potential changes in the supply – Primary competitive hotel supply [facilities, tariffs, conference facilities, occupancy rates] – Revenue from restaurants / bar facilities /functions – Input costs (electricity, laundry services, reception, cleaning, etc) Demand for accommodation/Corporate conferences/tourist/airline crew Taxation ( building and plant depreciation allowances) Terminal value (may be significant if hotel is in prime area. There are cases of older hotels being redeveloped into prime residential units or a head office)
Comprehensive class example
Equipment cost is R350 000 for 3 mutually exclusive projects (A,, B & C). Useful lives of the equipment equal that of the projects, with residual values of Nil. The company favours project C with the highest accounting profit in year 3, when a higher share price will be required. The following information is available: Year Proj A Proj B Proj C
Undiscounted cash flows (R'000) year 0 to 8 0 1 2 3 4 350 100 110 104 112 350 40 100 210 260 350 200 150 240 40
NPV % 5 138 160 
6 160 
7 180 
8 
27,5 26,4 33,0
The cost of capital is 20% and depreciation is allocated on a straightline. Ignore taxation and: a) Calculate the payback period for each project. ( 5) b) Calculate the accounting rate of return for each project. ( 8) c) Calculate the NPV of the three projects. ( 8) d) Use the NPV calculations in (c) and employ one other appropriate discount rate to calculate (by interpolation) the estimated IRR of the three projects( 6) e) Discuss the results in (a) and (b) above and indicate, with supporting calculations, which project should be undertaken. (19) f) Show how the answer in (b) above would change if project A had a disposal value at the end of its useful life of R75 000. ( 4) (England & Wales 1981 amended)
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a) Payback period for each project  ie. time taken to repay original outlay of R350 000 in R’000. Undiscounted cash flows Project A Project B Project C Cash in first 3, 3 and 2 years 314 350 350 _ _ Cash in year 4 36/112 36 Investment 350 350 350 Payback period (undiscounted) 3,32 yrs 3 yrs 2 yrs Best Discounted (20%) cash flows Project A Project B Project C Cash in first 5, 4 and 2 years 328,2 348,8 269,5 yr 5 1,2 yr 3 80,5 Cash in year 6 (21,8/52,8=0,4 yrs) 21,8 Investment 350 350 350 Payback period (discounted) 5,4 yrs 4,02 yrs 2,6yrs Best % of undiscounted payback 163% 134% 130% Discounted payback periods are more appropriate (timevalue of money).
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b) Accounting rate of return Project (R’000) Total cash flow Less: Total depreciation Total accounting profit Project life (years) Average profit per annum (1) Average capital employed 350/2 (2) Accounting rate of return (1)/(2) ARR as Average profit/Investment (R375)
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c) Net present value calculations: Year 20% Project A PV 0 1,00 (350) (350,0) 1 0,83 100 83,0 2 0,69 110 75,9 3 0,58 104 60,3 4 0,48 112 53,8 5 0,40 138 55,2 6 0,33 160 52,8 7 0,28 180 50,4 NPV at 20% 81,4 Ranking 1
A 904 350 554 7 79 175 45% 22,5%
Project B PV (350) (350,0) 40 33,2 100 69,0 210 121,8 260 124,8 160 64,0 62,8 3
B C 770 630 350 350 420 280 5 4 84 70 175 175 48% Best 40% 24% Best 20% Project C (350) 200 150 240 40
PV (350,0) 166,0 103,5 139,2 19,2
77,9 2
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d) IRR (using interpolation) (Provide input data when using financial calculators) Year 25% Project A PV Project B PV Project C 0 1,00 (350) (350,0) (350) (350,0) (350) 1 0,8 100 80,0 40 32,0 200 2 0,64 110 70,4 100 64,0 150 3 0,512 104 53,3 210 107,5 240 4 0,41 112 45,9 260 106,6 40 5 0,328 138 45,3 160 52,5 6 0,262 160 41,9 7 0,21 180 37,8 NPV at 25% 24,6 12,6 NPV at 20%
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81,4
62,8
Effect of 5% 56,8 50,2 % to 0NPV (5%x24,6/56,8) 2,2 (5%x12,6/50,2) 1,3 5x45/33 Estimated IRR 27,2% (25+2,2) 26,3% (25+1,3) Ranking 2 3
PV (350,0) 160,0 96,0 122,9 16,4
45,3 77,9
33,4 6,8% 31,8%(25+6,8) 1
e) The strengths and weaknesses of various techniques The Net Present Value appraisal method is recommended and reveals that project A is marginally better than project B. However, the uncertainty of the cash flow estimates of projects A and C should be considered. The payback method is easy to calculate, understand and indicates how long the investment will be at risk. It does not measure profitability or increase in investor wealth. Project C has the shortest payback period and A has the longest. However, the cash flows of A last much longer than those of C, which may make A more profitable in the long run.
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Suggested solution
The accounting rate of return gives a measure of relative project profitability by comparing the average accounting profit per annum to come from the project with the average capital employed in it. It is relatively easy to understand, measures profitability of returns compared with outlay and can show whether the firm's target return on capital employed is achieved. It does not regard the timing of project returns and ignores the fact that cash received at an early stage is more valuable than the same cash received in a few years time. Project C returns cash very quickly compared with project B, but this effect is lost in the process of averaging profits. Thus B has a higher ARR than C even though its IRR (see later) is lower. The ARR is a relative rate of return, rather than an absolute measure of gain in wealth. All rateofreturn methods ignore the size of the project. The NPV and IRR techniques discount all future cash flows to equivalent present values. The NPV method gives the best estimate of the total increase in wealth accruing to the shareholders if the project is accepted and should be reflected in an increased market value of the shares. The IRR will normally provide the same result as the NPV and ignores the absolute gain in wealth. Project C has the highest IRR, but although the original outlay is as high as the other two projects, it returns most of that outlay after one year and thereafter effectively becomes a smaller project with a high rate of return. The IRR incorrectly assumes cash surpluses can be reinvested at the IRR and is not recommended for the comparison of projects. There are many other factors which affect the investment decision, including an assessment of project risk. It may be that A is regarded as riskier than C simply because it takes longer to pay back. It can then be argued that A should be discounted at a higher rate than C. This may give it a lower NPV than C.
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Important: As the projects are of unequal lives it is assumed that cash available from projects B & C can be reinvested at the company's WACC (NPV) of 20% up to the end of year 7.
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If projects A, B and C can be continuously replaced in the future the correct project comparison is to restate the NPV as a perpetual project (Value chain or NPV∞) [NPV/i∑{1/1+i}n]. The company would in such a situation be indifferent between the NPV for the projects and the annuity. Project A B C Life (years) 7 5 4 Discount rate 20% 20% 20% Annuity factor 3,59 2,98 2,58 NPV 81,4 62,8 77,9 Replacement chain (perpetual 113,4 105,4 151,0 Ranking 2 3 1 Or Perpetual annual return (NPV/∑{1/1+i}n) 22,7 21,1 30,2 Ranking 2 3 1
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The equivalent annual annuity method will tend to favour projects with high internal rates of return.
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Suggested solution f) Accounting rate of return for Project A if it had a disposal
value of R75 000 at the end (Both annual depreciation and average investment will change): R’000 Total operating cash flows (as before) 904 [1] Less total depreciation (350 – 75) 275 Total accounting profit 629 Average profit over 7 years (629/7) 89,86 Average investment (350 + 75) / 2 212,50 ARR 42,3% Note: The average investment comprises two parts: R275 reducing to zero over 7 years (average of {275+0}/2 or R137,5) plus R75 outstanding for the whole 7 years. The total average investment is thus: R137,5 + R75 = R212,50) [1] Note, the disposal value of R75 000 is a capital cash flow being the recovery of the capital cost (not operational) hence excluded.
Published on Jul 25, 2008
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