CHAPTER 12
CAPITAL BUDGETING
ALLOCATION/INVESTMENT OF SCARCE CAPITAL TO LONG-TERM
(USUALLY FIXED) ASSETS. THE ASSETS (INVESTMENT OPPORTUNITIES) ARE
ALSO REFERRED TO AS PROJECTS.
A. INDEPENDENT PROJECTS DO NOT AFFECT EACH OTHER’S CASH FLOWS AND
ARE EVALUATED INDEPENDENTLY WITHOUT A NEED FOR RANKING.
B. NON-INDEPENDENT PROJECTS AFFECT EACH OTHER’S CASH FLOWS. THEY
MAY HAVE TO BE COMBINED BEFORE RANKING AND EVALUATION
C. MUTUALLY EXCLUSIVE PROJECTS ARE EXTREME CASES OF NON-INDEPENDENT
PROJECTS.
FROM A SET OF MUTUALLY EXCLUSIVE PROJECTS ONLY ONE
CAN BE ACCEPTED.
FOR EVALUATION THEY HAVE TO BE RANKED.
PROJECT VALUATION
The valuation of a real asset (project) is similar to the valuation of a
security.
VALUE OF A PROJECT = ∑CFt/1+k)t FOR t = 1 THRU n
Where
CFt = Expected risky cash flow in period t
K = Risk-Appropriate Required rate of
Return
n = The project’s cash Flow Producing
Life
AS IN THE CASE OF SECURITY VALUATION, THE VALUE OF
A PROJECT COMPUTED AS ABOVE IS COMPARED TO ITS
REQUIRED CAPITAL ALLOCATION THAT IS, ITS COST
(PRICE) AND AN ACCEPT/REJECT (INVEST/DO NOT
INVEST) DECISION IS MADE
METHODS OF PROJECT EVALUATION
1. ACCOUNTING RATE OF RETURN (ARR)
2. PAYBACK PERIOD (PAYBACK)/ DISCOUNTED PAYBACK
3. NET PRESENT VALUE (NPV)
4. INTERNAL RATE OF RETURN (IRR)/ MODIFIED
INTERNAL RATE OF RETURN (MIRR)
5. PROFITABILITY INDEX (PI)
THE NPV, IRR AND PI METHODS ARE KNOWN AS
DISCOUNTED CASH FLOW (DCF) METHODS
WE WILL USE THE FOLLOWING EXAMPLE TO ILLUSTRATE
THE ABOVE METHODS
CAPITAL PROJECT EVALUATION (EXAMPLE)
NET AFTER-TAX CASH FLOWS (DOLLARS)
YEAR
0
PROJECT A
(100,000)
PROJECT B
(100,000)
1
40,000
10,000
2
40,000
20,000
3
40,000
40,000
4
40,000
70,000
5
40,000
90,000
FOR SIMPLICITY IT WILL BE ASSUMED THAT BOTH
PROJECTS WILL BE DEPRECIATED ON A STRAIGHT
LINE BASIS OVER 5 YEARS TO ZERO SALVAGE VALUE.
NOTE: LATER, IN CHAPTER 13, WE WILL LOOK AT A
COMMONLY USED DEPRECIATION METHOD, MODIFIED
ACCELERATED COST RECOVERY SYSTEM (MACRS). FOR
SUCH PROJECTS THE FIRM USES BENCHMARK ARR OF
28%; BENCHMARK PAYBACK OF 3.5 YEARS;
BENCHMARK DISCOUNTED PAYBACK OF 4.25 YEARS AND
COST OF CAPITAL OF 15%. IT IS ALSO ASSUMED
THAT THERE IS NO CAPITAL RATIONING WE WILL
DISCUSS CAPITAL BUDGETING UNDER CAPITAL
RATIONING LATER.
ACCOUNTING RATE OF RETURN (ARR)
ARR = AVERAGE NET INCOME / AVERAGE INVESTMENT
WHERE
NET INCOME = AFTER-TAX CASH FLOW – DEPRECIATION
STRAIGHT-LINE DEPRECIATION
=(INITIAL COST–EXPECTED SALVAGE VALUE)/(EXPECTED USEFUL LIFE)
AVERAGE INVESTMENT = (INITIAL COST + EXPECTED SALVAGE VALUE)/ 2
IN OUR EXAMPLE,
AVERAGE INVESTMENT
AVERAGE INVESTMENT
DEPRECIATION FOR A
DEPRECIATION FOR B
FOR A = (100000+0)/2 = 50000
FOR B = (100000+0)/2 = 50000
= (100000-0)/5 = 20000
= (100000-0)/5 = 20000
PROJECT A
NET INCOME = 40000 – 20000 = 20000 EACH YEAR
AVERAGE NET INCOME = 20000
AVERAGE INVESTMENT = 50000
ARR = (20000/50000) = 40%
PROJECT B
NET INCOME = -10000; 0; 20000; 50000; 70000 FOR YEARS 1 -5
AVERAGE NET INCOME =(-10000+0+20000+50000+70000)/5 = 26000
AVERAGE INVESTMENT = 50000
ARR = (26000/50000) = 52%
DECISION RULE USING ARR:
ACCEPT IF ARR > BENCHMARK ARR
REJECT IF ARR < BENCHMARK ARR
INDIFFERENT/NEUTRAL IF ARR = BENCHMARK ARR
SINCE BENCHMARK IS 28%,
ACCEPT BOTH A AND B, IF THEY ARE INDEPENDENT (ARR OF A AND B > 28%)
ACCEPT B, IF A AND B ARE MUTUALLY EXCLUSIVE (ARR OF B IS LARGER)
PAYBACK PERIOD
THE PAYBACK PERIOD IS THE TIME IT TAKES TO RECOVER A PROJECT"S
INVESTMENT FROM ITS NET AFTER-TAX CASH FLOWS.
IT IS COPUTED AS
FOLLOWS:
PROJECT A
YEAR
0
1
2
3
NET AFTER-TAX
CASH FLOWS
(100,000)
40,000
40,000
40,000
CUMULATIVE NET AFTER-TAX
CASH FLOWS
(100,000)
( 60,000)
( 20,000)
20,000
PAYBACK PERIOD = 2+ (20,000/40,000)= 2.5 YEARS
THE ABOVE RESULT CAN ALSO BE FOUND AS FOLLOWS:
PAYBACK PERIOD = 100000/40000 = 2.5 YEARS
PROJECT B
YEAR
0
1
2
3
4
NET AFTER-TAX
CASH FLOWS
(100,000)
10,000
20,000
40,000
70,000
CUMULATIVE NET AFTER-TAX
CASH FLOWS
(100,000)
( 90,000)
( 70,000)
( 30,000)
40,000
PAYBACK PERIOD = 3+(30,000/70,000)= 3.4286 YEARS
DECISION RULE USING PAYBACK PERIOD:
ACCEPT IF PAYBACK < BENCHMARK PAYBACK
REJECT IF PAYBACK > BENCHMARK PAYBACK
INDIFFERENT/NEUTRAL IF PAYBACK = BENCHMARK PAYBACK
FOR PROJECTS A AND B,
ACCEPT BOTH, IF THEY ARE INDEPENDENT
(PAYBACK OF A AND B < BENCHMARK PAYBACK 3.5 YEARS)
ACCEPT A, IF THEY ARE MUTUALLY EXCLUSIVE (SHORTER PAYBACK)
DISCOUNTED PAYBACK PERIOD
THE DISCOUNTED PAYBACK PERIOD IS THE TIME IT TAKES TO RECOVER A
PROJECT’S INVESTMENT FROM ITS NET AFTER-TAX CASH FLOWS DISCOUNTED
AT COST OF CAPITAL. IT IS COPUTED AS FOLLOWS:
PROJECT A
YEAR NET AFTER-TAX
CASH FLOWS
0
1
2
3
4
(100,000)
40,000
40,000
40,000
40,000
NET DISCOUNTED
CASH FLOWS
CUMULATIVE NET
DISCOUNTED CASH FLOWS
(100,000)
34,783
30,246
26,301
22,870
(100000)
( 65,217)
( 34,971)
(
8,670)
14,199
DISCOUNTED PAYBACK PERIOD = 3+ (8670/22,870)= 3.3791 YEARS
PROJECT B
YEAR
0
1
2
3
4
5
NET AFTER-TAX
CASH FLOWS
(100,000)
10,000
20,000
40,000
70,000
90,000
NET DISCOUNTED
CASH FLOWS
CUMULATIVE NET
DISCOUNTED CASH FLOWS
(100,000)
8,696
15,123
26,301
40,023
44,746
(100000)
( 91,304)
( 76,181)
( 49,880)
( 9,857)
34,889
DISCOUNTED PAYBACK PERIOD = 4+ (9857/44746)= 4.2203 YEARS
DECISION RULE USING DISCOUNTED PAYBACK PERIOD:
ACCEPT IF DISCOUNTED PAYBACK < BENCHMARK DISCOUNTED PAYBACK
REJECT IF DISCOUNTED PAYBACK > BENCHMARK DISCOUNTED PAYBACK
INDIFFERENT/NEUTRAL IF DISCOUNTED PAYBACK = BENCHMARK
FOR PROJECTS A AND B,ACCEPT BOTH, IF THEY ARE INDEPENDENT
(DISCOUNTED PAYBACK OF A AND B < BENCHMARK DISCOUNTED
PAYBACK 4.25 YEARS)
ACCEPT A, IF THEY ARE MUTUALLY EXCLUSIVE (SHORTER DISCOUNTED
PAYBACK)
NET PRESENT VALUE (NPV)
THE NET PRESENT VALUE OF A PROJECT IS DEFINED AS:
PV OF CASH INFLOWS - PV OF CASH OUTFLOWS
WHERE PVS ARE COMPUTED USING THE COST OF CAPITAL
PROJECT A
NPV =-100,000+ 40,000 + 40,000 + 40,000 + 40,000 + 40,000
-------------------------2
3
4
1.15
(1.15)
(1.15)
(1.15)
(1.15)5
= 34,086.2039
NPV can be more easily computed using a financial calculator.
PROJECT B
NPV =-100,000+ 10,000 + 20,000 + 40,000 + 70,000 + 90,000
-------------------------1.15
(1.15)2 (1.15)3
(1.15)4 (1.15)5
= 34,887.8082
NPV can be more easily computed using a financial calculator.
DECISION RULE USING NPV:
ACCEPT IF NPV > 0
REJECT IF NPV < 0
INDIFFEREN/NEUTRAL IF NPV = 0
FOR PROJECTS A AND B,
ACCEPT BOTH, IF THEY ARE INDEPENDENT (NPV >0)
ACCEPT B, IF THEY ARE MUTUALLY EXCLUSIVE (HIGHER POSITIVE NPV)
INTERNAL RATE OF RETURN (IRR)
THE IRR OF A PROJECT IS THE DISCOUNT RATE THAT MAKES
PV CASH INFLOWS = PV CASH OUTFLOWS, THAT IS, NPV = 0
IT IS THE EXPECTED RATE OF RETURN OF THE PROJECT
COMPUTATION OF IRRS CAN BE BY
1. TRIAL AND ERROR USING INTERPOLATION, BUT IT IS TEDIOUS
2. USING NPV PROFILES (COMPUTE NPVS AT DIFFERENT DISCOUNT RATES
AND PLOT THESE NPVS AGAINST THE RATES AS A GRAPH (NPV
PROFILE). THE INTERSECTION OF THE NPV PROFILE WITH THE X-AXIS
IS THE IRR.
3. USING A FINANCIAL CALCULATOR (EASY)
PROJECT A
USING A FINANCIAL CALCULATOR, IRR = 28.6493%
PROJECT B
USING FINANCIAL CALCULATOR, IRR = 24.8059%
DECISION RULE USING IRR:
ACCEPT IF IRR > COST OF CAPITAL
REJECT IF IRR < COST OF CAPITAL
INDIFFERENT/NEUTRAL IF IRR = COST OF CAPITAL
FOR PROJECTS A AND B,
ACCEPT BOTH, IF THEY ARE INDEPENDENT (IRR > COST OF CAPITAL 15%)
ACCEPT A, IF THEY ARE MUTUALLY EXCLUSIVE (HIGHER IRR OF 28.65%)
MODIFIED INTERNAL RATE OF RETURN
TO OVERCOME THE CONFLICT BETWEEN NPV AND IRR WHEN PROJECTS ARE
MUTUALLY EXCLUSIVE, A MODIFIED INTERNAL RATE OF RETURN CAN BE
CALCULATED AND COMPARED WITH THE PROJECTS’ COST OF CAPITAL. THE
MIRR APPROACH HELPS IN SITUATIONS WHERE CONFLICT IS DUE TO TIMING
OF CASH FLOWS.
STEPS TO COMPUTE MIRR
1. FIND THE FUTURE VALUE OF EACH INTERMEDIATE (TIME 1, 2, 3
ETC) CASH FLOWS AT THE END OF THE PROJECT USING THE COST OF
CAPITAL
2. SUM ALL THE FUTURE CASH FLOWS IN STEP 1 AND CALL THE SUM
TERMINAL VALUE (TV) . DO NOT CONFUSE TV WITH TERMINATION
CASH FLOWS WHICH OCCUR UPON TERMINATION OF THE PROJECT. OF
COURSE TERMINATION CASH FLOWS WILL BECOME PART OF TV
3. FIND THE IRR OF THE PROJECT WITH INITIAL INVESTMENT AT TIME
0 (PV) AND TV AT THE END OF THE PROJECT (FV). THIS IS THE
MIRR.
MIRR OF PROJECT A:
TV= 40000*(1.15)4+ 40000*(1.15)3 +40000*(1.15)2 +40000*(1.15)1 +
40000
=269,695.2500
PV=-100,000
MIRR=21.9480%
MIRR OF PROJECT B:
TV= 10000 *(1.15)4+ 20000 *(1.153+40000*(1.15)2+ 70000* (1.15)1 +
90000
=271,307.5625
PV=-100,000
MIRR=22.0935%
UNLIKE IRR, THE MIRR OF PROJECT B IS GREATER THAN THAT OF PROJECT
A, JUST LIKE NPV OF PROJECT B IS GREATER THAN THAT OF PROJECT A.
THUS, IF PROJECTS A AND B ARE MUTUALLY EXCLUSIVE, BOTH NPV AND
MIRR WILL FAVOR PROJECT B OVER PROJECT A, THUS ELIMINATING A
CONFLICT.
PROFITABILITY INDEX (PI)
PI = (PV OF CASH INFLOWS/PV OF CASH OUTFLOWS)
WHERE THE DISCOUNT RATE USED TO FIND THE PVS OF CASH INFLOWS AND
OUTFLOWS IS THE COST OF CAPITAL OF THE PROJECT
PROJECT A
PI = 134086.2039/ 100000 = 1.3409
PROJECT B
PI = 134887.2039/ 100000 = 1.3489
DECISION RULE USING PI:
ACCEPT IF PI > 1
REJECT IF PI < 1
INDIFFERENT/NEUTRAL IF PI = 1
FOR PROJECTS A AND B,
ACCEPT BOTH, IF THEY ARE INDEPENDENT (PI > 1)
ACCEPT B, IF THEY ARE MUTUALLY EXCLUSIVE (HIGHER PI OF 1.3489)
SUMMARY OF CONCLUSIONS
ASSUMPTIONS:
1. NO CAPITAL RATIONING
2. PROJECTS ARE INDEPENDENT
METHOD
PROJECTS
A
BENCHMARK
ACCEPT
B
ARR
40%
PAYBACK
2.5 YEARS
DISCOUNTED PAYBACK 3.3791 YEARS
NPV
34,086.2039
IRR
28.6493%
MIRR
21.9480%
PI
1.3409
52%
28%
3.4286 YEARS 3.5 YEARS
4.2203 YEARS 4.25 YEARS
34,887.8082
0
24.8059%
15%
22.0935%
15%
1.3489
1
BOTH
BOTH
BOTH
BOTH
BOTH
BOTH
BOTH
ASSUMPTIONS:
1. NO CAPITAL RATIONING
2. PROJECTS ARE MUTUALLY EXCLUSIVE
METHOD
PROJECTS
A
ARR
40%
PAYBACK
2.5 YEARS
DISCOUNTED PAYBACK 3.3791 YEARS
NPV
34,086.2039
IRR
28.6493%
MIRR
21.9480%
PI
1.3409
BENCHMARK
ACCEPT
B
52%
3.4286 YEARS
4.2203 YEARS
34,887.8082
24.8059%
22.0935%
1.3489
28%
3.5 YEARS
4.25 YEARS
0
15%
15%
1
B
A
A
B
A
B
B
THUS, CONFLICTS MAY ARISE IF PROJECTS ARE MUTUALLY EXCLUSIVE
BECAUSE OF THE NEED TO RANK AND EVALUATE. HOWEVER, THERE ARE NO
CONFLICTS, IF PROJECTS ARE INDEPENDENT, SINCE THERE IS NO NEED TO
RANK AND EVALUATE.
REASONS FOR CONFLICT AND BEST METHOD IF
THERE IS A CONFLICT
CONFLICTS MAY ARISE DUE TO
1. SCALING DIFFERENCES (ONE PROJECT COSTS MORE THAN THE OTHER)
2. TIMING DIFFERENCES (CASH FLOWS OCCUR EARLIER OR LATER)
WHEN A CONFLICT ARISES , USE NPV METHOD.
WHY?
NPV METHOD IS SUPERIOR, BECAUSE
1. IT USES COST OF CAPITAL FOR DISCOUNTING (REINVESTING)
2. IT GIVES ABSOLUTE CHANGE IN WEALTH
3. IT IS EASIER TO CALCULATE
IRR METHOD IS INFERIOR, BECAUSE
1. IT USES IRR FOR DISCOUNTING (REINVESTING)
2. IT GIVES % CHANGE IN WEALTH
3. IT IS DIFFICULT TO CALCULATE (MULTIPLE IRRS, ETC.)
PI IS ALSO INFERIOR, BECAUSE
IT IS A RATIO, THAT IS, A RELATIVE MEASURE OF WEALTH CHANGE
USING MIRR RESOLVES THE CONFLICT BETWEEN NPV AND IRR, IF THERE ARE
ONLY CASH FLOW TIMING DIFFERENCES. HOWEVER, MIRR MAY NOT RESOLVE
THE CONFLICT, IF THERE ARE SCALING DIFFERENCES. THEREFORE IT IS
ALWAYS BETTER TO USE NPV.