University of the West Indies

Department of Management Studies

MS61T Corporate Finance
Capital Budgeting – Introduction – Chapter 10

1. Capital budgeting decisions involve investments requiring

rather large cash outlays at the beginning of the project and
commit the firm to a particular course of action over a
relatively long period of time. The process is important, as
any decision taken would be both costly and difficult to
reverse.

2. Cash flows are used rather than accounting profits, because

these are the flows that the firm receives and can invest.
Cash flows are better able to correctly analyse the timing of
the benefits and costs of an investment. Accounting profits
can be subjective while cash flows are not.

3. The internal rate of return method indicates the rate of

return that a project should earn to break-even. The
advantages of this capital budgeting decision method are:-

 It is relatively easy to understand and use because it incorporates the

notion of ‘break-even’
 It deals with cash flows rather than accounting profits.
 It recognises the time value of money.
 It is consistent with the firm’s goal of shareholder’s wealth
maximisation.

The disadvantage of the internal rate of return is that:-

 If a series of positive annual cash flows is followed by a series of

negative annual cash flows, the following may occur:
o The IRR may arrive at the wrong accept-reject decision
o There may be multiple IRRs
o There may be no IRR

4. 10-1 $52,125/$12,000 = 4.3438, so the payback is about 4 years.

5. 10-2 NPV = -$52,125 + $12,000(PVIFA12%,8)

= -$52,125 + $12,000(4.9676) = $7,486.20.
Financial calculator: Input the appropriate cash flows into the cash
flow register, input I = 12, and then solve for NPV = $7,486.68.

1
6. 10-3 Let NPV = 0. Therefore,

0 = PMT(PVIFAi,n) - Investment outlay

PVIFAi,n = Investment outlay/PMT
PVIFAi,8 = $52,125/$12,000 = 4.3438.

This is a PVIFA for 8 years, so using Table A-2, we look across the 8
year row until we find 4.3438. In the 16 percent column we find the
value 4.3436. Therefore, the IRR is approximately 16 percent.

Financial calculator: Input the appropriate cash flows into the cash
flow register and then solve for IRR = 16%.

7. 10-4 Project K’s discounted payback period is calculated as follows:

Annual Discounted @12%

Period Cash Flows Cash Flows Cumulative
0 ($52,125) ($52,125.00) ($52,125.00)
1 12,000 10,714.80 (41,410.20)
2 12,000 9,566.40 (31,843.80)
3 12,000 8,541.60 (23,302.20)
4 12,000 7,626.00 (15,676.20)
5 12,000 6,808.80 (8,867.40)
6 12,000 6,079.20 (2,788.20)
7 12,000 5,427.60 2,639.40
8 12,000 4,846.80 7,486.20

$2,788.20
The discounted payback period is 6 + years, or 6.51 years.
$5,427.60
Alternatively, since the annual cash flows are the same, one can divide
$12,000 by 1.12 (the discount rate = 12%) to arrive at CF 1 and then
continue to divide by 1.12 seven more times to obtain the discounted
cash flows (Column 3 values). The remainder of the analysis would be
the same.

8. 10-5 MIRR: PV Costs = $52,125.

FV Inflows:

PV FV
0 1 2 3 4 5 6 7 8
12% | | | | | | | |
|
12,0 00 12,000
12,000 12,000 12,000
12,000 12,000 12,000
13,4 40
15,053
16,859

2
 18,882
21,148
23,686
26,528
52,125 MIRR = 13.89% 147,596

Financial calculator: Obtain the FVA by inputting N = 8, I = 12, PV =

0, PMT = 12000, and then solve for FV = $147,596. The MIRR can be
obtained by inputting N = 8, PV = -52125, PMT = 0, FV = 147596, and then
solving for I = 13.89%.

9. a.
Project A Project B Project C
Year Cash Flow Amt Cash Flow Amt Cash Flow Amt Recovered
Recovered Recovered
1 4,000 4,000 2,000 2,000 10,000 10,000
2 4,000 8,000 8,000 10,000 1,000
3 4,000 10,000 2,000 1,000

b.Payback Period A = 2 + ($2,000 / $4,000) = 2.5 years

Payback Period B = 2 years
Payback Period C = 1 year

The project with the lowest payback period, i.e., Project C.

The payback method is a measure of a project’s liquidity.

10. 10-7 Truck:

NPV = -$17,100 + $5,100(PVIFA14%,5)
= -$17,100 + $5,100(3.4331) = -$17,100 + $17,509
= $409. (Accept)

Financial calculator: Input the appropriate cash flows into the cash
flow register, input I = 14, and then solve for NPV = $409.

Let NPV = 0. Therefore,

$17,100 = $5,100(PVIFAi,5)
PVIFAi,5 = 3.3529
IRR  15%. (Accept)

Financial calculator: Input the appropriate cash flows into the cash
flow register and then
solve for IRR = 14.99%  15%.
3
MIRR: PV Costs = $17,100.

FV Inflows:

PV FV
0 1 2 3 4 5
| 14% | | | | |
5,100 5,100 5,100 5,100 5,100
5,814
6,628
7,556
8,614
17,100 MIRR = 14.54% (Accept) 33,712

Financial calculator: Obtain the FVA by inputting N = 5, I = 14, PV =

0, PMT = 5100, and then solve for FV = $33,712. The MIRR can be
obtained by inputting N = 5, PV = -17100, PMT = 0, FV = 33712, and then
solving for
I = 14.54%.

Pulley:

NPV = -$22,430 + $7,500(3.4331) = -$22,430 + $25,748

= $3,318. (Accept)

Financial calculator: Input the appropriate cash flows into the cash
flow register, input I = 14, and then solve for NPV = $3,318.

Let NPV = 0. Therefore,

$22,430 = $7,500(PVIFAi,5)
PVIFAi,5 = 2.9907
IRR = 20%. (Accept)

Financial calculator: Input the appropriate cash flows into the cash
flow register and then solve for IRR = 20%.

MIRR: PV Costs = $22,430.

FV Inflows:

PV FV

4
 0 1 2 3 4 5
| 14% | | | | |
7,500 7,500 7,500 7,500 7,500
8,550
9,747
11,112
12,667
22,430 MIRR = 17.19% (Accept) 49,576

Financial calculator: Obtain the FVA by inputting N = 5, I = 14, PV = 0,

PMT = 7500, and then solve for FV = $49,576. The MIRR can be obtained by
inputting N = 5, PV = -22430, PMT = 0, FV = 49576, and then solving for
I = 17.19%.

11. a. NPV= -$17,291.42 + $5,000(PVIF12%,1) + $8,000(PVIF12%,2) +

$10,000(PVIF12%,3)
= -$17,291.42 + $5,000(0.8929) + $8,000(0.7972) + $10,000(0.7118)
= -$17,291.42 + $4,464.50 + $6,377.60 + $7,118.00
= $668.68

b. PI = $17,960.10 / $17,291.42 = 1.04

c. To find the IRR we will use the interpolation method.

So, we need one discount rate that gives a positive NPV and
another discount rate that gives a negative discount rate.

At 12% the NPV is $668.68 so try a higher discount rate to

obtain a negative NPV. Try 15%.

NPV@15% = -$17,291.42+ $5,000(PVIF15%,1)+$8,000(PVIF15%,2)+$10,000(PVIF15%,3)

= -$17,291.42 + $5,000(0.8696) + $8,000(0.7561) + $10,000(0.6575)
= -$17,291.42 + $4,348.00 + $6,048.80 + $6,575.00
= -$319.62

12% IRR 15%

-------------------------------------
668.68 $0 -$319.62

12 - IRR = 668.68 – 0__

12 - 15 668.68 – -319.62
5
 12 - IRR = 668.68__
- 3 988.30

12 - IRR = 0.6766
-3

12 - IRR = -2.0298

IRR = 14.0298  14.03%

d. Yes the truck should be purchased, as the NPV is

positive, the PI is greater than 1, and the IRR is greater
than the firm’s required return of 12%.

12. a. NPV V = -$100,000 + $22,611(PVIFA12%,7)

= -$100,000 + $22,611(4.5638)
= -$100,000 + $103,192.08 = $3,192.08

NPV W = -$300,000 + $63,655(PVIFA12%,7)

= -$300,000 + $63,655(4.5638)
= -$300,000 + $290,508.69 = -$9,491.31

b. PI V = $103,192.08 / $100,000 = 1.03

PI W = $290,508.69 / $300,000 = 0.97

c. For V: 0 = -$100,000 + $22,611(PVIFAIRR%,7)

At 12% the NPV is $3,192.08 so try a higher discount rate to

obtain a negative NPV. Try 14%.

NPV@14% = -$100,000 + $22,611(PVIFA14%,7)

= -$100,000 + $22,611(4.2883)
= -$100,000 + $96,962.75 = -$3,037.25

12% IRR 14%

-----------------------------------------
$3,192.08 $0 -$3,037.25

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12 - IRR = 3,192.08 – 0__
12 - 14 3,192.08 – -3,037.25

12 - IRR = 3,192.08__
- 2 6229.33

12 - IRR = 0.5124
-2

12 - IRR = -1.0249

IRRV = 13.0249  13.02%

For W: 0 = -$300,000 + $63,655 (PVIFAIRR%,7)

At 12% the NPV is -$9,491.31 so try a lower discount rate to

obtain a positive NPV. Try 10%.

NPV@10% = -$300,000 + $63,655(PVIFA10%,7)

= -$300,000 + $63,655(4.8684)
= -$300,000 + $309,898.00 = $9,898.00

12% IRR 10%

-----------------------------------------
-$9,491.31 $0 $9,898.00

12 - IRR = -9,491.31 – 0__

12 - 10 -9,491.31 – 9,898.00

12 - IRR = -9,491.31_
2 -19,389.31

12 - IRR = 0.4895
2

12 - IRR = 0.9790

IRRW= 11.021 11.02%

d. Project V should be selected as its NPV is positive,

its PI is greater than 1, and the IRR is greater than the
firm’s cost of capital. Project V could not be accepted as
its NPV is negative, its PI is less than 1, and the IRR is
7
 less than the firm’s cost of capital.

e. No, there is no conflict between the decisions, as both

the NPV and IRR methods gave the same decision, i.e., to
select Project V.

13. a
Printer 1 Printer 2
Year Cash Flow Amt Cash Flow Amt
Recovered Recovered
1 9,000 9,000 1,500 1,500
2 1,100 2,000 1,300 2,500
3 1,300 800
Payback Period 1 = 2 years
Payback Period 2 = 1 + ($1,000 / $1,300) = 1.77 years

b. NPV 1 = -$2,000 + $900(PVIF10%, 1)+$1,100(PVIF10%, 2) +

$1,300(PVIF10%, 3)

= -$2,000 + $900(0.9091) + $1,100(0.8264) +

$1,300(0.7513)

= -$2,000 + $818.19 + $909.04 + $976.69

= $703.92

NPV 2 = -$2,500 + $1,500(PVIF10%, 1) +$1,300(PVIF10%, 2) +

$800(PVIF10%, 3)

= -$2,500 + $1,500(0.9091) + $1,300(0.8264)

+ $800(0.7513)

= -$2,500 + $1,363.65 + $1,074.32 + $601.04

= $539.01

c. Finding IRR for Printer 1:

NPV @ 24% = $123.14 & NPV @ 28% = -$5.55

Note: Even though the NPV @24% gave us $123.14 (which is

not negative), we can still use it to interpolate (thereby
disregarding the $703.92 @10%) because when interpolating,
the closer the NPVs are to zero, the more accurate the
answer is.

8
 24% IRR 28%
--------------------------------------
$123.14 $0 -$5.55

24 - IRR = 123.14 – 0__

24 - 28 123.14 – -5.55

24 - IRR = 123.14__
- 4 128.69

24 - IRR = 0.9569
-4

24 - IRR = -3.8275

IRR1 = 27.8275  27.83%

Finding IRR for Printer 2:

NPV @ 20% = $115.63 & NPV @ 24% = -$25.13

Note: Even though the NPV @20% gave us $115.63 (which is

not negative), we can still use it to interpolate (thereby
disregarding the $539.01 @10%) because when interpolating,
the closer the NPVs are to zero, the more accurate the
answer is.

20% IRR 24%

-----------------------------------------
$115.63 $0 -$25.13

20 - IRR = 115.63 – 0__

20 - 24 115.63 – -25.13

20 - IRR = 115.63__
- 4 140.76

20 - IRR = 0.8215
-4

20 - IRR = -3.2860

9
 IRR2 = 23.2860  23.29%

d. Printer 1 should be chosen as it has the higher NPV and IRR when
compared with Printer 2.

e. No, the NPV for Printer 1 would still be higher than the
NPV of Printer 2 when the discount rate of 16% is used.

14. 10-8 Using a financial calculator:

NPVS = $448.86; NPVL = $607.20.

IRRS = 15.24%; IRRL = 14.67%.

MIRR:
PV costsS = $15,000.
FV inflowsS = $29,745.47.
MIRRS = 14.67%.

PV costsL = $37,500.
FV inflowsL = $73,372.16.
MIRRL = 14.37%.

Thus, NPVL > NPVS , IRRS > IRRL , and MIRRS > MIRRL . The scale
difference between Projects S and L results in IRR and MIRR selecting S
over L. However, NPV favors Project L, and hence Project L should be
chosen.

15. 10-9
a.The IRRs of the two alternatives are undefined. To calculate an IRR,
the cash flow stream must include both cash inflows and outflows.

b. The PV of costs for the conveyor system is -$556,717, while the PV of

costs for the forklift system is -$493,407. Thus, the forklift
system is expected to be -$493,407 - (-$556,717) = $63,310 less
costly than the conveyor system, and hence the forklifts should be
used. (Note: If the PVIFA interest factors are used, then
PVc = - $556,720 and PVF
= -$493,411.)

16.
Project Initial Outlay NPV PI Ranking
1 -$10,000 $4,000 ($4,000 + $10,000) / $10,000 = 1.40 1
2 -$25,000 3,600 ($3,600 + $25,000) / $25,000 = 1.14 2
3 -$35,000 3,250 ($3,250 + $35,000) / $35,000 = 1.09 4
4 -$40,000 2,500 ($2,500 + $40,000) / $40,000 = 1.06 5
5 -$20,000 2,100 ($2,100 + $20,000) / $20,000 = 1.11 3

Based on the PI rankings, we should select all the projects except project 4, as this

10
 combination of projects will give the highest NPV and stay within the budget limit of
$100,000.

17. 10-13
a. Purchase price $ 900,000
Installation 165,000
Inntial outlay $1,065,000

CF0 = -1065000; CF1-5 = 350000; I = 14; NPV = ?

NPV = $136,578; IRR = 19.22%.

b. Ignoring environmental concerns, the project should be undertaken

because its NPV is positive and its IRR is greater than the firm’s
cost of capital.

c. Environmental effects could be added by estimating penalties or any

other cash outflows that might be imposed on the firm to help return
the land to its previous state (if possible). These outflows could
be so large as to cause the project to have a negative NPV, in which
case the project should not be undertaken.

18. 10-14
a. Year Sales Royalties Marketing Net
0 (20,000) (20,000)
1 75,000 (5,000) (10,000) 60,000
2 52,500 (3,500) (10,000) 39,000
3 22,500 (1,500) 21,000

Payback period = $20,000/$60,000 = 0.33 year.

NPV = $60,000/(1.11)1 + $39,000/(1.11)2 + $21,000/(1.11)3 - $20,000

= $81,062.35.

IRR = 261.90%.

b. Finance theory dictates that this investment should be accepted.

However, ask your students “Does this service encourage cheating?”
If yes, does a businessperson have a social responsibility not to
make this service available?

11
19. 10-19

a. At k = 12%, Project A has the greater NPV, specifically $200.41 as

compared to Project B’s NPV of $145.93. Thus, Project A would be
selected. At k = 18%, Project B has an NPV of $63.68 which is higher
than Project A’s NPV of $2.66. Thus, choose Project B if k = 18%.

12
b.

NPV
($)
1,000

90 0

80 0

70 0

60 0

50 0
Pro ject A
400

300

20 0
Project B
10 0 Co st of
Ca pital (%)
5 10 15 20 25 30
-100

-2 00

-300

k NPVA NPVB
0.0% $890 $399
10.0 283 179
12.0 200 146
18.1 0 62
20.0 (49) 41
24.0 (138) 0
30.0 (238) (51)

c. IRRA = 18.1%; IRRB = 24.0%.

e. Here is the MIRR for Project A when k = 12%:

PV costs = $300 + $387/(1.12)1 + $193/(1.12)2

+ $100/(1.12)3 + $180/(1.12)7 = $952.00.

TV inflows = $600(1.12)3 + $600(1.12)2 + $850(1.12)1 = $2,547.60.

Now, MIRR is that discount rate which forces the TV of $2,547.60 in

7 years to equal $952.00:

$952.00 = $2,547.60(PVIFi,7)
MIRRA = 15.10%.
Similarly, MIRRB = 17.03%.

At k = 18%,
MIRRA = 18.05%.
MIRRB = 20.49%.

13
20. 10-21
a. Using a financial calculator, we get:

NPVA = $14,486,808. NPVB = $11,156,893.

IRRA = 15.03%. IRRB = 22.26%.

b.
NPV
(Millions of
Dollars)

80

60

40

Crossover Point = 11.7%

20
IRRS = 22.26%

0
5 10 15 20 25 k (%)
-10 IRRA = 15.03%

The crossover rate is somewhere between 11 percent and 12 percent.

The exact crossover rate is calculated as 11.7 percent, the IRR of
Project , the difference between the cash flow streams of the two
projects.

c. The NPV method implicitly assumes that the opportunity exists to

reinvest the cash flows generated by a project at the cost of
capital, while use of the IRR method implies the opportunity to
reinvest at the IRR. The firm will invest in all independent
projects with an NPV > $0. As cash flows come in from these
projects, the firm will either pay them out to investors, or use them
as a substitute for outside capital which, in this case, costs 10
percent. Thus, since these cash flows are expected to save the firm
10 percent, this is their opportunity cost reinvestment rate.
The IRR method assumes reinvestment at the internal rate of return
itself, which is an incorrect assumption, given a constant expected
future cost of capital, and ready access to capital markets.

21. 10-23 a. Payback A (cash flows in thousands):

Annual
Period Cash Flows Cumulative
0 ($25,000) ($25,000)
1 5,000 ( 20,000)
2 10,000 ( 10,000)
3 15,000 5,000
4 20,000 25,000

14
 PaybackA = 2 + $10,000/$15,000 = 2.67 years.

Payback B (cash flows in thousands):

Annual
Period Cash Flows Cumulative
0 ($25,000) ($25,000)
1 20,000 ( 5,000)
2 10,000 5,000
3 8,000 13,000
4 6,000 19,000

PaybackB = 1 + $5,000/$10,000 = 1.50 years.

b. Discounted payback A (cash flows in thousands):

Annual Discounted @10%

Period Cash Flows Cash Flows Cumulative
0 ($25,000) ($25,000.00) ($25,000.00)
1 5,000 4,545.45 ( 20,454.55)
2 10,000 8,264.46 ( 12,190.09)
3 15,000 11,269.72 ( 920.37)
4 20,000 13,660.27 12,739.90

Discounted PaybackA = 3 + $920.37/$13,660.27 = 3.07 years.

Discounted payback B (cash flows in thousands):

Annual Discounted @10%

Period Cash Flows Cash Flows Cumulative
0 ($25,000) ($25,000.00) ($25,000.00)
1 20,000 18,181.82 ( 6,818.18)
2 10,000 8,264.46 1,446.28
3 8,000 6,010.52 7,456.80
4 6,000 4,098.08 11,554.88

Discounted PaybackB = 1 + $6,818.18/$8,264.46 = 1.825 years.

c. NPVA = $12,739,908; IRRA = 27.27%.

NPVB = $11,554,880; IRRB = 36.15%.

Both projects have positive NPVs, so both projects should be

undertaken.

d. At a discount rate of 5 percent, NPVA = $18,243,813.

At a discount rate of 5 percent, NPVB = $14,964,829.

At a discount rate of 5 percent, Project A has the higher NPV;

consequently, it should be accepted.

15
e. At a discount rate of 15 percent, NPVA = $8,207,071.
At a discount rate of 15 percent, NPVB = $8,643,390.

At a discount rate of 15 percent, Project B has the higher NPV;

consequently, it should be accepted.

g. Use 3 steps to calculate MIRRA @ k = 10%:

Step 1: Calculate the NPV of the uneven cash flow stream, so its FV
can then be calculated. With a financial calculator, enter
the cash flow stream into the cash flow registers, then
enter I = 10, and solve for NPV = $37,739,908.

Step 2: Calculate the FV of the cash flow stream as follows:

Enter N = 4, I = 10, PV = -37739908, and PMT = 0 to solve
for FV = $55,255,000.

Step 3: Calculate MIRRA as follows:

Enter N = 4, PV = -25000000, PMT = 0, and FV = 55255000 to

solve for I = 21.93%.

Use 3 steps to calculate MIRRB @ k = 10%:

Step 1: Calculate the NPV of the uneven cash flow stream, so its FV
can then be calculated. With a financial calculator, enter
the cash flow stream into the cash flow registers, then
enter I = 10, and solve for NPV = $36,554,880.

Step 2: Calculate the FV of the cash flow stream as follows:

Enter N = 4, I = 10, PV = -36554880, and PMT = 0 to solve
for FV = $53,520,000.

Step 3: Calculate MIRRB as follows:

Enter N = 4, PV = -25000000, PMT = 0, and FV = 53520000 to
solve for I = 20.96%.

According to the MIRR approach, if the 2 projects were mutually

exclusive, Project A would be chosen because it has the higher MIRR.
This is consistent with the NPV approach.

16