Solution manual financial management 10e by keown chapter 09

CHAPTER 9

Capital Budgeting Decision
Criteria
CHAPTER ORIENTATION
Capital budgeting involves the decision making process with respect to the investment in
fixed assets; specifically, it involves measuring the incremental cash flows associated with
investment proposals and evaluating the attractiveness of these cash flows relative to the
project's costs. This chapter focuses on the various decision criteria.

CHAPTER OUTLINE
I.

Methods for evaluating projects
A.

The payback period method
1.

The payback period of an investment tells the number of years
required to recover the initial investment. The payback period is
calculated by adding the cash inflows up until they are equal to the
initial fixed investment.

2.

Although this measure does, in fact, deal with cash flows and is easy
to calculate and understand, it ignores any cash flows that occur
after the payback period and does not consider the time value of
money within the payback period.

3.

To deal with the criticism that the payback period ignores the time
value of money, some firms use the discounted payback period
method. The discounted payback period method is similar to the
traditional payback period except that it uses discounted free cash
flows rather than actual undiscounted free cash flows in calculating
the payback period.

4.

The discounted payback period is defined as the number of years
needed to recover the initial cash outlay from the discounted free
cash flows.

226


B.

Present-value methods
1.

The net present value of an investment project is the present value of
its free cash flows less the investment’s initial outlay
n

NPV

=

∑

t =1

FCFt
(1 + k) t

- IO

where:

a.

FCFt =

the annual free cash flow in time period t (this
can take on either positive or negative values)

k

=

the required rate of return or appropriate
discount rate or cost of capital

IO

=

the initial cash outlay

n

=

the project's expected life

The acceptance criteria are
accept if NPV ≥ 0
reject if NPV < 0

b.

2.

The advantage of this approach is that it takes the time value
of money into consideration in addition to dealing with cash
flows.

The profitability index is the ratio of the present value of the
expected future free cash flows to the initial cash outlay, or
n

∑

profitability index =
a.

t =1

FCFt
(1 + k) t
IO

The acceptance criteria are
accept if PI ≥ 1.0
reject if PI < 1.0

b.

The advantages of this method are the same as those for the
net present value.

c.

Either of these present-value methods will give the same
accept-reject decisions to a project.

227


C.

The internal rate of return is the discount rate that equates the present value
of the project's future net cash flows with the project's initial outlay. Thus
the internal rate of return is represented by IRR in the equation below:
n

IO =

∑

t =1

1.

FCFt
(1 + IRR)t

The acceptance-rejection criteria are:
accept if IRR ≥ required rate of return
reject if IRR < required rate of return
The required rate of return is often taken to be the firm's cost of
capital.

2.

The advantages of this method are that it deals with cash flows and
recognizes the time value of money; however, the procedure is rather
complicated and time-consuming. The net present value profile
allows you to graphically understand the relationship between the
internal rate of return and NPV. A net present value profile is simply
a graph showing how a project’s net present value changes as the
discount rate changes. The IRR is the discount rate at which the
NPV equals zero.

3.

The primary drawback of the internal rate of return deals with the

reinvestment rate assumption it makes. The IRR implicitly assumes
that the cash flows received over the life of the project can be
reinvested at the IRR while the NPV assumes that the cash flows
over the life of the project are reinvested at the required rate of
return. Since the NPV makes the preferred reinvestment rate
assumption it is the preferred decision technique. The modified
internal rate of return (MIRR) allows the decision maker the intuitive
appeal of the IRR coupled with the ability to directly specify the
appropriate reinvestment rate.
a.

To calculate the MIRR we take all the annual free tax cash
inflows, ACIFt's, and find their future value at the end of the
project's life compounded at the required rate of return - this
is called the terminal value or TV. All cash outflows, ACOFt,
are then discounted back to present at the required rate of
return. The MIRR is the discount rate that equates the
present value of the free cash outflows with the present value
of the project's terminal value.

b.

If the MIRR is greater than or equal to the required rate of
return, the project should be accepted.

228


ANSWERS TO
END-OF-CHAPTER QUESTIONS

9-1.

Capital budgeting decisions involve investments requiring rather large cash outlays
at the beginning of the life of the project and commit the firm to a particular course
of action over a relatively long time horizon. As such, they are costly and difficult
to reverse, both because of: (1) their large cost and (2) the fact that they involve
fixed assets, which cannot be liquidated easily.

9-2.

The criticisms of using the payback period as a capital budgeting technique are:
(1)
(2)
(3)

It ignores the timing of the free cash flows that occur during the payback
period.
It ignores all free cash flows occurring after the payback period.
The selection of the maximum acceptable payback period is arbitrary.

The advantages associated with the payback period are:
(1)
(2)
(3)

It deals with cash flows rather than accounting profits, and therefore focuses
on the true timing of the project's benefits and costs.
It is easy to calculate and understand.
It can be used as a rough screening device, eliminating projects whose
returns do not materialize until later years.

These final two advantages are the major reasons why it is used frequently.
9-3.

Yes. The payback period eliminates projects whose returns do not materialize until
later years and thus emphasizes the earliest returns, which in a country
experiencing frequent expropriations would certainly have the most amount of
uncertainty surrounding the later returns. In this case, the payback period could be
used as a rough screening device to filter out those riskier projects, which have long
lives.

9-4.

The three, discounted cash flow capital budgeting criteria are the net present value,
the profitability index, and the internal rate of return. The net present value method
gives an absolute dollar value for a project by taking the present value of the
benefits and subtracting out the present value of the costs. The profitability index
compares these benefits and costs through division and comes up with a measure of
the project's relative value—a benefit/cost ratio. On the other hand, the internal
rate of return tells us the rate of return that the project earns. In the capital
budgeting area, these methods generally give us the same accept-reject decision on
projects but many times rank them differently. As such, they have the same general
advantages and disadvantages, although the calculations associated with the
internal rate of return method can become quite tedious and it assumes cash flows
over the life of the life of the project are reinvested at the IRR. The advantages
associated with these discounted cash flow methods are:
(1)
They deal with cash flows rather than accounting profits.
(2)
They recognize the time value of money.

(3)
They are consistent with the firm's goal of shareholder wealth maximization.

229


9-5

The advantage of using the MIRR, as opposed to the IRR technique is that the
MIRR technique allows the decision maker to directly input the reinvestment rate
assumption. With the IRR method it is implicitly assumed that the cash flows over
the life of the project are reinvested at the IRR.

SOLUTIONS TO
END-OF-CHAPTER PROBLEMS
Solutions to Problem Set A
9-1A. (a)

(b)

(c)

(d)

9-2A. (a)

(b)

IO

=

FCFt [PVIF IRR%,t yrs ]

$10,000

=

$17,182 [PVIF IRR%,8 yrs]

0.582

=

PVIFIRR%,8 yrs

Thus, IRR

=

7%

$10,000

=

$48,077 [PVIF IRR%,10 yrs ]

0.208

=

PVIFIRR%,10 yrs

Thus, IRR

=

17%

$10,000

=

$114,943 [PVIF IRR%,20 yrs ]

0.087

=

PVIFIRR%,20 yrs

Thus, IRR

=

13%

$10,000

=

$13,680 [PVIF IRR%,3 yrs]

.731

=

PVIFIRR%,3 yrs

Thus, IRR

=

11%

I0

=

FCFt [PVIFA IRR%,t yrs ]

$10,000

=

$1,993 [PVIFA IRR%,10 yrs ]

5.018

=

PVIFA IRR%,10 yrs

Thus, IRR

=

15%

$10,000

=

$2,054 [PVIFA IRR%,20 yrs ]

4.869

=

PVIFA IRR%,20 yrs

Thus, IRR

=

20%

230

(c)

(d)

9-3A. (a)

$10,000

=

$1,193 [PVIFA IRR%,12 yrs ]

8.382

=

PVIFA IRR%,12 yrs

Thus, IRR

=

6%

$10,000

=

$2,843 [PVIFA IRR%,5 yrs ]

3.517

=

PVIFA IRR%,5 yrs

Thus, IRR

=

13%

$10,000

=

$2,000
(1 + IRR)1

+

$5,000
(1 + IRR)

2

+

$8,000

(1 + IRR)3

Try 18%:
$10,000

=

$2,000(0.847) + $5,000 (0.718) + $8,000 (0.609)

=

$1,694 + $3,590 + $4,872

=

$10,156

=

$2,000 (0.840) + $5,000 (0.706) + $8,000 (0.593)

=

$1,680 + $3,530 + $4,744

=

$9,954

Thus, IRR

=

approximately 19%

$10,000

=

$5,000
$2,000
+
+
(1 + IRR)1
(1 + IRR)2
(1 + IRR)3

=

$8,000 (0.769) + $5,000 (0.592) + $2,000 (0.455)

=

$6,152 + $2,960 + $910

=

$10,022

=

$8,000 (0.763) + $5,000 (0.583) + $2,000 (0.445)

=

$6,104 + $2,915 + $890

=

$9,909

=

approximately 30%

Try 19%
$10,000

(b)

$8,000

Try 30%
$10,000

Try 31%:
$10,000

Thus, IRR

231


(c)

$10,000

=

5

$2,000

t =1

(1 + IRR)t

∑

+

$5,000
(1 + IRR )6

Try 11%
$10,000

=

$2,000 (3.696) + $5,000 (0.535)

=

$7,392 + $2,675

=

$10,067

=

$2,000 (3.605) + $5,000 (0.507)

=

$7,210 + $2,535

=

$9,745

Thus, IRR

=

approximately 11%

NPV

=

Try 12%
$10,000

9-4A. (a)

(b)

(c)

(d)

6

$450,000

t =1

(1 + .09) t

∑

- $1,950,000

=

$450,000 (4.486) - $1,950,000

=

$2,018,700 - $1,950,000 = $68,700

=

$2,018,700
$1,950,000

=

1.0352

$1,950,000

=

$450,000 [PVIFA IRR%,6 yrs ]

4.333

=

PVIFA IRR%,6 yrs

IRR

=

about 10% (10.1725%)

PI

Yes, the project should be accepted.

232


9-5A. (a)

Payback Period = $80,000/$20,000 = 4 years
Discounted Payback Period Calculations:

Year

Undiscounted
Cash Flows

PVIF10%,n

-$80,000
20,000
20,000
20,000
20,000
20,000
20,000

1.000
.909
.826
.751

.683
.621
.564

0
1
2
3
4
5
6

Discounted
Cash Flows

Cumulative
Discounted
Cash Flows

-$80,000
18,180
16,520
15,020
13,660
12,420
11,280

Discounted Payback Period = 5.0 + 4,200/11,280 = 5.37 years.
(b)

(c)

(d)

9-6A. (a)

NPV

=

6

$20,000

t =1

(1 + .10) t

∑

- $80,000

=

$20,000 (4.355) - $80,000

=

$87,100 - $80,000 = $7,100

=

$87,100
$80,000

=

1.0888

$80,000

=

$20,000 [PVIFA IRR%,6 yrs ]

4.000

=

PVIFA IRR%,6 yrs

IRR

=

about 13% (12.978%)

NPVA

=

PI

NPVB

6

$12,000

t =1

(1 + .12) t

∑

- $50,000

=

$12,000 (4.111) - $50,000

=

$49,332 - $50,000 = -$668

=

6

$13,000

t =1

(1 + .12) t

∑

- $70,000

=

$13,000 (4.111) - $70,000

=

$53,443 - $70,000 = -$16,557

233

-$80,000
-61,820
-45,300
-30,280
-16,620
-4,200
7,080


(b)

=

$49,332
$50,000

=

0.9866

=

$53,443
$70,000

=

0.7635

$50,000

=

$12,000 [PVIFA IRR%,6 yrs ]

4.1667

=

PVIFA IRR%,6 yrs

IRRA

=

11.53%

$70,000

=

$13,000 [PVIFA IRR%,6 yrs ]

5.3846

=

PVIFA IRR%,6 yrs

IRRB

=

3.18%

PIA

PIB

(c)

Neither project should be accepted.
9-7A. (a)

Project A:
Payback Period = 2 years + $100/$200 = 2.5 years
Project A:
Discounted Payback Period Calculations:

Year
0
1
2
3
4
5

Undiscounted
Discounted
Cash Flows PVIF10%,n Cash Flows
-$1,000
600
300
200
100
500

1.000
.909
.826
.751

.683
.621

234

-$1,000
545
248
150
68
311

Cumulative
Discounted
Cash Flows
-$1,000
-455
-207
-57
11
322


Discounted Payback Period = 3.0 + 57/68 = 3.84 years.
Project B:
Payback Period = 2 years + $2,000/$3,000 = 2.67 years
Project B:
Discounted Payback Period Calculations:

Year

Undiscounted
Cash Flows PVIF10%,n

Discounted
Cash Flows

Cumulative
Discounted
Cash Flows

0
1

-$10,000
5,000

1.000
.909

-$10,000
4,545

-$10,000
-5,455

2
3
4
5

3,000
3,000
3,000
3,000

.826
.751
.683
.621

2,478
2,253
2,049
1,863

-2,977
-724
1,325
3,188

Discounted Payback Period = 3.0 + 724/2,049 = 3.35 years.
Project C:
Payback Period = 3 years + $1,000/$2,000 = 3.5 years
Project C:
Discounted Payback Period Calculations:
Year
0
1
2

3
4
5

Undiscounted
Cash Flows
-$5,000
1,000
1,000
2,000
2,000
2,000

PVIF10%,n

Discounted
Cash Flows

Cumulative
Discounted
Cash Flows

1.000
.909
.826
.751
.683
.621

-$5,000

909
826
1,502
1,366
1,242

-$5,000
-4,091
-3,265
-1,763
-397
845

235


Discounted Payback Period = 4.0 + 397/1,242 = 4.32 years.

9-8A. NPV9%

NPV11%

NPV13%

NPV15%

Project

Traditional Payback

Discounted Payback

A

Accept

Reject

B

Accept

Reject

C

Reject

Reject

=

8

$1,000,000

t =1

(1 + .09) t

∑

- $5,000,000

=

$1,000,000 (5.535) - $5,000,000

=

$5,535,000 - $5,000,000 = $535,000

=

8

$1,000,000

t =1

(1 + .11) t

∑

- $5,000,000

=

$1,000,000 (5.146) - $5,000,000

=

$5,146,000 - $5,000,000 = $146,000

=

$1,000,000
- $5,000,000
t = 1 (1 + .13)t

=

$1,000,000 (4.799) - $5,000,000

=

$4,799,000 - $5,000,000 = -$201,000

=

8

∑

8

$1,000,000

t =1

(1 + .15) t

∑

- $5,000,000

=

$1,000,000 (4.487) - $5,000,000

=

$4,487,000 - $5,000,000 = -$513,000

9-9A. Project A:
$50,000

=

$10,000
(1 + IRR A )1
+

+

$15,000
(1 + IRR A )

$25,000
(1 + IRR A )

236

4

+

2

+

$20,000
(1 + IRR A )3

$30,000
(1 + IRR A )5


Try 23%
$50,000

=

$10,000(.813) + $15,000(.661) + $20,000(.537)
+ $25,000(.437) + $30,000(.355)

=

$8,130 + $9,915 + $10,740 + $10,925 + $10,650

=

$50,360

=

$10,000(.806) + $15,000(.650) +$20,000(.524)

Try 24%
$50,000

+ $25,000(.423) + $30,000(.341)
=

$8,060 + $9,750 + $10,480 + $10,575 + $10,230

=

$49,095

=

just over 23%

$100,000

=

$25,000 [PVIFA IRR%,5 yrs]

4.00

=

PVIFA IRR%,5 yrs

Thus, IRR

=

8%

$450,000

=

$200,000 [PVIFA IRR%,3 yrs ]

2.25

=

PVIFA IRR%,3 yrs

Thus, IRR

=

16%

Thus, IRR
Project B:

Project C:

9-10A. (a)

(b)

NPV

NPV

=

$18,000

t =1

(1 + .10) t

∑

- $100,000

=

$18,000(6.145) - $100,000

=

$110,610 - $100,000

=

$10,610

=
=
=
=

(c)

10

10

$18,000

t =1

(1 + .15) t

∑

- $100,000

$18,000(5.019) - $100,000
$90,342 - $100,000

-$9,658

If the required rate of return is 10% the project is acceptable as in part (a).

237


(d)

9-11A. (a)

(b)

(c)

$100,000

=

5.5556

=

$18,000 [PVIFA IRR%,10 yrs ]
PVIFA IRR%,10 yrs

IRR

=

Between 12% and 13% (12.41%)

n

ACOFt

t =0

(1 + k) t

∑

n

∑

=

t =0

ACIFt (1 + k) n − t
(1 + MIRR)n

$3,000,000(FVIFA10%10years )

$10,000,000

=

$10,000,000

=

$10,000,000

=

(1 + MIRR )10

MIRR

=

16.9375%

$10,000,000

=

$10,000,000

=

$10,000,000

=

(1 + MIRR )10

MIRR

=

18.0694%

$10,000,000

=

$10,000,000

=

$10,000,000

=

(1 + MIRR )10

MIRR

=

19.2207%

(1 + MIRR)10
$3,000,000(15.937)
(1 + MIRR )10
$47,811,000

$3,000,000(FVIFA12%10years )
(1 + MIRR)10
$3,000,000(17.549)
(1 + MIRR )10
$52,647,000

$3,000,000(FVIFA14%10 years )
(1 + MIRR )10
$3,000,000(19.337)
(1 + MIRR )10
$58,011,000

238


SOLUTION TO INTEGRATIVE PROBLEM
1.

Capital budgeting decisions involve investments requiring rather large cash outlays
at the beginning of the life of the project and commit the firm to a particular course
of action over a relatively long time horizon. As such, they are both costly and
difficult to reverse, both because of: (1) their large cost; (2) the fact that they
involve fixed assets which cannot be liquidated easily.

2.

Axiom 5: The Curse of Competitive Markets—Why It's Hard to Find Exceptionally
Profitable Projects deals with the problems associated with finding profitable
projects. When we introduced that axiom we stated that exceptionally successful
investments involve the reduction of competition by creating barriers to entry either

through product differentiation or cost advantages. In effect, without barriers to
entry, whenever extremely profitable projects are found competition rushes in,
driving prices and profits down unless there is some barrier to entry.

3.

Payback periodA

= 3 years +

Payback PeriodB

=

20,000
years
50,000

110,000
years
40,000

=

=

3.4 years

2.75 years

Project B should be accepted while project A should be rejected.
4.

The disadvantages of the payback period are: 1) ignores the time value of money,
2)ignores cash flows occurring after the payback period, 3)selection of the
maximum acceptable payback period is arbitrary.

5.

Discounted Payback Period Calculations, Project A:
Cumulative
Year
0
1
2
3
4
5

Undiscounted
Cash Flows
-$110,000
20,000
30,000
40,000
50,000
70,000

PVIF12%,n
1.000

.893
.797
.712
.636
.567

Discounted
Cash Flows
-$110,000
17,860
23,910
28,480
31,800
39,690

Discounted Payback Period = 4.0 + 7,950/39,690 = 4.20 years.

239

Cash Flows
-$110,000
-92,140
-68,230
-39,750
-7,950
31,740


Discounted Payback Period Calculations, Project B:

Year
0
1
2
3
4
5

Undiscounted
Cash Flows

PVIF12%,n

-$110,000
40,000
40,000
40,000
40,000
40,000

1.000
.893
.797
.712
.636
.567

Discounted
Cash Flows

Cumulative
Discounted
Cash Flows

-$110,000
35,720
31,880
28,480
25,440
22,680

-$110,000
-74,280
-42,400
-13,920
11,520
34,200

Discounted Payback Period = 3.0 + 13,920/25,440 = 3.55 years.
Using the discounted payback period method and a 3-year maximum acceptable
project hurtle, neither project should be accepted.
6.

The major problem with the discounted payback period comes in setting the firm's
maximum desired discounted payback period. This is an arbitrary decision that
affects which projects are accepted and which ones are rejected. Thus, while the
discounted payback period is superior to the traditional payback period, in that it
accounts for the time value of money in its calculations, its use should be limited
due to the problem encountered in setting the maximum desired payback period. In
effect, neither method should be used.

7.

NPVA

n

=

∑

t =1

=

=

FCFt
(1 + k) t

- IO

$20,000(PVIF 12%, 1 year) + $30,000 (PVIF 12%, 2 years )
+

$40,000(PVIF 12%, 3 years ) + $50,000 (PVIF 12%, 4 years )

+

$70,000(PVIF12%, 5 years ) - $110,000

$20,000(.893) + $30,000 (.797) + $40,000 (.712) + $50,000
(.636) + $70,000 (.567) - $110,000

NPVB

=

$17,860 + $23,910 + $28,480 + $31,800 + $39,690 - $110,000

=

$141,740-$110,000

=

$31,740

=

$40,000(PVIFA 12%, 5 years ) - $110,000

=

$40,000(3.605) - $110,000

=

$144,200-$110,000

=

$34,200

Both projects should be accepted
240


8.

9.

The net present value technique discounts all the benefits and costs in terms of cash
flows back to the present and determines the difference. If the present value of the
benefits outweighs the present value of the costs, the project is accepted, if not, it is
rejected.

PIA

PIB

=

 n

 ∑ FCFt 
 t =1


t 

 (1 + k) 




IO

=

$141,740
$110,000

=

1.2885

=

$144,200
$110,000

=

1.3109

Both projects should be accepted
10.

The net present value and the profitability index always give the same accept reject
decision. When the present value of the benefits outweighs the present value of the

costs the profitability index is greater than one, and the net present value is positive.
In that case, the project should be accepted. If the present value of the benefits is
less than the present value of the costs, then the profitability index will be less than
one, and the net present value will be negative, and the project will be rejected.

11.

For both projects A and B all of the costs are already in present dollars and, as such,
will not be affected by any change in the required rate of return or discount rate.
All the benefits for these projects are in the future and thus when there is a change
in the required rate of return or discount rate their present value will change. If the
required rate of return increased, the present value of the benefits would decline
which would in turn result in a decrease in both the net present value and the
profitability index for each project.

12.

IRRA

=

20.9698%

IRRB

=

23.9193%

13.

The required rate of return does not change the internal rate of return for a project,
but it does affect whether a project is accepted or rejected. The required rate of
return is the hurdle rate that the project's IRR must exceed in order to accept the
project.

14.

The net present value assumes that all cash flows over the life of the project are
reinvested at the required rate of return, while the internal rate of return implicitly
assumes that all cash flows over the life of the project are reinvested over the
remainder of the project's life at the IRR. The net present value method makes the
most acceptable, and conservative assumption and thus is preferred.

241


15.

Project A:
n

n

ACOFt

t =0

(1 + k) t

∑

=

∑
t =0

ACIFt (1 + k) n − t
(1 + MIRR) n

=

$20,000(FVIF12% , 4 years) + $30,000(FVIF12% , 3 years)
+ $40,000(FVIF12% , 2 years) + $50,000(FVIF12% , 1 year)
+ $70,000
(1 + MIRR A ) 5

$110,000

=

$20,000(1.574) + $30,000(1.405)
+ $40,000(1.254) + $50,000(1.120) + $70,000
(1 + MIRR A ) 5

$110,000

=

$31,480 + $42,150 + $50,160 + $56,000 + $70,000

(1 + MIRR A ) 5

$110,000

=

(1 + MIRR A )5

MIRRA

=

17.8247%

$110,000

$249,790

Project B:
$40,000(FVIFA12%,5years )

$110,000

=

$110,000

=

$110,000

=

(1 + MIRR B )5

MIRRB

=

18.2304%

(1 + MIRR B )5
$40,000(6.353)
(1 + MIRR B )5
$254,120

Both projects should be accepted because their MIRR exceeds the required rate of return.
The modified internal rate of return is superior to the internal rate of return method because
MIRR assumes the reinvestment rate of cash flows is the required rate of return.

242


Solutions to Problem Set B
9-1B. (a)

(b)

(c)

(d)

9-2B. (a)

(b)

(c)

(d)

IO

=

FCFt [PVIFIRR%,t yrs]

$10,000

=

$19,926 [PVIFIRR%,8 yrs]

0.502

=

PVIFIRR%,8 yrs

Thus, IRR

=

9%

$10,000

=

$20,122 [PVIFIRR%,12 yrs]

0.497

=

PVIFIRR%,12 yrs

Thus, IRR =

6%

$10,000

=

$121,000 [PVIFIRR%,22 yrs]

0.083

=

PVIFIRR%,22 yrs

Thus, IRR

=

12%

$10,000

=

$19,254 [PVIF IRR%,5 yrs]

0.519

=

PVIFIRR%,5 yrs

Thus, IRR

=

14%

IO

=

FCFt [PVIFA IRR%,t yrs ]

$10,000

=

$2,146 [PVIFA IRR%,10 yrs ]

4.66

=

PVIFA IRR%,10 yrs

Thus, IRR

=

17%

$10,000

=

$1,960 [PVIFA IRR%,20 yrs ]

5.102

=

PVIFA IRR%,20 yrs

Thus, IRR

=

19%

$10,000

=

$1,396 [PVIFA IRR%,12 yrs ]

7.163

=

PVIFA IRR%,12 yrs]

Thus, IRR

=

9%

$10,000

=

$3,197 [PVIFA IRR%,5 yrs]

3.128

=

PVIFA IRR%,5 yrs

Thus, IRR

=

18%

243


9-3B. (a)

$10,000

=

$3,000
(1 + IRR)1

+

$5,000
(1 + IRR)

2

$7,500

+

(1 + IRR)3

Try 21%:
$10,000

=

$3,000(0.826) + $5,000 (0.683) + $7,500 (0.564)

=

$2,478+ $3,415 + $4,230

=

$10,123

=

$3,000 (0.820) + $5,000 (0.672) + $7,500 (0.551)

=

$2,460 + $3,360 + $4,132.50

=

$9,952.50

Thus, IRR

=

approximately 22%

$12,000

=

(1 + IRR)1

=

$9,000 (0.800) + $6,000 (0.640) + $2,000 (0.512)

=

$7,200 + $3,840 + $1,024

=

$12,064

=

$9,000 (0.794) + $6,000 (0.630) + $2,000 (0.500)

=

$7,146 + $3,780 + $1,000

=

$11,926

Thus, IRR

=

nearest percent is 25%

$8,000

=

Try 22%
$10,000

(b)

$9,000

+

$6,000
(1 + IRR)2

+

$2,000
(1 + IRR)3

Try 25%
$12,000

Try 26%:
$12,000

5

(c)

∑

t =1

$2,000
(1 + IRR)

t

+

$5,000
(1 + IRR)6

Try 18%
$8,000

=

$2,000 (3.127) + $5,000 (0.370)

=

$6,254 + $1,850

=

$8,104

=

$2,000 (3.058) + $5,000 (0.352)

=

$6,116 + $1,760

=

$7,876

=

nearest percent is 18%

Try 19%
$8,000

Thus, IRR

244


9-4B. (a)

(b)

(c)

(d)
9-5B. (a)
(b)

(c)

(d)

9-6B. (a)

NPV

PI

=

6

$750,000

t =1

(1 + .11) t

∑

- $2,500,000

=

$750,000 (4.231) - $2,500,000

=

$3,173,250 - $2,500,000

=

$673,250

=

$3,173,250
$2,500,000

=

1.2693

$2,500,000 =

$750,000 [PVIFA IRR%,6 yrs]

3.333

=

PVIFA IRR%,6 yrs

IRR

=

about 20% (19.90%)

Yes, the project should be accepted.
Payback Period = $160,000/$40,000 = 4 years
NPV

=

6

$40,000

t =1

(1 + .10) t

∑

- $160,000

=

$40,000 (4.355) - $160,000

=

$174,200 - $160,000 = $14,200

=

$174,200
$160,000

=

1.0888

$160,000

=

$40,000 [PVIFA IRR%,6 yrs ]

4.000

=

PVIFA IRR%,6 yrs

IRR

=

about 13% (12.978%)

NPVA

=

PI

NPVB

6

$12,000

t =1

(1 + .12) t

∑

- $45,000

=

$12,000 (4.111) - $45,000

=

$49,332 - $45,000 = $4,332

=

6

$14,000

t =1

(1 + .12) t

∑

- $70,000

=

$14,000 (4.111) - $70,000

=

$57,554 - $70,000 = -$12,446

245


(b)

=

$49,332
$45,000

=

1.0963

=

$57,554
$70,000

=

0.822

$45,000

=

$12,000 [PVIFA IRR%,6 yrs ]

3.75

=

PVIFA IRR%,6 yrs

IRRA

=

15.34%

$70,000

=

$14,000 [PVIFA IRR%,6 yrs ]

5.0000

=

PVIFA IRR%,6 yrs

IRRB

=

5.47%

PIA

PIB

(c)

Project A should be accepted.
9-7B. (a)

Project A:
Payback Period

=

2 years

=

2 years + $1,000/$3,000 = 2.33 years

=

3 years + $1,000/$2,000 = 3.5 years

Project B:

Payback Period
Project C:
Payback Period

9-8B. NPV9%

=

Project

Payback Period Method

A

Accept

B

Accept

C

Reject

8

$2,500,000

t =1

(1 + .09) t

∑

- $10,000,000

=

$2,500,000 (5.535) - $10,000,000

=

$13,837,500 - $10,000,000 = $3,837,500

NPV11% =

8

$2,500,000

t =1

(1 + .11) t

∑

- $10,000,000

=

$2,500,000 (5.146) - $10,000,000

=

$12,865,000 - $10,000,000 = $2,865,000

246


NPV13% =

$2,500,000

t =1

(1 + .13) t

- $10,000,000

=

$2,500,000 (4.799) - $10,000,000

=

$11,997,500 - $10,000,000 = $1,997,500

NPV15% =

9-9B.

8

∑

8

$2,500,000

t =1

(1 + .15) t

∑

- $10,000,000

=

$2,500,000 (4.487) - $10,000,000

=

$11,217,500 - $10,000,000 = $1,217,500

Project A:
$75,000

=

$10,000
1

(1 + IRR A )
+

+

$10,000
(1 + IRR A )

$25,000
(1 + IRR A ) 4

+

2

+

$30,000
(1 + IRR A )3

$30,000
(1 + IRR A )5

Try 10%
$75,000

=

$10,000(.909) + $10,000(.826) + $30,000(.751)
+ $25,000(.683) + $30,000(.621)

=

$9,090 + $8,260 + $22,530 + $17,075 + $18,630

=

$75,585

=

$10,000(.901) + $10,000(.812) +$30,000(.731)

Try 11%
$75,000

+ $25,000(.659) + $30,000(.593)

Thus, IRR

=

$9,010 + $8,120 + $21,930+ $16,475 + $17,790

=

$73,325

=

just over 10%

$95,000

=

$25,000 [PVIFA IRR%,5 yrs ]

3.80

=

PVIFA IRR%,5 yrs

Thus, IRR

=

just below 10%

=

$150,000 [PVIFA IRR%,3 yrs ]

2.633

=

PVIFA IRR%,3 yrs

Thus, IRR

=

just below 7%

Project B:

Project C:
$395,000

247


10

9-10B. (a)

NPV

=

∑
t =1

(b)

NPV

$25,000
- $150,000
(1 + .09) t

=

$25,000(6.418) - $150,000

=

$160,450 - $150,000

=

$10,450

=

10

$25,000

t =1

(1 + .15) t

∑

- $150,000

=

$25,000(5.019) - $150,000

=

$125,475 - $150,000

=

-$24,525

(c)

If the required rate of return is 9% the project is acceptable in part (a). It
should be rejected in part (b) with a negative NPV.

(d)

$150,000 =

$25,000 [PVIFA IRR%,10 yrs ]

6.000

=

PVIFA IRR%,10 yrs

IRR

=

Between 10% and 11% (10.558%)

n

ACOFt

t= 0

(1 + k) t

9-11B. (a)

b)

∑

n

=

n-t
∑ ACIFt (1 + k)

t =0

(1 + MIRR)n

$2,000,000(FVIFA10%,8years )

$8,000,000

=

$8,000,000

=

$8,000,000

=

(1 + MIRR)8

MIRR

=

14.0320%

$8,000,000

=

$8,000,000

=

$8,000,000

=

(1 + MIRR)8

MIRR

=

15.0749%

(1 + MIRR)8
$2,000,000(11.436)
(1 + MIRR)8
$22,872000

$2,000,000(FVIFA12%,8years )
(1 + MIRR)8
$2,000,000(12.300)
(1 + MIRR)8
$24,600,000

248


c)

$2,000,000(FVIFA14%,8years )

$8,000,000

=

$8,000,000

=

$8,000,000

=

(1 + MIRR)8

MIRR

=

16.1312%

(1 + MIRR)8
$2,000,000(13.233)
(1 + MIRR)8
$26,466,000

FORD'S PINTO
(Ethics in Capital Budgeting)
OBJECTIVE:

To force the students to recognize the role ethical behavior plays in all
areas of Finance.

DEGREE OF DIFFICULTY:

Easy

Case Solution:
With ethics cases there are no right or wrong answers - just opinions. Try to bring
out as many opinions as possible without being judgmental.

249