Solution Manual Cost and Managerial Accounting 3rd by BarfieldCapital Budgeting

Chapter 14
Capital Budgeting
Questions
1.

Capital assets are the long-lived assets that are acquired by
a firm. Capital assets provide the essential production and
distributional capabilities required by all organizations.

2.

Each criterion provides different information about projects.
By using multiple criteria, more dimensions of competing
projects can be compared as a basis for allocating scarce
capital to new investment.

3.

Cash flows are the final objective of capital budgeting
investments just as cash flows are the final objective of any
investment. Accounting income ultimately becomes cash flow but

is reported based on accruals and other accounting assumptions
and conventions. These accounting practices and assumptions
detract from the purity of cash flows and are, therefore, not
used in capital budgeting.

4.

Analysts separate the act of financing a business's many
integrated investments and the related financing cash flows
from the selection of capital projects and the cash flows
related to such selections because of the virtual
impossibility of convincingly assigning dollars obtained from
the many general financing sources to the particular projects
being selected during a given year.

5.

Timelines provide clear visual models of the expected cash
inflows and outflows for each point in time for a project.
They provide an efficient and effective means to help organize

the information needed to perform capital budgeting analyses.

6.

The payback
recover its
expected to
ignores the

method measures the time expected for the firm to
investment. The method ignores the receipts
occur after the investment is recovered and
time value of money.

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Chapter 14
Capital Budgeting

7.

The time value of money is important because having a sum of
money now allows a company to earn a return on it; if the same
amount were not received until some time in the future, a
return could not be earned on it between now and the time it
is received. All else being equal, managers prefer to have
cash receipts now rather than in the future and would prefer
to make cash disbursements in the future rather than now.
Future values can be converted into equivalent present values
by the process of discounting. The following methods use the
time value of money concept: net present value, internal rate
of return, and the profitability index. The accounting rate of
return and payback period do not use the time value of money
concept.

8.

Return of capital means the investor is receiving the

principal that was originally invested. Return on capital
means the investor is receiving an amount earned on the
investment.

9.

The NPV of a project is the present value of all cash inflows
less the present values of all outflows associated with a
project. If the NPV is zero, it is acceptable because, in
that case, the project will exactly earn the required cost of
capital rate of return. Also, when NPV equals zero, the
project’s internal rate of return equals the cost of capital.

10.

It is highly unlikely that the estimated NPV will exactly
equal the actual NPV achieved because of the number of
estimates necessary in the original computation. These
estimates include the project life, the discount rate chosen
and the timing and amounts of cash inflows and outflows. The

original investment may also include an estimate of the amount
of working capital that is needed at the beginning of the
project life.

11.

The NPV method subtracts the initial investment from the
discounted net cash inflows to arrive at the net present
value. The PI divides the discounted cash inflows by the
initial investment to arrive at the profitability index. Thus,
each computation uses the same set of amounts in different
ways. The PI model attempts to measure the planned efficiency
of the use of the money (i.e., output/input) in that it
reflects the expected dollars of discounted cash inflows per
dollar of investment in the project.

12.

The PI will exceed 1 only in instances where the net present
value exceeds 0. This is because the NPV is positive only if

the present value of cash inflows exceeds the present value of
cash outflows. Similarly, the present value of cash inflows

Chapter 14
Capital Budgeting
must exceed the present value of cash outflows if the
numerator of the PI formula is to exceed the denominator.

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Chapter 14
Capital Budgeting

13.

The IRR is the rate that would cause the NPV of a project to
equal zero. A project is considered potentially successful
(all other factors being acceptable) if the calculated IRR

exceeds the company's cost of capital.

14.

On any prospective project, when the NPV exceeds zero, the
project's IRR will exceed the firm's discount rate that was
used to find the NPV. If the IRR equals the firm's discount
rate, the NPV will equal zero. If the IRR is less than the
firm's discount rate, the NPV will be negative. This
relationship holds true because, ultimately, under either
method the calculations for project selection are designed to
hinge on the project's cash flows in relation to the firm's
discount rate.

15.

The amount of depreciation for a year is one factor that helps
determine the amount of cash outflow for income taxes.
Therefore, although depreciation is not a cash flow item
itself, it does affect the size of another item (income taxes)

that is a cash flow.

16.

The tax shield is the amount of revenue on which the
depreciation prevents taxation. The tax benefit is the tax
that is saved because of the depreciation and is found by
multiplying the company's tax rate by the tax shield provided
by depreciation.

17.

The four questions are:
1. Is the activity worthy of an investment?
2. Which assets can be used for the activity?
3. Of the assets available for each activity, which is the
best investment?
4. Of the best investments for all worthwhile activities, in
which ones should the company invest?

18.

NPV: Ranks projects in descending order of magnitude.
PI: Ranks projects in descending order of magnitude if a
positive cash flow project.
IRR: Ranks projects in descending order of magnitude.
Payback: Ranks projects in ascending order of magnitude.
ARR: Ranks projects in descending order of magnitude.

19.

Several techniques should be used because each technique
provides valuable and different information. Of preferred use
as the primary evaluator is the net present value in
conjunction with the present value index, because management's
goal should be to maximize, within budget and risk
constraints, the net present value of the firm.

Chapter 14
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373

20.

Capital rationing exists because a firm often finds that it
has the opportunity to invest in more acceptable projects than
it has money available. Projects are first screened as to
desirability and then ranked as to impact on company
objectives.

21.

Risk is defined as the likely variability of the future
returns of an asset. Aspects of a project for which risk is
involved are:
* Life of the asset
* Amount of cash flows
* Timing of cash flows
* Salvage value of the asset

* Tax rates
When risk is considered in capital budgeting analysis, the NPV
of a project is lowered.

22.

Sensitivity analysis is used to determine the limits of value
for input variables (e.g., discount rate, cash flows, asset
life, etc.) beyond which the project's outcome will be
significantly affected. This process gives the decision maker
an indication of how much room there is for error in estimates
for input variables and which input variables need special
attention.

23.

Postinvestment audits are performed for two reasons: to
obtain feedback on past projects and to make certain that the
champions of proposed projects submit realistic numbers
knowing their estimates will ultimately be compared to actual
numbers. These audits can provide information to correct
problems and to assess how well the capital investment
selection process is working. The larger the capital
expenditure, the more important it is to perform
postinvestment audits. Postinvestment audits are performed at
the completion of a project.

24.

The time value of money refers to the concept that money has
time-based earnings power. Money can be loaned or invested to
earn an expected rate of return. Present value is always less
than future value because of the time value of money. A
future value must be discounted to determine its equivalent
(but smaller) present value. The discounting process strips
away the imputed rate of return in future values, thus
resulting in smaller present values.

25.

An annuity is a cash flow that is repeated in successive
periods. Single cash flows occur only in one period.

Chapter 14
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374
26.

ARR = Average annual profits ÷ Average investment
Unlike the rate used to discount cash flows or to compare
to the cost of capital rate, the ARR is not a discount rate to
apply to cash flows. It is measured from accrual-based
accounting information and is not intended to be associated
with cash flows.

Exercises
27. a. 3
b. 10
c. 2
d. 9
e. 5
f. 8
g. 6
h. 4
i. 1
j. 7
28.

a.
b.
c.
d.
e.
f.
g.
h.
i.
j.

29.

a.
b.

9
4
7
3
6
5
10
2
8
1
Payback = $750,000 ÷ $150,000 per year = 5.00 years
Year
1
2
3
4
5
6
7
8
9

Amount
$ 75,000
75,000
75,000
75,000
75,000
100,000
100,000
100,000
100,000

Cumulative Amount
$ 75,000
150,000
225,000
300,000
375,000
475,000
575,000
675,000
775,000

Payback = 8 + ($75,000 ÷ $100,000) years
= 8.75 years, or 8 years and 9 months

Chapter 14
Capital Budgeting
30.

a.

Year
1
2
3
4
5
6
7

Amount
$ 5,000
9,000
16,000
18,000
15,000
14,000
12,000

375

Cumulative Amount
$ 5,000
14,000
30,000
48,000
63,000
77,000
89,000

Payback = 4 years + ($12,000 ÷ $15,000)
= 4.8 years
b.

31.

Yes. Bach’s should also use a discounted cash flow
technique for two reasons: (1) to take into account the
time value of money and (2) to consider those cash flows
that occur after the payback period.

Point in time
0
1
2
3
4
5
6
7
8
9
10

Cash flows
$(400,000)
70,000
70,000
85,000
85,000
85,000
86,400
86,400
86,400
62,000
62,000
NPV

PV Factor
1.0000
0.8929
0.7972
0.7118
0.6355
0.5674
0.5066
0.4524
0.4039
0.3606
0.3220

Present Value
$(400,000)
62,503
55,804
60,503
54,018
48,229
43,770
39,087
34,897
22,357
19,964
$ 41,132

Based on the NPV, this is an acceptable investment.
32.

a.

The contribution margin of each part is $28 ($50 - $22)
Contribution margin per year = $28 × 50,000 = $1,400,000
Point in time Cash flows
0
$ (500,000)
1 - 8
(40,000)
1 - 8
1,400,000
NPV

b.

PV factor
1.0000
5.7466
5.7466

Present Value
$ (500,000)
(229,864)
8,045,240
$7,315,376

Based on the NPV, this is a very acceptable investment.

Chapter 14
Capital Budgeting

376
c.

Other considerations would include whether the company
has the necessary capacity to produce the additional
output, the possibility that the customer would decide to
purchase elsewhere or would no longer have need for the
parts after Machado Industrial has made its investment,
and whether the company has considered all of the costs
that would be affected by the decision to produce the new
part—especially labor and overhead.

33.

PI = PV of cash inflows  PC of cash outflows
= ($6,000 + $30,000)  $30,000 = 1.20

34.

a.

PV of inflows
$590,489 ($88,000  6.7101)
PV of investment $500,000
PI = $590,489 ÷ $500,000 = 1.18

b.

The OTA should accept the project because its PI is
greater than 1.00.

c.

To be acceptable, a project must generate a PI of at
least 1.

a.

PV = discount factor  annual cash inflow
$140,000 = discount factor  $28,180
Discount factor = $140,000 ÷ $28,180 = 4.968
The IRR is 12%

b.

Yes. The IRR on this proposal is greater than the firm's
hurdle rate of 10%.

c.

$140,000 = 5.335  Cash flow
Cash flow = $26,242

a.

Year
Amount
Cumulative Amount
1
$14,000
$ 14,000
2
14,000
28,000
3
11,000
39,000
4
11,000
50,000
Payback = 4 years + (52,000 - 50,000)  $9,000
= 4.22 years

b.

Point in time
0
1 - 2
3 - 4
5 - 6
6
NPV

35.

36.

Cash flows
$(52,000)
14,000
11,000
9,000
7,500

PV Factor
1.0000
1.7356
1.4343
1.1854
0.5645

Present Value
$(52,000)
24,298
15,777
10,669
4,234
$ 2,978

Chapter 14
Capital Budgeting

c.

PI = ($52,000 + $2,978)  $52,000 = 1.06

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378
37.

38.

a.

Investment ÷ Annual Savings = $2,300,000 ÷ $300,000 =
7.67 years.

b.

Point in Time Cash Flows
0
$(2,300,000)
1 - 11
300,000
NPV

c.

PI = $1,948,530 ÷ $2,300,000 = 0.85

d.

PV = discount factor  annual cash inflow
$2,300,000 = discount factor  $300,000
discount factor = $2,300,000 ÷ $300,000 = 7.6667
discount factor of 7.6667 corresponds to an IRR ≈ 7%

a.

Straight-line method
Annual depreciation = $1,000,000 ÷ 5 years
= $200,000 per year
Tax benefit = $200,000  0.35 = $70,000
PV = $70,000  3.7908 = $265,356

PV Factor
1.0000
6.4951

Present Value
$(2,300,000)
1,948,530
$ (351,470)

b.
Accelerated method
$1,000,000  0.40  0.35  .9091 =
$127,274.00
$ 600,000  0.40  0.35  .8265 =
69,426.00
$ 360,000  0.40  0.35  .7513 =
37,865.52
$ 216,000  0.40  0.35  .6830 =
20,653.92
*
$ 129,600  0.35  .6209 =
28,164.02
Total
$283,383.46
*In the final year, the remaining undepreciated cost is
expensed.
c.

The depreciation benefit computed in part (b). exceeds that
computed in part (a). solely because of the time value of
money. The depreciation method in part (b). allows for
faster recapture of the cost; therefore, there is less
discounting of the future cash flows.

Chapter 14
Capital Budgeting
39.

a.

379

SLD = $40,000,000 ÷ 8 years = $5,000,000 per year
Before-tax CF
Less depreciation
Before-tax NI
Less tax (30%)
NI
Add depreciation
After-tax CF

$8,400,000
5,000,000
$3,400,000
1,020,000
$2,380,000
5,000,000
$7,380,000

Point in Time
Cash Flows
0
$(40,000,000)
1 - 8
7,380,000
NPV
The project is acceptable.
b.
Before-tax CF
Less Depreciation
Before-tax NI
Tax (tax benefit)
After-tax NI
Add Depreciation
After-tax CF

PV Factor
1.0000
5.7466

Years 1 and 2
$ 8,400,000
9,200,000
$ (800,000)
(240,000)
$ (560,000)
9,200,000
$ 8,640,000

Point in time
Cash flows
0
$(40,000,000)
1 - 2
8,640,000
3 - 8
6,960,000
NPV
The project is acceptable.

PV factor
1.0000
1.7833
3.9633

Present Value
$(40,000,000)
42,409,908
$ 2,409,908

Years 3-8
$8,400,000
3,600,000
$4,800,000
1,440,000
$3,360,000
3,600,000
$6,960,000

Present Value
$(40,000,000)
15,407,712
27,584,568
$ 2,992,280

Chapter 14
Capital Budgeting

380
c.

Recomputation of part (a):
Before-tax CF
$8,400,000
Less depreciation
5,000,000
NIBT
$3,400,000
Less tax (50%)
1,700,000
NI
$1,700,000
Add depreciation
5,000,000
After-tax CF
$6,700,000
Point in Time
Cash Flows
PV Factor
0
$(40,000,000)
1.0000
1 - 8
6,700,000
5.7466
NPV
The project is not acceptable.
Recomputation of part (b):
Years 1 and 2
Before-tax CF
$ 8,400,000
Less Depreciation
9,200,000
NIBT
$ (800,000)
Less Tax(tax benefit)
(400,000)
After-tax NI
$ (400,000)
Add Depreciation
9,200,000
After-tax CF
$ 8,800,000

Present Value
$(40,000,000)
38,502,220
$ (1,497,780)

Years 3-8
$8,400,000
3,600,000
$4,800,000
2,400,000
$2,400,000
3,600,000
$6,000,000

Point in Time
Cash Flows
PV Factor
0
$(40,000,000)
1.0000
1 - 2
8,800,000
1.7833
3 - 8
6,000,000
3.9633
NPV
The project is not acceptable.
40.

Present Value
$(40,000,000)
15,693,040
23,779,800
$
(527,160)

a.

Tax: $25,000 - $8,000 = $17,000
Financial accounting:
$25,000 - $15,000 = $10,000

b.

CFAT = Market value now minus taxes
= $17,000 - (($17,000 - $8,000)  .40)
= $13,400

c.

CFAT = $4,000 - (($4,000 - $8,000)  .40) = $5,600

Chapter 14
Capital Budgeting
41.

a.

381

Find the rate that will cause the NPVs of the two
projects to be equal. By trial and error, the
indifference rate is just above 4%. At a 4% rate the NPV
of each project is computed as follows:
Project 1:
NPV = (8.1109  $85,000) - $400,000
NPV = $289,427
Project 2:
NPV = (8.1109  $110,000) - $600,000
NPV = $292,199

b.

This rate is known as the Fisher rate.

c.

Project 1:
NPV = (5.6502  $85,000) - $400,000
NPV = $80,267
Project 2:
NPV = (5.6502  $110,000) - $600,000
NPV = $21,522
Project 1 would be preferred due to its higher NPV,

42.

43.

a.

cash flow  annuity factor = $30,000
cash flow  3.6048 = $30,000
cash flow = $8,322

b.

$30,000 ÷ $8,322 = 3.6 years

PV factor  $180,000 = $400,000
PV factor = $400,000 ÷ $180,000 = 2.2222
This factor falls between 1.7591 (at 2 years) and 2.5313 (at 3
years) in the table using the 9% column.
Thus, the cash flow
would have to persist for over 2 years but under 3 years.

44.

a.

cash flow  discount factor = investment
cash flow  7.1607 = $1,200,000
cash flow = $167,581

b.

cash flow  discount factor = investment
$193,723  discount factor = $1,200,000
discount factor = 6.1944
This PV factor for 12 periods corresponds to 12%.

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Capital Budgeting

382
45.

future value × discount factor = present value
future value × .5674 = $14,000
future value = $24,674

46.

Cost = $9,000 + PV($1,200 annuity)
= $9,000 + ($1,200 × 30.1075)
= $45,129

47.

a.

PV = future value × discount factor
= $50,000  .6302
= $31,510 should be invested to achieve the goal

b.

PV = future value  discount factor
= $200,000  .3083
= $61,660 would be equivalent today

c.

PV = future value  discount factor
= $60,000  .3522
= $21,132

d.

timeline
time
t0
amount

t1
$210

t2
$210

t3
$210

t4
$210

t5
$210

Year 1 receipt:
Year 2 receipt:
Year 3 receipt:
Year 4 receipt:
Year 5 receipt:
Present value
Discount factors

$210,000
$210,000
$210,000
$210,000
$210,000

×
×
×
×
×

.9246
.8548
.7903
.7307
.6756

= $194,166
= 179,508
= 165,963
= 153,447
= 141,876
$834,960
based on semi-annual rate of 4 percent.

e.

Year 1 receipt:
Year 2 receipt:
Year 3 receipt:
Year 4 receipt:
Year 5 receipt:
Year 6 receipt:
Year 7 receipt:
Year 8 receipt:
Year 9 receipt:
Year 10 receipt:
Present value

$ 30,000
$ 50,000
$ 60,000
$100,000
$100,000
$100,000
$100,000
$100,000
$ 70,000
$ 45,000












.9259
.8573
.7938
.7350
.6806
.6302
.5835
.5403
.5003
.4632

f.

No. Using any discount rate above 0, the present value
of the future annual cash flows is well below $1,000,000.

= $ 27,777
=
42,865
=
47,628
=
73,500
=
68,060
=
63,020
=
58,350
=
54,030
=
35,021
=
20,844
$491,095

Chapter 14
Capital Budgeting

383

Only if the friend has substantial other assets would she
be a millionaire.

Chapter 14
Capital Budgeting

384
48.

a.

Change in net income = $250,000 - ($500,000 ÷ 5)
= $150,000
ARR = $150,000 ÷ ($500,000 ÷ 2) = 60%
Payback = $500,000 ÷ $250,000 per year = 2 years

49.

50.

b.

Yes. The equipment investment meets all investment
criteria. The payback is less than 5 years and the
accounting rate of return exceeds 18%.

a.

Annual cash receipts
Cash expenses
Net cash flow before taxes
Depreciation
Income before tax
Taxes
Net income
Depreciation
Annual after-tax cash flow

b.

Payback = $50,000  $12,017 per year = 4.16 years

c.

ARR = $3,684  ($50,000  2) = 14.74%

a.

Before-tax cash flow
Depreciation ($60,000 ÷ 5)
Income before tax
Tax (28%)
Net income
Depreciation
Annual after-tax cash flow

b.

c.

Point in time
Cash flows
PV factor
0
$(60,000)
1.0000
1-5
$ 21,360
3.7908
NPV
From part a. accounting income = $9,360

d.

ARR = $9,360 ÷ (($60,000 + $0) ÷ 2)

$16,000
(2,000)
$14,000
8,333
$ 5,667
(1,983)
$ 3,684
8,333
$12,017

$ 25,000
(12,000)
$ 13,000
(3,640)
$ 9,360
12,000
$ 21,360
Present Value
$(60,000)
80,971
$ 20,971

= 31.2%

Payback = $60,000  $21,360 = 2.81 years

Chapter 14
Capital Budgeting
51.

52.

385

a.

Payback = $750,000  $250,000 annually

b.

One of the other cost savings may come in the form of
improved quality. By adopting the higher technology,
fewer defects should occur. Additionally, the company
may be able to lower its costs because of its enhanced
flexibility to switch production from one job to another.
Additional costs may come in the form of maintenance and
repairs as well as training costs to upgrade skills of
workers to operate the new equipment.

= 3 years

Some of the factors that would weigh in favor of proceeding
with the investment as planned include these:
• The cost savings will be received now instead of later.
• Any learning curve effects will be enjoyed earlier.
• Any quality effects on operations will be recognized
sooner.
• The reduced maintenance cost benefit will occur now rather
than later.
• Demand for services may accelerate unexpectedly.
• Delays in installing the equipment may result in price
hikes
that could be avoided if the equipment is installed on
schedule.
The factors that might weigh in favor of delaying investment
include these:
• Risk associated with the new investment may increase
because of the likelihood that demand will not pick up in
the near future.
• Possible price reductions might be realized by delaying
acquisition of the equipment. Price reductions are more
likely on computerized equipment.
• Possible layoffs of employees can be deferred.
• More time is now available to evaluate alternative
technologies that may have emerged or will emerge soon.
• The company should protect its cash flow in light of a
local, stagnating economy.

386

Chapter 14
Capital Budgeting

53.

A company’s R&D program is the major source of distant, future
cash flows. It is from the R&D effort that new products are
identified and developed. Without a successful R&D program,
the stream of future cash flows will dry up. Similarly, the
present products and services offered by a firm are
attributable to past R&D programs. Hence, the linkage is
established between R&D activity, and present and future cash
flows.
It is not surprising that much long-term planning should
be concentrated on the R&D activity. Managing the investment
in R&D activities is the main method available to managers to
balance current and present cash flows, as well as present and
future growth. R&D is expensed when incurred and this reduces
current earnings. This often tends to depress stock prices.

54.

The capital budget interacts with the cash budget in that
acquisition of capital items represents a use of cash. The
capital budget also interacts with the statement of cash flows
investing activities section. Further, the capital budget
impacts depreciation expense on the budgeted income statement,
and assets on the budgeted balance sheet. Indirectly, the
capital budget interacts with other lines on the income
statement because the various projects included in the capital
budget will influence a variety of expenses including labor,
overhead, administration and marketing.

55.

No response provided.

56.

The market must be expecting an enormous increase in future
cash flows relative to current cash flows. If the total value
of the shares is viewed as the present value of the future
cash flows accruing to the equity holders, the only possible
explanation for the incredibly high value of the stock is that
investors expect future cash flows to be many times the level
of current cash flows.

57.

If the value of a share of stock is viewed as the present
value of the future cash flows that will accrue to that share
of stock, then any change in the discount rate applied by
investors would affect the share price. If interest rates
move up and down, it is reasonable to expect stock prices to
move inversely to the change in interest rates because the
change in the prevailing interest rates represents a change in
the discount rate applied by investors.

Chapter 14
Capital Budgeting
58.

387

The capital budget is a key control tool for a .com firm. Few
.com firms have turned a profit yet. They are very early in
the process of developing products and services to deliver
over the Internet and this process requires substantial
capital investment. Consequently, their investing activities,
managed by the capital budgeting process, are the focus of
much managerial time and talent. Only if these firms invest
in the right projects will the eventual success of the firm be
realized.

Problems
59.

a. ($000s omitted)
t0
t1
t2
t3
t4
t5
t6
t7
t8
Investment
-90.0
New CM
24.00 24.0 24.0 24.0 24.00 24.00 24.00 24.00
Oper. costs
0.0 -6.50 -7.2 -7.2 -7.2 -7.95 -9.45 -10.00 -11.25
Ann. savings -90.0 17.50 16.8 16.8 16.8 16.05 14.55 14.00 12.75

Year
Cash Savings
Cumulative Savings
1
$17,500
$17,500
2
16,800
34,300
3
16,800
51,100
4
16,800
67,900
5
16,050
83,950
Payback = 5 + (($90,000 - $83,950)  $14,550) = 5.42 years

b.

60.

c.

Time
0
1
2
3
4
5
6
7
8
NPV

Cash Flow
$(90,000)
17,500
16,800
16,800
16,800
16,050
14,550
14,000
12,750

a.

Time:
t0
t1
t2
t3
t4
t5
t6
t7
Amount: ($31,000) $6,800 $7,100 $7,300 $7,000 $7,000 $7,100 $7,200

b.

Year
Year
Year
Year
Year

1
2
3
4

PV Factor for 10%
1.0000
.9091
.8265
.7513
.6830
.6209
.5645
.5132
.4665

Cash Flow
$6,800
7,100
7,300
7,000

Present Value
$(90,000)
15,909
13,885
12,622
11,474
9,965
8,213
7,185
5,948
$(4,799)

Cumulative
$ 6,800
13,900
21,200
28,200

Payback = 4 years + (($31,000-$28,200)$7,000) = 4.40 years

Chapter 14
Capital Budgeting

388
c.
Cash flow
Description
Purchase the car
Cost savings
Cost savings
Cost savings
Cost savings
Cost savings
Cost savings
Cost savings
NPV
61.

62.

Time
t0
t1
t2
t3
t4
t5
t6
t7

Amount
($31,000)
6,800
7,100
7,300
7,000
7,000
7,100
7,200

Discount Present
Factor
Value
1.0000 ($31,000)
.8929
6,072
.7972
5,660
.7118
5,196
.6355
4,448
.5674
3,972
.5066
3,597
.4524
3,257
$ 1,202

a.

Payback period = $64,000 ÷ ($25,000 - $4,500) = 3.12
years; the project does meet the payback criterion.

b.

Discount factor = Investment ÷ annual cash flow
= $64,000 ÷ $20,500 = 3.1220
Discount factor of 3.1220 indicates IRR > 10.5%
which is an unacceptable IRR. The actual IRR is 10.71%.

a.

Year
0
1-7
7
NPV

b.

No, the NPV is negative; therefore this is an
unacceptable project.

c.

PI = ($2,111,344 + $109,400) ÷ $2,500,000
= 0.89

d.

The company should consider the quality of the work
performed by the machine versus the quality of the work
performed by the individuals; the reliability of the
manual process versus the reliability of the mechanical
process; and perhaps most importantly, the effect on
worker morale and the ethical considerations in
displacing 14 workers.

Cash flow
$(2,500,000)
419,500
200,000

PV factor
1.0000
5.0330
.5470

PV
$(2,500,000)
2,111,344
109,400
$ (279,256)

Chapter 14
Capital Budgeting
63.

a.

389

The incremental cost of the new machine: $290,000 - $6,000
= $284,000

Cash flow
Discount
Description
Time
Amount
Factor
Incremental cost t0
$(284,000)
1.0000
Cost savings
t1-t7
60,000
4.9676
NPV
PI = $298,056 ÷ $284,000 = 1.05

Present
Value
$(284,000)
298,056
$ 14,056

Yes, the machine should be purchased because the NPV > 0
and the PI > 1.
b.

Payback = $284,000 ÷ 60,000 per year = 4.73 years

c.

Net investment ÷ annual annuity = discount factor of IRR
$284,000 ÷ 60,000 = 4.7333
Discount factor of 4.7333 is between 13.0 and 13.5%
Using interpolation, the actual rate is  13.40%

64.

a.

Computation of net annual cash flow:
Increase in revenues
$172,000
Increase in cash expenses
(75,000)
Increase in pretax cash flow
$ 97,000
Less Depreciation
(39,000)
Income before tax
$ 58,000
Income taxes (30 percent)
(17,400)
Net income
$ 40,600
Add Depreciation
39,000
After-tax cash flow
$ 79,600
Cash Flow
Discount
Description
Time
Amount
Factor
Initial cost
t0
$(780,000) 1.0000
Annual cash flow t1-t20
79,600
7.9633
NPV

b.

Present
Value
$(780,000)
633,879
$(146,121)

No, this is not an acceptable investment. The net
present value is not close to the cutoff value of $0.

Chapter 14
Capital Budgeting

390

c.

Minimum annual cash flow  discount factor = $780,000
Minimum annual cash flow  7.9633 = $780,000
Minimum annual cash flow = $97,949
After-tax cash flow increase = Minimum cash flow - Actual
cash flow
After-tax cash flow increase = $97,949 - $79,600
After-tax cash flow increase = $18,349
Increase in revenues = After-tax cash flow increase ÷ (1tax rate)
Increase in revenues = $18,349 ÷ 0.70
Increase in revenues = $26,213

65.

a.

Cash flow after tax (CFAT):
Year
Pretax CF Depreciation
1
$52,000
$32,000
2
59,000
51,200
3
59,000
30,400
4
51,000
24,000
5
43,000
22,400
Timeline:
t0
t1
$(160,000) $46,000

b.

t2
$56,660

Tax
$6,000
2,340
8,580
8,100
6,180

t3
$50,420

CFAT
$46,000
56,660
50,420
42,900
36,820

t4
$42,900

t5
$36,820

Year
Net Cash Flow
Cumulative Cash Flow
1
$46,000
$ 46,000
2
56,660
102,660
3
50,420
153,080
Payback = 3 years + (($160,000-153,080)  $42,900)
= 3.16 years.
Net present value:
Time
Amount
Year 0
$(160,000)
Year 1
$46,000
Year 2
56,660
Year 3
50,420
Year 4
42,900
Year 5
36,820
NPV

Discount Factor
1.0000
.9259
.8573
.7938
.7350
.6806

Present Value
$(160,000)
42,591
48,575
40,023
31,532
25,060
$ 27,781

Profitability index = ($160,000 + $27,781) ÷ $160,000 =
1.17
IRR, is between 14.5% and 15%.
is found to be 14.68%.

Using a computer, the IRR

Chapter 14
Capital Budgeting

391

Chapter 14
Capital Budgeting

392
66.

a.

b.

Maple Commercial Plaza:
t0
t1-t10
$(800,000)
$210,000

t10
$400,000

High Tower:
t0
$(3,400,000)

t10
$1,500,000

t1-t10
$830,000

Maple Commercial Plaza:
Calculation of annual cash flow:
Pretax cost savings
Depreciation ($800,000  25)
Pretax income
Taxes (40 percent)
Aftertax income
Depreciation
Aftertax cash flow

$210,000
(32,000)
$178,000
(71,200)
$106,800
32,000
$138,800

t0
t1-t10
t10
$(800,000)
$138,800
$432,000*
*Includes $32,000 from tax loss on sale
(0.40  ($400,000 - $480,000))
High Tower:
Calculation of annual cash flow:
Pretax cost savings
Depreciation ($3,400,000  25)
Pretax income
Taxes
Aftertax income
Depreciation
Aftertax cash flow

$ 830,000
(136,000)
$ 694,000
(277,600)
$ 416,400
136,000
$ 552,400

t0
t1-t10
t10
$(3,400,000)
$552,400
$1,716,000*
*Includes $216,000 from tax loss on sale
(0.40  ($1,500,000 - $2,040,000))

Chapter 14
Capital Budgeting
c.

After-tax NPV, Maple Commercial Plaza:
Amount
Discount Factor
Year 0
$(800,000)
1.0000
Year 1-10
138,800
5.8892
Year 10
432,000
.3522
NPV

393

Present Value
$(800,000)
817,421
152,150
$ 169,571

After-tax NPV, Hightower:
Amount
Discount Factor
Present Value
Year 0
$(3,400,000)
1.0000
$(3,400,000)
Year 1-10
552,400
5.8892
3,253,194
Year 10
1,716,000
.3522
604,375
NPV
$
457,569
Based on the NPV criterion, Hightower is the preferred
investment
d.

After-tax NPV, Hightower:
Amount
Discount factor
Year 0
$(3,400,000)
1.0000
Year 1-10
180,400
5.8892
*
Year 1-10
372,000
4.1925
Year 10
1,716,000
.3522
NPV
*Rental

Present Value
$(3,400,000)
1,062,412
1,559,610
604,375
$ (173,603)

portion of cash flow = $620,000  (1 - tax rate)
= $620,000  0.60
= $372,000

Under this circumstance, Maple Commercial Plaza is the
preferred investment.

Chapter 14
Capital Budgeting

394
67.

a.
Year
0
1-6
NPV

Cash Flow
$(96,000)
25,600

Project A
PV Factor
1.0000
4.1114

PV
$(96,000)
105,252
$ 9,252

PI = $105,252 ÷ $96,000 = 1.10
IRR: Discount factor for 6 periods is $96,000 ÷ $25,600 =
3.7500, which yields a rate of just under 15.5%.

Year
0
1-10
NPV

Project B
Cash Flow
PV Factor
$(160,000)
1.0000
30,400
5.6502

PV
$(160,000)
171,766
$ 11,766

PI = $171,766 ÷ $160,000 = 1.07
IRR: Discount factor for 6 periods is $160,000 ÷ $30,400
= 5.2631, which yields a rate of about 13.75%.
b.

Although the methods give conflicting results, the NPV of
B is greater than that of A and this is probably the best
indication for choice. Although the IRR for Project A is
higher, the reinvestment assumption of that method is
less attainable. Even though the PI of Project A is
slightly higher, its NPV is less and usually dollars are
the deciding criterion when rates are close.

c.

Project A's IRR is 15.5% and Project B's is 13.75%. Above
13.75%, Project B will have a negative NPV. At 12%,
Project A's NPV is $9,252 and Project B's is $11,766. By
repeated trials, the Fisher rate (the rate at which the
NPVs are equal) is estimated to be between 12.50% and
13.0%. By programmable calculator, the rate is found to
be 12.64%.

Chapter 14
Capital Budgeting
68.

69.

395

a.

Project name
NPV
Film studios
$3,578,846
Cameras & equipment 1,067,920
Land investment
2,250,628
Motion picture #1
1,040,276
Motion picture #2
1,026,008
Motion picture #3
3,197,363
Corporate aircraft
518,916

PVI
1.18
1.33
1.45
1.06
1.09
1.40
1.22

b.

Ranking according to:
NPV
PVI
1. Film Studios
Land investment
2. MP #3
MP#3
3. Land Invest.
Camera & Equip.
4. Cam. & Equip.
Corp. Aircraft
5. MP #1
Film Studio
6. MP #2
MP #2
7. Corp. aircraft MP #1

IRR
13.03%
18.62
19.69
12.26
14.22
21.34
18.15

IRR
MP #3
Land Investment
Camera & Equip.
Corp. Aircraft
MP #2
Film Studios
MP #1

c.

Suggested purchases
1. MP #3 @ $8,000,000
2. Land invest. @ $5,000,000
3. Cam. & Equip. @ $3,200,000
4. Corp. Aircraft @ $2,400,000
Total NPV

NPV
$3,197,363
2,250,628
1,067,920
518,916
$7,034,827

a.

Depreciation per year = $2,000,000 ÷ 14 = $142,857
Before tax cash flows = [300  0.80  ($75 - $10)  50] $100,000
= $680,000 per year
Before-tax CF
$680,000
Less Depreciation
(142,857)
Income before tax
$537,143
Less tax (35%)
(188,000)
Net income
$349,143
Add Depreciation
142,857
After-tax cash flow $492,000
PV of 14 yr. annuity of $492,000 @ 13%
Less cost
NPV

$3,100,830
(2,000,000)
$1,100,830

b.

It exceeds the highest rate provided in the table. By
computer it is 23.29%.

c.

Cash flow  discount factor = $2,000,000
Cash flow  (6.3025) = $2,000,000

Chapter 14
Capital Budgeting

396
Cash flow

= $317,334

Chapter 14
Capital Budgeting

70.

397

d.

6 years

e.

$217,425 after tax CF
[($217,425 - $142,857) ÷ 0.65] + $142,857 + $100,000 =
$357,577 before tax CF ($357,577 ÷ 300) ÷ $65 = 19 rooms
(rounded up)

a.

Year
1 - 4
5 - 8
9 - 10

Revenue
$125,000
175,000
100,000

Year
0
1 - 4
5 - 8
9 - 10
10
NPV

Cash Flow
$(145,000)
30,000
50,000
20,000
10,000

Year
1 - 4
5 - 8
9 - 10

Revenue
$120,000
200,000
103,000

Year
0
1 - 4
5 - 8
9 - 10
10

Cash flow
$(137,500)
27,000
52,500
11,050
23,500

b.

c.

VC
$ 75,000
105,000
60,000

FC
$20,000
20,000
20,000

PV Factor
1.0000
3.1699
2.1651
.8096
.3855

VC
$ 78,000
130,000
66,950

FC
$15,000
17,500
25,000

PV Factor
1.0000
3.1699
2.1651
.8096
.3855
NPV

Net Cash Flow
$ 30,000
50,000
20,000
PV
$(145,000)
95,097
108,255
16,192
3,855
$ 78,399
Net Cash Flow
$27,000
52,500
11,050
PV
$(137,500)
85,587
113,668
8,946
9,059
$ 79,760

The biggest factors are the increased level of variable
costs, the additional working capital, the lower
initial revenues, and the lower cost of production
equipment.

Chapter 14
Capital Budgeting

398
71.

a.

Year
1
2
3
4
5
6
7
8

Net Income
$(107,500)
(40,000)
5,500
88,000
240,000
240,000
72,000
(42,000)
$456,000

Average annual income = $456,000 ÷ 8 = $57,000
Average Investment = (Cost + Salvage) ÷ 2
= ($1,600,000 + $0) ÷ 2 = $800,000
ARR = $57,000 ÷ $800,000 = 7.125%
b.
Year
1
2
3
4
5
6

Cash
Receipts
$750,000
800,000
930,000
1,280,000
1,600,000
1,600,000

Cash
Expenses
$ 657,500
640,000
724,500
992,000
1,160,000
1,160,000

Net
Inflows
$ 92,500
160,000
205,500
288,000
440,000
440,000

Cumulative
Cash Flows
$
92,500
252,500
458,000
746,000
1,186,000
1,626,000

Payback = 5 + (($1,600,000-$1,186,000)÷ $440,000) years
= 5.94 years
c.

Year
0
1
2
3
4
5
6
7
8
NPV

Cash flow
$(1,600,000)
92,500
160,000
205,500
288,000
440,000
440,000
272,000
158,000

PV factor
1.0000
.8929
.7972
.7118
.6355
.5674
.5066
.4524
.4039

PV
$(1,600,000)
82,593
127,552
146,275
183,024
249,656
222,904
123,053
63,816
$ (401,127)

Chapter 14
Capital Budgeting
72.

a.

399

Initial cost: t0 = $(730,000) + $170,000 = $(560,000)
Annual cash flow:
Additional revenue ($1.20  110,000)
$132,000
Labor savings
30,000
Other operating savings ($192,000 - $80,000) 112,000
Total
$274,000
NPV = $(560,000) + ($274,000  6.1446) = $1,123,620

b.

Discount factor = $560,000  $274,000 = 2.0438
The IRR exceeds numbers reported in the present value
appendix. By computer, the IRR is found to be 47.96%.

c.

$560,000  $274,000 = 2.04 years

d.

ARR = ($274,000 - $31,000)  (($560,000 + $0)  2)
= 86.79%

e.

Incremental revenue ($132,000  10 years)
Labor cost savings ($30,000  10 years)
Savings in other costs ($112,000  10 years)
Less incremental cost
Incremental profit

$1,320,000
300,000
1,120,000
(560,000)
$2,180,000

Because the incremental profit is greater than $0, the
firm should buy the new equipment.

Chapter 14
Capital Budgeting

400
Cases

73. Note: Students may have slightly different answers. The CMA
solution uses only two-digit present value factors.
a.

Present Value Analysis (using 6%)
Initial
Outlay
2003
2004

Internal
Financing
Outlay
($1,000,000)
Depr.
tax
shield
Net CF
($1,000,000)
PV factors
1.00
NPV
($1,000,000)

Bank
Loan
Outlay
Loan
payment
Interest
tax shield
Depr.
tax shield
Net CF
PV factors
NPV
Lease
Outlay
Tax shield
on outlay
Payments
net of tax
($220,000
 60%)
NCF
PV factors
NPV

$160,000
$160,000
0.94
$150,400

$ 96,000
$ 96,000
0.89
$ 85,440

2005

$ 57,600
$ 57,600
0.84
$ 48,384

2006

$ 43,200
$ 43,200
0.79
$ 34,128

2007

NPV

$ 43,200
$ 43,200
0.75
$ 32,400 $(649,248)

($100,000)
($237,420)($237,420)($237,420)($237,420)($237,420)
36,000

30,103

23,617

16,482

8,638

$160,000 $ 96,000 $ 57,600 $ 43,200 $ 43,200
($100,000) ($ 41,420)($111,317)($156,203)($177,738)($185,582)
1.00
0.94
0.89
0.84
0.79
0.75
($100,000) ($ 38,935)($ 99,072)($131,211)($140,413)($139,187)$(648,818)

($ 50,000)
$ 20,000

($132,000)($132,000)($132,000)($132,000)($132,000)
($ 50,000) ($112,000)($132,000)($132,000)($132,000)($132,000)
1.00
0.94
0.89
0.84
0.79
0.75
($ 50,000) ($105,280)($117,480)($110,880)($104,280)($ 99,000)$(586,920)

NPV for internal financing = $(649,248)
NPV for bank loan = $(648,818)
NPV for lease = $(586,920)

Chapter 14
Capital Budgeting

401

Supporting calculations
Depreciation tax shield
Year
Depreciation Rate Tax shield
1
$1,000,000  0.40 = $400,000  0.40 = $160,000
2
($1,000,000-$400,000)  0.40 = 240,000  0.40 =
96,000
3
($1,000,000-$640,000)  0.40 = 144,000  0.40 =
57,600
4
($1,000,000-$784,000)  0.50 = 108,000  0.40 =
43,200
5
($1,000,000-$784,000)  0.50 = 108,000  0.40 =
43,200
Interest tax shield
Year Interest Rate Tax shield
1
$90,000
0.40 $36,000
2
75,258
0.40 30,103
3
59,042
0.40 23,617
4
41,204
0.40 16,482
5
21,596
0.40
8,638
1.

Metrohealth should employ the cost of debt of six
percent (which represents the after-tax effect of the
ten percent incremental borrowing rate) as a discount
rate in calculating the net present value for all three
financing alternatives.
Investment decisions (accept versus reject) and
financing decisions should be separated. Cost of
capital or hurdle rates apply to investment decisions
but not to financing decisions. This application is a
financing decision. Incremental cost of debt is the
basic rate used for discounting in financing decisions
because the assumption made is that the firm would have
no idle cash available for funding and would have to
borrow from an outside lending institution at the
incremental borrowing rate (10 percent in this case).

2.

The financing alternative most advantageous to
Metrohealth is leasing. This alternative has the lowest
net present value ($586,920) when compared to the other
two alternatives.

Chapter 14
Capital Budgeting

402

74.

b.

Some qualitative factors Paul Monden should include for
management consideration before deciding on the financing
alternatives are:
◼
The differential impact from one financing method versus
another for equipment acquisitions due to various health
care, third-party payor, reimbursement scenarios (the
federal government with DRG reimbursement or insurance
company reimbursement).
◼
The technology of the equipment along with the risk of
technological obsolescence. If major technological
advances are expected, the preferred qualitative choice
would be leasing from a lessor who would absorb any loss
due to equipment obsolescence.
◼
The maintenance agreement included in the operating
lease.
(CMA adapted)

a.

Incremental annual after-tax cash flows:
Purchase
Purchase of new equipment
One time production expense
net of tax ($30,000  .6)
Sale of old equipment
net of tax ($5,000  .6)
Total initial cash outflow

Year 1
Cash operating
savings
$ 90,000
Less tax effect(40%) (36,000)
Cash savings
after-tax
$ 54,000
Depr. tax shield
(see sched. below)
48,000
After-tax operating
cash flows
$102,000

Year
1
2
3
4

Annual Operations
Year 2
Year 3

Year 0
$(300,000)
(18,000)
3,000
$(315,000)

Year 4

$150,000
(60,000)

$150,000 $150,000
(60,000) (60,000)

$ 90,000

$ 90,000

$ 90,000

36,000

24,000

12,000

$126,000

$114,000

$102,000

Depreciation Schedule
Depreciable base: $300,000
Life: four-year limit
Method: Sum-of-the-years'-digits
Rate
Depreciation
Depr. Shield
4/10
$120,000
$48,000
3/10
90,000
36,000
2/10
60,000
24,000
1/10
30,000
12,000

Chapter 14
Capital Budgeting
b.

403

The company should accept the proposal since the NPV is
positive.
Year
0
1
2
3
4
NPV

Cash Flow
$(315,000)
102,000
126,000
114,000
102,000

12% PV Factor
1.0000
.8929
.7972
.7118
.6355

PV
$(315,000)
91,076
100,447
81,145
64,821
$ 22,489
(CMA)

75.

a. The benefits of a postcompletion audit program for capital
expenditure projects include these:
• The comparison of actual results with projected
results to validate that a project is meeting expected
performance or to take corrective action or terminate
a project not achieving expected performance.
• An evaluation of the accuracy of projections from
different departments.
• The improvement of future capital project revenue and
cost estimates through analyzing variations between
expected and actual results from previous projects and
the motivational effect on personnel arising from the
knowledge that a postinvestment audit will be done.
b.

Practical difficulties that would be encountered in
collecting and accumulating information include:
• Isolating the incremental changes caused by one
capital project from all the other factors that change
in a dynamic manufacturing and/or marketing
environment.
• Identifying the impact of inflation on all costs in
the capital project justification.
• Updating of the original proposal for approval of
changes that may have occurred after the initial
approval.
• Having a sufficiently sophisticated information
accumulation system to measure actual costs incurred
by the capital project.
• Allocating sufficient administrative time and expenses
for the postcompletion audit.
(CMA adapted)

Chapter 14
Capital Budgeting

404
Reality Check
76.

77.

78.

a.

It is no easier for a healthcare concern than any other
business to invest in capital assets when doing so is not
justified on financial grounds. The problem described in
the article would seem to describe a failure of the
information systems of healthcare providers to fairly
capture all relevant financial dimensions of long-term
strategic investments. It is unreasonable to think that
benefits such as “improving quality of care or patient
satisfaction” have no financial return.

b.

As an accountant with a healthcare provider, you could
identify “nonfinancial” benefits such as those described
in part a. and, if appropriate, assign values to them.
The key contribution you would make is to provide a
rigorous investment analysis that includes not only those
costs and benefits usually captured by accounting
systems, but to add other benefits that may be missed
because the financial impact is indirect (e.g., increased
consumer satisfaction) rather than direct.

a.

For labor-intensive operations, labor cost and quality
would be substantial considerations in locating new
investments. Having skilled labor available at a
competitive cost would determine the likelihood that the
new investment would be profitable.

b.

In addition to labor cost and quality, firms would also
consider these factors:
• Political risks of the alternative investment
locations
• Nearness to suppliers and markets
• Tax rates of the alternative locations
• Incentives offered by local governments
• Location of competitors

a.

When short-run economic conditions become difficult,
companies must be very careful when cutting costs to
protect profits. In particular, cutting spending on
training, research and development, and customer service
will surely have a deleterious effect on product and
service quality. Alternatively, cutting advertising
costs and other marketing costs may have much less effect
on product quality.

Chapter 14
Capital Budgeting

79.

80.

405

b.

Any cost-cutting measures that affect employee and
managerial training or research and development will have
long-term implications. In cutting these activities, the
firm is essentially mining future profitability to
protect current profitability. The consequence will be
lower future profits, fewer product innovations, and
underdeveloped human resources.

a.

Managers bear the burden of maximizing the wealth of
their investors. To the extent that holding assets (as
opposed to selling them) results in diminished wealth,
the managers are failing in their obligation to the
shareholders. Managers may have incentives to hold
nonperforming assets if their compensation and incentives
are related to the size of the firm. Even so, managers
have an ethical obligation to pursue the maximization of
investor wealth subject to ethical treatment of other
stakeholders. This obligation is no less binding merely
because it conflicts with the managers’ personal
incentives.

b.

Spin-offs may result in the firing of workers or the
downgrading of their jobs. Managers have a
responsibility to see that workers who are involved in
spin-offs are treated ethically. Disaffected workers
should be given all the support services necessary to
find comparable alternative employment. If possible,
workers should be given opportunities to transfer to
other operations of the company. Otherwise, workers
should be provided with employment counseling and
training necessary to finding equivalent employment with
another firm.

a.

A lease is often found appealing by consumers because it
results in a lower monthly payment in many instances than
the monthly payment that is required to purchase a car.
This allows the consumer either to enjoy a lower monthly
payment or, for the same monthly payment required to
amortize the cost of one vehicle, pay a similar monthly
amount for a more expensive car.

b.

Yes. A consumer should be provided with all necessary
information to make a fair comparison between the lease
and purchase alternative.

c.

As an accountant, you could provide a financial
comparison of the lease and purchase alternatives. Using
a discounted cash flow approach, you could compare the
present value of purchasing the vehicle to the present

406

Chapter 14
Capital Budgeting
value of leasing the vehicle.