Chapter 13 - Capital Budgeting Decisions
Chapter 13
Capital Budgeting Decisions
Solutions to Questions
13-1 Capital budgeting screening decisions
concern whether a proposed investment project
passes a preset hurdle, such as a 15% rate of
return. Capital budgeting preference decisions
are concerned with choosing from among two or
more alternative investment projects, each of
which has passed the hurdle.
13-7 One simplifying assumption is that all
cash flows occur at the end of a period. Another
is that all cash flows generated by an
investment project are immediately reinvested
at a rate of return equal to the discount rate.
13-8 No. The cost of capital is not simply the
interest paid on long-term debt. The cost of
capital is a weighted average of the individual
costs of all sources of financing, both debt and
equity.
13-2 The “time value of money” refers to the
fact that a dollar received today is more valuable
than a dollar received in the future simply
because a dollar received today can be invested
to yield more than a dollar in the future.
13-9 The internal rate of return is the rate of
return on an investment project over its life. It is
computed by finding the discount rate that
results in a zero net present value for the
project.
13-3 Discounting is the process of computing
the present value of a future cash flow.
Discounting gives recognition to the time value
of money and makes it possible to meaningfully
add together cash flows that occur at different
times.
13-10 The cost of capital is a hurdle that must
be cleared before an investment project will be
accepted. In the case of the net present value
method, the cost of capital is used as the
discount rate. If the net present value of the
project is positive, then the project is acceptable
because its rate of return is greater than the
cost of capital. In the case of the internal rate of
return method, the cost of capital is compared
to a project’s internal rate of return. If the
project’s internal rate of return is greater than
the cost of capital, then the project is
acceptable.
13-4 Accounting net income is based on
accruals rather than on cash flows. Both the net
present value and internal rate of return
methods focus on cash flows.
13-5 Discounted cash flow methods are
superior to other methods of making capital
budgeting decisions because they recognize the
time value of money and take into account all
future cash flows.
13-6 Net present value is the present value of
cash inflows less the present value of the cash
outflows. The net present value can be negative
if the present value of the outflows is greater
than the present value of the inflows.
13-1
Chapter 13 - Capital Budgeting Decisions
13-11 No. As the discount rate increases, the
present value of a given future cash flow
decreases. For example, the present value factor
for a discount rate of 12% for cash to be
received ten years from now is 0.322, whereas
the present value factor for a discount rate of
14% over the same period is 0.270. If the cash
to be received in ten years is $10,000, the
present value in the first case is $3,220, but only
$2,700 in the second case. Thus, as the
discount rate increases, the present value of a
given future cash flow decreases.
13-13 The project profitability index is
computed by dividing the net present value of
the cash flows from an investment project by
the investment required. The index measures
the profit (in terms of net present value)
provided by each dollar of investment in a
project. The higher the project profitability
index, the more desirable is the investment
project.
13-14 The payback period is the length of time
for an investment to fully recover its initial cost
out of the cash receipts that it generates. The
payback method is used as a screening tool for
investment proposals. The payback method is
useful when a company has cash flow problems.
The payback method is also used in industries
where obsolescence is very rapid.
13-12 The internal rate of return is more than
14% since the net present value is positive. The
internal rate of return would be 14% only if the
net present value (evaluated using a 14%
discount rate) is zero. The internal rate of return
would be less than 14% if the net present value
(evaluated using a 14% discount rate) is
negative.
13-15 Neither the payback method nor the
simple rate of return method considers the time
value of money. Under both methods, a dollar
received in the future is weighed the same as a
dollar received today. Furthermore, the payback
method ignores all cash flows that occur after
the initial investment has been recovered.
13-2
Chapter 13 - Capital Budgeting Decisions
Exercise 13-1 (10 minutes)
1.
Item
Annual cost savings ..
Initial investment .....
Net present value .....
1-8
Now
Cash
Flow
12%
Factor
$7,000 4.968
$(40,000) 1.000
Cash
Flow
Years
Total
Cash
Flows
Year(s)
Present
Value of
Cash
Flows
$ 34,776
(40,000)
$ (5,224)
2.
Item
Annual cost savings ..
$7,000
Initial investment ..... $(40,000)
Net cash flow ...........
8
1
13-3
$ 56,000
(40,000)
$ 16,000
Chapter 13 - Capital Budgeting Decisions
Exercise 13-2 (30 minutes)
1. Annual savings in part-time help ............................
Added contribution margin from expanded sales
(1,000 dozen × $1.20 per dozen) ........................
Annual cash inflows ...............................................
$3,800
1,200
$5,000
2. Factor of the internal
Investment required
=
rate of return
Annual cash inflow
=
$18,600
= 3.720
$5,000
Looking in Exhibit 13B-2, and scanning along the six-period line, we can
see that a factor of 3.720 falls closest to the 16% rate of return.
3. The cash flows will not be even over the six-year life of the machine
because of the extra $9,125 inflow in the sixth year. Therefore, the
above approach cannot be used to compute the internal rate of return in
this situation. Using trial-and-error or some other method, the internal
rate of is 22%:
Item
Initial investment .....
Annual cash inflows ..
Salvage value ...........
Net present value .....
Present
Amount of 22%
Value of
Year(s) Cash Flows Factor Cash Flows
Now
1-6
6
$(18,600)
$5,000
$9,125
13-4
1.000
3.167
0.303
$(18,600)
15,835
2,765
$
0
Chapter 13 - Capital Budgeting Decisions
Exercise 13-3 (15 minutes)
The equipment’s net present value without considering the intangible
benefits would be:
Item
Cost of the equipment ..
Annual cost savings ......
Net present value .........
Year(s)
Now
1-15
Amount of
Cash Flows
20% Present Value
Factor of Cash Flows
$(2,500,000) 1.000
$400,000 4.675
$(2,500,000)
1,870,000
$ (630,000)
The annual value of the intangible benefits would have to be great enough
to offset a $630,000 negative present value for the equipment. This annual
value can be computed as follows:
Required increase in present value
$630,000
=
= $134,759
Factor for 15 years
4.675
13-5
Chapter 13 - Capital Budgeting Decisions
Exercise 13-4 (10 minutes)
1. The project profitability index for each proposal is:
Proposal
Number
A
B
C
D
Net Present
Value
(a)
$36,000
$38,000
$35,000
$40,000
Investment
Required
(b)
$90,000
$100,000
$70,000
$120,000
Project Profitability
Index
(a)  (b)
0.40
0.38
0.50
0.33
2. The ranking is:
Proposal Project Profitability
Number
Index
C
A
B
D
0.50
0.40
0.38
0.33
Note that proposal D has the highest net present value, but it ranks
lowest in terms of the project profitability index.
13-6
Chapter 13 - Capital Budgeting Decisions
Exercise 13-5 (10 minutes)
1. The payback period is determined as follows:
Unrecovered
Investment
Year Investment Cash Inflow
1
2
3
4
5
6
7
8
9
10
$15,000
$8,000
$1,000
$2,000
$2,500
$4,000
$5,000
$6,000
$5,000
$4,000
$3,000
$2,000
$14,000
$20,000
$17,500
$13,500
$8,500
$2,500
$0
$0
$0
$0
The investment in the project is fully recovered in the 7th year. To be
more exact, the payback period is approximately 6.5 years.
2. Because the investment is recovered prior to the last year, the amount
of the cash inflow in the last year has no effect on the payback period.
13-7
Chapter 13 - Capital Budgeting Decisions
Exercise 13-6 (10 minutes)
This is a cost reduction project, so the simple rate of return would be
computed as follows:
Operating cost of old machine ....................
Less operating cost of new machine ...........
Less annual depreciation on the new
machine ($120,000 ÷ 10 years) ...............
Annual incremental net operating income ...
$ 30,000
12,000
12,000
$ 6,000
Cost of the new machine ...........................
Scrap value of old machine ........................
Initial investment.......................................
$120,000
40,000
$ 80,000
Simple rate = Annual incremental net operating income
of return
Initial investment
=
$6,000
= 7.5%
$80,000
13-8
Chapter 13 - Capital Budgeting Decisions
Exercise 13-7 (15 minutes)
1. The payback period is:
Payback period =
Investment required
Annual net cash inflow
=
¥432,000
= 4.8 years
¥90,000
No, the equipment would not be purchased because the payback period
(4.8 years) exceeds the company’s maximum payback time (4.0 years).
2. The simple rate of return would be computed as follows:
Annual cost savings ...............................................
Less annual depreciation (¥432,000 ÷ 12 years) ......
Annual incremental net operating income ...............
Simple rate of return =
=
¥90,000
36,000
¥54,000
Annual incremental net operating income
Initial investment
¥54,000
= 12.5%
¥432,000
No, the equipment would not be purchased because its 12.5% rate of
return is less than the company’s 14% required rate of return.
13-9
Chapter 13 - Capital Budgeting Decisions
Exercise 13-8 (10 minutes)
Item
Project X:
Initial investment ...
Annual cash inflow .
Net present value ...
Project Y:
Initial investment ...
Single cash inflow ..
Net present value ...
Amount of
Year(s) Cash Flows
18%
Factor
Present
Value of
Cash Flows
Now
1-10
$(35,000)
$9,000
1.000
4.494
$(35,000)
40,446
$ 5,446
Now
10
$(35,000)
$150,000
1.000
0.191
$(35,000)
28,650
$( 6,350)
Project X should be selected. Project Y does not provide the required 18%
return, as shown by its negative net present value.
13-10
Chapter 13 - Capital Budgeting Decisions
Exercise 13-9 (10 minutes)
Purchase of the stock .....
Annual cash dividends ....
Sale of the stock ............
Net present value ..........
Present
Amount of 14%
Value of
Year(s) Cash Flows Factor Cash Flows
Now
1-3
3
$(13,000)
$420
$16,000
1.000
2.322
0.675
$(13,000)
975
10,800
$ (1,225)
No, Kathy did not earn a 14% return on the Malti Company stock. The
negative net present value indicates that the rate of return on the
investment is less than the minimum required rate of return of 14%.
13-11
Chapter 13 - Capital Budgeting Decisions
Exercise 13-10 (15 minutes)
Item
Project A:
Cost of equipment ....
Annual cash inflows ..
Salvage value of
the equipment .......
Net present value .....
Project B:
Working capital
investment ............
Annual cash inflows ..
Working capital
released ................
Net present value .....
Year(s)
Amount of
Cash Inflows
14%
Factor
Present
Value of
Cash Flows
Now
1-6
$(100,000)
$21,000
1.000
3.889
$(100,000)
81,669
0.456
3,648
$ (14,683)
6
$8,000
Now
1-6
$(100,000)
$16,000
1.000
3.889
$(100,000)
62,224
6
$100,000
0.456
45,600
$
7,824
The $100,000 should be invested in Project B rather than in Project A.
Project B has a positive net present value whereas Project A has a negative
net present value.
13-12
Chapter 13 - Capital Budgeting Decisions
Exercise 13-11 (30 minutes)
1.
Item
Initial investment .......
Annual cash inflows ....
Net present value .......
Amount of 14% Present Value
Year(s) Cash Flows Factor of Cash Flows
Now
1-12
$(84,900)
$15,000
1.000
5.660
$(84,900)
84,900
$
0
Yes, this is an acceptable investment because it provides exactly the
minimum required 14% rate of return.
2.
Factor of the internal = Investment in the project
rate of return
Annual net cash inflow
=
Cost of the new press
Annual cost savings
=
$217,500
= 7.250
$30,000
Looking in Exhibit 13B-2, and reading along the 18-period line, we find
that a factor of 7.250 represents an internal rate of return of 12%. Since
the required rate of return is 16%, the investment is not acceptable.
3. Factor of the internal
Investment in the project
=
rate of return
Annual net cash inflow
We know that the investment is $217,500, and we can determine the
factor for an internal rate of return of 16% by looking in Exhibit 13B-2
along the 18-period line. This factor is 5.818. Using these figures in the
formula, we get:
$217,500
= 5.818 (factor for 16% for 18 years)
Annual cash inflow
Therefore, the annual cash inflow would have to be: $217,500 ÷ 5.818
= $37,384.
13-13
Chapter 13 - Capital Budgeting Decisions
Exercise 13-12 (15 minutes)
1. Computation of the annual cash inflow associated with the new pinball
machines:
Net operating income ..........................................
Add noncash deduction for depreciation ................
Annual net cash inflow .........................................
$40,000
35,000
$75,000
The payback computation would be:
Payback period =
=
Investment required
Annual net cash inflow
$300,000
= 4.0 years
$75,000 per year
Yes, the pinball machines would be purchased. The payback period is
less than the maximum 5 years required by the company.
2. The simple rate of return would be:
Simple rate = Annual incremental net income
of return
Initial investment
=
$40,000
= 13.3%
$300,000
Yes, the pinball machines would be purchased. The 13.3% return
exceeds 12%.
13-14
Chapter 13 - Capital Budgeting Decisions
Exercise 13-13 (30 minutes)
1. Factor of the internal
Investment required
=
rate of return
Annual net cash inflow
=
$130,400
= 5.216
$25,000
Looking in Exhibit 13B-2 and scanning along the 10-period line, a factor
of 5.216 represents an internal rate of return of 14%.
2.
Item
Year(s)
Initial investment ............ Now
Annual net cash inflows ... 1-10
Net present value ............
Amount of
Cash Flows
$(130,400)
$25,000
Present
14%
Value of
Factor Cash Flows
1.000 $(130,400)
5.216
130,400
$
0
The reason for the zero net present value is that 14% (the discount rate
we have used) represents the machine’s internal rate of return. The
internal rate of return is the discount rate that results in a zero net
present value.
3. Factor of the internal
Investment required
=
rate of return
Annual net cash inflow
=
$130,400
= 5.796 (rounded)
$22,500
Looking in Exhibit 13B-2 and scanning along the 10-period line, a factor
of 5.796 falls closest to the factor for 11%. Thus, to the nearest whole
percent, the internal rate of return is 11%.
13-15
Chapter 13 - Capital Budgeting Decisions
Exercise 13-14 (10 minutes)
Factor of the internal = Investment in the project
rate of return
Annual net cash inflow
=
$106,700
= 5.335
$20,000
Looking in Exhibit 13B-2, and scanning down the 10% column, we find
that a factor of 5.335 equals 8 periods. Thus, the equipment will have to
be used for 8 years in order to yield a return of 10%.
13-16
Chapter 13 - Capital Budgeting Decisions
Exercise 13-15 (10 minutes)
Note: All present value factors in the computation below have been taken
from Exhibit 13B-1 in Appendix 13B, using a 12% discount rate.
Amount of the investment ............................
$104,950
Less present value of Year 1 and Year 2
cash inflows:
Year 1: $30,000 × 0.893 ........................... $26,790
Year 2: $40,000 × 0.797 ........................... 31,880
58,670
Present value of Year 3 cash inflow...............
$ 46,280
Therefore, the expected cash inflow for Year 3 is:
$46,280 ÷ 0.712 = $65,000.
13-17
Chapter 13 - Capital Budgeting Decisions
Problem 13-16 (30 minutes)
1. The project profitability index is computed as follows:
Project
Project
Net Present Investment Profitability
Value
Required
Index
(a)
(b)
(a) ÷ (b)
A ............
$44,323
$160,000
0.28
B ............
$42,000
$135,000
0.31
C ............
$35,035
$100,000
0.35
D............
$38,136
$175,000
0.22
2. a., b., and c.
First preference ........
Second preference ....
Third preference .......
Fourth preference .....
Net Present
Value
A
B
D
C
13-18
Project
Profitability Internal Rate
Index
of Return
C
B
A
D
D
C
A
B
Chapter 13 - Capital Budgeting Decisions
Problem 13-16 (continued)
3. Oxford Company’s opportunities for reinvesting funds as they are
released from a project will determine which ranking is best. The
internal rate of return method assumes that any released funds are
reinvested at the rate of return shown for a project. This means that
funds released from project D would have to be reinvested in another
project yielding a rate of return of 22%. Another project yielding such a
high rate of return might be difficult to find.
The project profitability index approach also assumes that funds
released from a project are reinvested in other projects. But the
assumption is that the return earned by these other projects is equal to
the discount rate, which in this case is only 10%. On balance, the
project profitability index is generally regarded as being the most
dependable method of ranking competing projects.
The net present value is inferior to the project profitability index as a
ranking device, because it looks only at the total amount of net present
value from a project and does not consider the amount of investment
required. For example, it ranks project C as fourth because of its low net
present value; yet this project is the best available in terms of the net
present value generated for each dollar of investment (as shown by the
project profitability index).
13-19
Chapter 13 - Capital Budgeting Decisions
Problem 13-17 (30 minutes)
1. The formula for the project profitability index is:
Project profitability index =
Net present value of the project
Investment required by the project
The indexes for the projects under consideration would be:
Project
Project
Project
Project
1:
2:
3:
4:
$66,140 ÷ $270,000 = 0.24
$72,970 ÷ $450,000 = 0.16
$73,400 ÷ $360,000 = 0.20
$87,270 ÷ $480,000 = 0.18
2. a., b., and c.
First preference ........
Second preference ....
Third preference .......
Fourth preference .....
Project
Net Present Profitability Internal Rate
Value
Index
of Return
4
3
2
1
1
3
4
2
13-20
2
1
4
3
Chapter 13 - Capital Budgeting Decisions
Problem 13-17 (continued)
3. Which ranking is best will depend on Revco Products’ opportunities for
reinvesting funds as they are released from the project. The internal
rate of return method assumes that any released funds are reinvested at
the internal rate of return. This means that funds released from project
#2 would have to be reinvested in another project yielding a rate of
return of 19%. Another project yielding such a high rate of return might
be difficult to find.
The project profitability index approach assumes that funds released
from a project are reinvested in other projects at a rate of return equal
to the discount rate, which in this case is only 10%. On balance, the
project profitability index is the most dependable method of ranking
competing projects.
The net present value is inferior to the project profitability index as a
ranking device because it looks only at the total amount of net present
value from a project and does not consider the amount of investment
required. For example, it ranks project #1 as fourth in terms of
preference because of its low net present value; yet this project is the
best available in terms of the amount of cash inflow generated for each
dollar of investment (as shown by the project profitability index).
13-21
Chapter 13 - Capital Budgeting Decisions
Problem 13-18 (20 minutes)
Item
Cost of new equipment ............
Working capital required ..........
Annual net cash receipts ..........
Cost to construct new roads .....
Salvage value of equipment ......
Working capital released ..........
Net present value ....................
Present
Amount of
20%
Value of
Year(s) Cash Flows Factor Cash Flows
Now
Now
1-4
3
4
4
R(275,000)
R(100,000)
R120,000
R(40,000)
R65,000
R100,000
1.000 R(275,000)
1.000 (100,000)
2.589
310,680
0.579
(23,160)
0.482
31,330
0.482
48,200
R (7,950)
No, the project should not be accepted; it has a negative net present value
at a 20% discount rate. This means that the rate of return on the
investment is less than the company’s required rate of return of 20%.
13-22
Chapter 13 - Capital Budgeting Decisions
Problem 13-19 (20 minutes)
1. The annual net cash inflows would be:
Reduction in annual operating costs:
Operating costs, present hand method .....
Operating costs, new machine .................
Annual savings in operating costs ............
Increased annual contribution margin:
6,000 boxes × $1.50 per box ...................
Total annual net cash inflows .....................
$30,000
7,000
23,000
9,000
$32,000
2.
Item
Cost of the machine ...
Replacement of parts..
Annual net cash
inflows (above) ........
Salvage value of the
machine ..................
Net present value .......
Amount of 20%
Year(s) Cash Flows Factor
Present
Value of
Cash Flows
Now
6
$(120,000)
$(9,000)
1.000
0.335
1-12
$32,000
4.439
142,048
$7,500
0.112
840
$ 19,873
12
13-23
$(120,000)
(3,015)
Chapter 13 - Capital Budgeting Decisions
Problem 13-20 (30 minutes)
1. The income statement would be:
Sales ........................................................
Variable expenses:
Cost of ingredients (20% × $300,000) ..... $60,000
Commissions (12.5% × $300,000) ...........
37,500
Contribution margin ...................................
Selling and administrative expenses:
Salaries .................................................. 70,000
Rent ($3,500 × 12) ................................. 42,000
Depreciation* ......................................... 16,800
Insurance ...............................................
3,500
Utilities ...................................................
27,000
Net operating income ................................
$300,000
97,500
202,500
159,300
$ 43,200
* $270,000 – $18,000 = $252,000
$252,000 ÷ 15 years = $16,800 per year.
2. The formula for the simple rate of return is:
Simple rate of return =
=
Annual incremental net operating income
Initial investment
$43,200
= 16.0%
$270,000
Yes, the franchise would be acquired because it promises a rate of
return in excess of 12%.
13-24
Chapter 13 - Capital Budgeting Decisions
Problem 13-20 (continued)
3. The formula for the payback period is:
Payback period =
=
Investment required
Annual net cash inflow
$270,000
= 4.5 years
$60,000*
*Net operating income + Depreciation = Annual net cash inflow
$43,200 + $16,800 = $60,000
According to the payback computation, the franchise would not be
acquired. The 4.5 years payback is greater than the maximum 4 years
allowed. Payback and simple rate of return can give conflicting signals
as in this example.
13-25
Chapter 13 - Capital Budgeting Decisions
Problem 13-21 (30 minutes)
1. The annual net cost savings would be:
Reduction in labor costs .........................................
Reduction in material waste ...................................
Total .....................................................................
Less increased maintenance costs ($3,000 × 12) ....
Annual net cost savings .........................................
$108,000
6,500
114,500
36,000
$ 78,500
2. Using this cost savings figure, and other data from the text, the net
present value analysis would be:
Item
Cost of the machine ..............
Software and installation .......
Salvage of the old
equipment .........................
Annual cost savings (above) ..
Replacement of parts ............
Salvage of the new machine..
Net present value .................
Present
Amount of 16%
Value of
Year(s) Cash Flows Factor Cash Flows
Now
Now
$(500,000)
$(80,000)
1.000
1.000
$(500,000)
(80,000)
Now
1-12
7
12
$12,000
$78,500
$(45,000)
$20,000
1.000
5.197
0.354
0.168
12,000
407,965
(15,930)
3,360
$(172,605)
No, the automated welding machine should not be purchased. Its net
present value is negative.
3. The dollar value per year that would be required for the intangible
benefits is:
Negative net present value to be offset
$172,605
=
= $33,212
Present value factor
5.197
Thus, the automated welding machine should be purchased if
management believes that the intangible benefits are worth at least
$33,212 per year.
13-26
Chapter 13 - Capital Budgeting Decisions
Problem 13-22 (30 minutes)
The annual net cash inflow from rental of the property would be:
Net operating income, as shown in the
problem ................................................ $32,000
Add back depreciation .............................. 16,000
Annual net cash inflow ............................. $48,000
Given this figure, the present value analysis would be as follows:
Item
Keep the property:
Annual loan payment ........
Annual net cash inflow ......
Resale value of the
property ........................
Present value of cash
flows .............................
Sell the property:
Pay-off of mortgage ..........
Down payment received ....
Annual payments
received ........................
Present value of cash
flows .............................
Year(s)
Amount
of Cash
Flows
1-8
1-15
$(12,000)
$48,000
15
12%
Factor
Present
Value of
Cash
Flows
4.968 $ (59,616)
6.811 326,928
$230,000 * 0.183
42,090
$309,402
Now
Now
$(90,000)
$175,000
1.000
1.000
$(90,000)
175,000
1-15
$26,500
6.811
180,492
$265,492
Net present value in favor
of keeping the property .....
$ 43,910
*Land, $50,000 × 3 = $150,000, plus building, $80,000 = $230,000.
Thus, Professor Martinas should be advised to keep the property. Note that
even if the property were worth nothing at the end of 15 years, it would
still be more desirable to keep the property rather than sell it under the
terms offered by the realty company.
13-27
Chapter 13 - Capital Budgeting Decisions
Problem 13-23 (30 minutes)
1. The annual incremental net operating income can be determined as
follows:
Ticket revenue (50,000 × $3.60) ................
Selling and administrative expenses:
Salaries ..................................................
Insurance ...............................................
Utilities ...................................................
Depreciation* .........................................
Maintenance ...........................................
Total selling and administrative expenses ....
Net operating income ................................
$180,000
$85,000
4,200
13,000
27,500
9,800
139,500
$ 40,500
*$330,000 ÷ 12 years = $27,500 per year.
2. The simple rate of return is:
Annual incremental net operating income
Simple rate =
of return
Initial investment (net of salvage from old equipment)
=
$40,500
$40,500
=
= 15%
$330,000 - $60,000
$270,000
Yes, the water slide would be constructed. Its return is greater than the
specified hurdle rate of 14%.
3. The payback period is:
Payback = Investment required (net of salvage from old equipment)
period
Annual net cash inflow
=
$330,000 - $60,000
$270,000
=
= 3.97 years (rounded)
$68,000*
$68,000*
*Net operating income + Depreciation = Annual net cash flow
$40,500 + $27,500 = $68,000.
Yes, the water slide would be constructed. The payback period is within
the 5 year payback required by Mr. Sharkey.
13-28
Chapter 13 - Capital Budgeting Decisions
Problem 13-24 (30 minutes)
1. Average weekly use of the auto wash and the vacuum will be:
Auto wash:
$1,350
= 675 uses
$2.00
Vacuum: 675 × 60% = 405 uses
The expected annual net cash flow from operations would be:
Auto wash cash receipts ($1,350 × 52) ...........
Vacuum cash receipts (405 × $1.00 × 52) ......
Total cash receipts ......................................
Less cash disbursements:
Water (675 × $0.20 × 52) ...........................
Electricity (405 × $0.10 × 52) .....................
Rent ($1,700 × 12) .....................................
Cleaning ($450 × 12) ..................................
Insurance ($75 × 12) ..................................
Maintenance ($500 × 12) ............................
Total cash disbursements ...............................
Annual net cash flow from operations .............
2.
Item
Cost of equipment ..............
Working capital needed ......
Annual net cash flow from
operations (above)...........
Salvage of equipment .........
Working capital released .....
Net present value ...............
$70,200
21,060
91,260
$ 7,020
2,106
20,400
5,400
900
6,000
Amount of
Cash
10%
Year(s)
Flows
Factor
Now
Now
$(200,000)
$(2,000)
1.000
1.000
1-8
8
8
$49,434
$20,000
$2,000
5.335
0.467
0.467
41,826
$49,434
Present
Value of
Cash Flows
$(200,000)
(2,000)
263,730
9,340
934
$ 72,004
Yes, Mr. Duncan should open the auto wash. The positive net present
value indicates that the rate of return on this investment exceeds the 10%
required rate of return.
13-29
Chapter 13 - Capital Budgeting Decisions
Problem 13-25 (30 minutes)
1. The present value of cash flows are:
Item
Purchase alternative:
Purchase cost of the cars
(10 × $17,000) ...................
Annual cost of servicing, etc. .
Repairs:
First year ...........................
Second year .......................
Third year ..........................
Resale value of the cars .........
Present value of cash flows ....
Lease alternative:
Security deposit ....................
Annual lease payments ..........
Refund of deposit ..................
Present value of cash flows ....
Present
Amount of 18%
Value of
Year(s) Cash Flows Factor Cash Flows
Now
1-3
$(170,000)
$(3,000)
1
2
3
3
$(1,500)
$(4,000)
$(6,000)
$85,000
Now
1-3
3
$(10,000)
$(55,000)
$10,000
Net present value in favor of
leasing the cars .....................
1.000 $(170,000)
2.174
(6,522)
0.847
0.718
0.609
0.609
(1,271)
(2,872)
(3,654)
51,765
$(132,554)
1.000 $ (10,000)
2.174 (119,570)
0.609
6,090
$(123,480)
$
9,074
2. The company should lease the cars because this alternative has the
lowest present value of total costs.
13-30
Chapter 13 - Capital Budgeting Decisions
Problem 13-26 (45 minutes)
1. A net present value computation for each investment follows:
Item
Common stock:
Purchase of the stock .........
Sale of the stock ................
Net present value ...............
Preferred stock:
Purchase of the stock .........
Annual cash dividend
(6%)...............................
Sale of the stock ................
Net present value ...............
Bonds:
Purchase of the bonds ........
Semiannual interest
received ..........................
Sale of the bonds ...............
Net present value ...............
Amount of
Year(s) Cash Flows
16%
Factor
Present
Value of
Cash Flows
Now
3
$(95,000)
$160,000
1.000
0.641
$ (95,000)
102,560
$
7,560
Now
$(30,000)
1.000
$ (30,000)
1-3
3
$1,800
$27,000
2.246
0.641
4,043
17,307
$ (8,650)
Now
$(50,000)
1.000
$ (50,000)
1-6*
6*
$3,000
$52,700
4.623**
0.630
$
13,869
33,201
(2,930)
* 6 semiannual interest periods.
** Factor for 6 periods at 8%.
Linda earned a 16% rate of return on the common stock, but not on the
preferred stock or the bonds.
13-31
Chapter 13 - Capital Budgeting Decisions
Problem 13-26 (continued)
2. Considering all three investments together, Linda did not earn a 16%
rate of return. The computation is:
Common stock .........................
Preferred stock .........................
Bonds ......................................
Overall net present value ..........
Net
Present
Value
$ 7,560
(8,650)
(2,930)
$(4,020)
The defect in the broker’s computation is that it does not consider the
time value of money and therefore has overstated the rate of return
earned.
3.
Factor of the internal = Investment required
rate of return
Annual net cash inflow
Substituting the $239,700 investment and the factor for 14% for 12
periods into this formula, we get:
$239,700
= 5.660
Annual cash inflow
Therefore, the required annual net cash inflow is: $239,700 ÷ 5.660 =
$42,350.
13-32
Chapter 13 - Capital Budgeting Decisions
Problem 13-27 (30 minutes)
1. The total-cost approach:
Item
Purchase the new truck:
Initial investment in the
new truck .......................
Salvage of the old truck .....
Annual cash operating
costs ..............................
Salvage of the new truck ....
Present value of the net
cash outflows ...................
Keep the old truck:
Overhaul needed now .........
Annual cash operating
costs ...............................
Salvage of the old truck.......
Present value of the net
cash outflows ...................
Present
Amount of 16%
Value of
Year(s) Cash Flows Factor Cash Flows
Now
Now
$(30,000)
$9,000
1.000
1.000
$(30,000)
9,000
1-8
8
$(6,500)
$4,000
4.344
0.305
(28,236)
1,220
$(48,016)
Now
$(7,000)
1.000
$ (7,000)
1-8
8
$(10,000)
$1,000
4.344
0.305
(43,440)
305
$(50,135)
Net present value in favor of
purchasing the new truck ....
$ 2,119
The company should purchase the new truck because the present value
of the net cash outflows is lower for that alternative.
13-33
Chapter 13 - Capital Budgeting Decisions
Problem 13-27 (continued)
2. The incremental-cost approach:
Item
Incremental investment in
the new truck* ...............
Salvage of the old truck .....
Savings in annual cash
operating costs ...............
Difference in salvage value
in 8 years .......................
Net present value in favor
of purchasing the new
truck ..............................
Amount of
Present
Cash
16%
Value of
Year(s)
Flows
Factor Cash Flows
Now
Now
$(23,000) 1.000
$9,000 1.000
$(23,000)
9,000
1-8
$3,500
4.344
15,204
8
$3,000
0.305
915
$ 2,119
*$30,000 – $7,000 = $23,000. The $9,000 salvage value of the old truck
could also be deducted, leaving an incremental investment for the new
truck of only $14,000.
13-34
Chapter 13 - Capital Budgeting Decisions
Problem 13-28 (60 minutes)
1. Computation of the annual net cost savings:
Savings in labor costs (25,000 hours × $16 per hour) .
Savings in inventory carrying costs .............................
Total .........................................................................
Less increased power and maintenance cost
($2,500 per month × 12 months) ............................
Annual net cost savings .............................................
2.
Cost of the robot ............
Installation and
software ......................
Cash released from
inventory.....................
Annual net cost savings ..
Salvage value .................
Net present value ...........
Year(s)
Amount of
Cash Flows
$400,000
210,000
610,000
30,000
$580,000
20% Present Value
Factor of Cash Flows
Now
$(1,800,000) 1.000
$(1,800,000)
Now
$(900,000) 1.000
(900,000)
1
1-10
10
$400,000
$580,000
$70,000
0.833
4.192
0.162
333,200
2,431,360
11,340
$ 75,900
Yes, the robot should be purchased. It has a positive net present value
at a 20% discount rate.
3. Recomputation of the annual net cost savings:
Savings in labor costs (22,500 hours × $16 per hour)
Savings in inventory carrying costs ...........................
Total .......................................................................
Less increased power and maintenance cost
($2,500 per month × 12 months) ..........................
Annual net cost savings ...........................................
13-35
$360,000
210,000
570,000
30,000
$540,000
Chapter 13 - Capital Budgeting Decisions
Problem 13-28 (continued)
Recomputation of the net present value of the project:
Cost of the robot .............
Installation and
software .......................
Cash released from
inventory......................
Annual net cost savings ...
Salvage value ..................
Net present value ............
Year(s)
Amount of
Cash Flows
20%
Factor
Present
Value of
Cash Flows
Now
$(1,800,000)
1.000 $(1,800,000)
Now
$(975,000)
1.000
(975,000)
1
1-10
10
$400,000
$540,000
$70,000
0.833
4.192
0.162
333,200
2,263,680
11,340
$ (166,780)
It appears that the company did not make a wise investment because
the rate of return that will be earned by the new equipment is less than
20%. However, see Part 4 below. This illustrates the difficulty in
estimating data, and also shows what a heavy impact even seemingly
small changes in the data can have on net present value. To mitigate
these problems, some companies require several analyses showing the
“most likely” results, the “best case” results, and the “worst case”
results. Probability analysis can also used when probabilities can be
attached to the various possible outcomes.
13-36
Chapter 13 - Capital Budgeting Decisions
Problem 13-28 (continued)
4. a. Several intangible benefits are usually associated with investments in
automated equipment. These intangible benefits include:
 Greater throughput.
 Greater variety of products.
 Higher quality.
 Reduction in inventories.
The value of these benefits can equal or exceed any savings that may
come from reduced labor cost. However, these benefits are hard to
quantify.
b. Negative net present value to be offset
$166,780
=
= $39,785
Present value factor, 10 years at 20%
4.192
Thus, the intangible benefits in (a) would have to generate a cash
inflow of $39,785 per year in order for the robot to yield a 20% rate
of return.
13-37
Chapter 13 - Capital Budgeting Decisions
Problem 13-29 (45 minutes)
1. Present cost of transient workers ..........................
$40,000
Less out-of-pocket costs to operate the cherry picker:
Cost of an operator and assistant ....................... $14,000
Insurance ..........................................................
200
Fuel .................................................................. 1,800
Maintenance contract ......................................... 3,000 19,000
Annual savings in cash operating costs ..................
$21,000
2. The first step is to determine the annual incremental net operating
income:
Annual savings in cash operating costs .............
Less annual depreciation ($90,000 ÷ 12 years) .
Annual incremental net operating income .........
Simple rate of return =
=
$21,000
7,500
$13,500
Annual incremental net operating income
Initial investment
$13,500
= 14.3% (rounded)
$94,500
No, the cherry picker would not be purchased. The expected return is
less than the 16% return required by the farm.
3. The formula for the payback period is:
Payback period =
=
Investment required
Annual net cash inflow
$94,500
= 4.5 years
$21,000*
* In this case, the cash inflow is measured by the annual savings
in cash operating costs.
Yes, the cherry picker would be purchased. The payback period is less
than 5 years. Note that this answer conflicts with the answer in Part 2.
13-38
Chapter 13 - Capital Budgeting Decisions
Problem 13-29 (continued)
4. The formula for the internal rate of return is:
Factor of the internal = Investment required
rate of return
Annual net cash inflow
=
$94,500
= 4.500
$21,000
Looking in Exhibit 13B-2, and reading along the 12-period line, a factor
of 4.500 represents an internal rate of return of approximately 20%.
No, the simple rate of return is not an accurate guide in investment
decisions. It ignores the time value of money.
13-39
Chapter 13 - Capital Budgeting Decisions
Problem 13-30 (90 minutes)
1. Factor of the internal
Investment required
=
rate of return
Annual net cash inflow
=
$330,000
= 4.125
$80,000
From Exhibit 13B-2, reading along the 9-period line, a factor of 4.125 is
closest to 19%.
2. Factor of the internal
Investment required
=
rate of return
Annual net cash inflow
We know the investment is $330,000, and we can determine the factor
for an internal rate of return of 14% by looking in Exhibit 13B-2 along
the 9-period line. This factor is 4.946. Using these figures in the
formula, we get:
$330,000
= 4.946
Annual net cash inflow
Therefore, the annual cash inflow would be: $330,000 ÷ 4.946 =
$66,721.
3. a. 6-year useful life:
The factor for the internal rate of return would still be 4.125 [as
computed in (1) above]. From Exhibit 13B-2, reading along the 6period line, a factor of 4.125 falls closest to 12%.
b. 12-year useful life:
The factor of the internal rate of return would again be 4.125. From
Exhibit 13B-2, reading along the 12-period line, a factor of 4.125 falls
closest to 22%.
13-40
Chapter 13 - Capital Budgeting Decisions
Problem 13-30 (continued)
The 12% return in part (a) is less than the 14% minimum return that
Ms. Winder wants to earn on the project. Of equal or even greater
importance, the following diagram should be pointed out to Ms. Winder:
6
Years
12%
3 years shorter
A decrease
of 7%
9
Years
19%
3 years longer
An increase of
3%
12
Years
22%
As this illustration shows, a decrease in years has a much greater impact
on the rate of return than an increase in years. This is because of the
time value of money; added cash inflows far into the future do little to
enhance the rate of return, but loss of cash inflows in the near term can
do much to reduce it. Therefore, Ms. Winder should be very concerned
about any potential decrease in the life of the equipment, while at the
same time realizing that any increase in the life of the equipment will do
little to enhance her rate of return.
13-41
Chapter 13 - Capital Budgeting Decisions
Problem 13-30 (continued)
4. a. The expected annual cash inflow would be:
$80,000 × 80% = $64,000
$330,000
= 5.156 (rounded)
$64,000
From Exhibit 13B-2, reading along the 9-period line, a factor of 5.156
is closest to 13%.
b. The expected annual cash inflow would be:
$80,000 × 120% = $96,000
$330,000
= 3.438 (rounded)
$96,000
From Exhibit 13B-2, reading along the 9-period line, a factor of 3.438
is closest to 25%.
Unlike changes in time, increases and decreases in cash flows at a given
point in time have basically the same impact on the rate of return, as
shown below:
20% decrease
$64,000
Cash Inflow
13%
$80,000
Cash Inflow
19%
20% increase
An increase
of 6%
A decrease
of 6%
13-42
$96,000
Cash Inflow
25%
Chapter 13 - Capital Budgeting Decisions
Problem 13-30 (continued)
5. The cash flows are not even over the 8-year period (there is an extra
$135,440 cash inflow from sale of the equipment at the end of the
eighth year), so the formula method cannot be used to compute the
internal rate of return. Using trial-and-error or more sophisticated
methods, it turns out that the internal rate of return is 10%. This can be
verified by computing the net present value of the project, which is zero
at the discount rate of 10%, as shown below:
Item
Present
Amount of 10%
Value of
Year(s) Cash Flows Factor Cash Flows
Investment in the equipment . Now
$(330,000) 1.000 $(330,000)
Annual cash inflow ................ 1-8
$50,000 5.335
266,750
Sale of the equipment ...........
8
$135,440 0.467
63,250
Net present value ...........................................................
$
0
13-43
Chapter 13 - Capital Budgeting Decisions
Problem 13-31 (60 minutes)
1. a. Sales revenue ..............................................
$300,000
Variable production expenses (@ 20%) .........
60,000
Contribution margin .....................................
240,000
Fixed expenses:
Advertising ................................................ $ 40,000
Salaries ..................................................... 110,000
Utilities .....................................................
5,200
Insurance..................................................
800
Depreciation ..............................................
31,500 *
Total fixed expenses .....................................
187,500
Net operating income ...................................
$ 52,500
* [$420,000 – (10% × $420,000)] ÷ 12 years = $31,500.
b. The formula for the simple rate of return is:
Simple rate = Annual incremental net operating income
of return
Initial investment
=
$52,500
= 12.5%
$420,000
c. The formula for the payback period is:
Payback period =
=
Investment required
Annual net cash inflow
$420,000
= 5 years
$84,000*
*$52,500 net operating income + $31,500 depreciation = $84,000.
13-44
Chapter 13 - Capital Budgeting Decisions
Problem 13-31 (continued)
2. a. The formula for the simple rate of return is:
Simple rate of return =
Annual incremental net operating income
Initial
- Salvage from
investment old equipment
The reduction in costs with the new equipment would be:
Annual costs, old equipment ..................
$78,000
Annual costs, new equipment:
Salary of operator ............................... $16,350
Maintenance .......................................
5,400 21,750
Annual cost savings ...............................
$56,250
Annual cost savings ...............................
Less annual depreciation on new
equipment ($234,000 ÷ 13 years) ........
Annual incremental net operating
income ...............................................
$56,250
18,000
$38,250
Thus, the simple rate of return would be:
$38,250
$38,250
=
= 17%
$234,000 - $9,000
$225,000
b. The formula for the payback period remains the same as in Part (1),
except we must reduce the investment required by the salvage from
sale of the old equipment:
Investment - Salvage from
required
old equipment
Payback period =
Annual net cash inflow
=
$234,000 - $9,000
$225,000
=
= 4 years
$56,250*
$56,250*
*See Part (2a) above.
3. According to the company’s criteria, machine B should be purchased.
Machine A does not meet either the required minimum rate of return or
4-year payback period.
13-45
Chapter 13 - Capital Budgeting Decisions
Problem 13-32 (60 minutes)
1. The net cash inflow from sales of the device for each year would be:
Year
1
2
3
4-12
Sales in units........................
6,000
12,000
15,000
18,000
Sales in dollars
(@ $35 each) .................... $ 210,000 $420,000 $525,000 $630,000
Variable expenses
(@ $15 each) ....................
90,000
180,000
225,000 270,000
Contribution margin .............. 120,000
240,000
300,000 360,000
Fixed expenses:
Salaries and other* ............ 110,000
110,000
110,000 110,000
Advertising ........................ 180,000
180,000
150,000 120,000
Total fixed expenses ............. 290,000
290,000
260,000 230,000
Net cash inflow (outflow) ...... $(170,000) $(50,000) $ 40,000 $130,000
* Depreciation is not a cash expense and therefore must be eliminated
from this computation. The analysis is:
($315,000 – $15,000 = $300,000) ÷ 12 years = $25,000 depreciation;
$135,000 total expense – $25,000 depreciation = $110,000.
13-46
Chapter 13 - Capital Budgeting Decisions
Problem 13-32 (continued)
2. The net present value of the proposed investment would be:
Item
Investment in equipment ........
Working capital needed ...........
Yearly cash flows (see above) ..
Yearly cash flows (see above) ..
Yearly cash flows (see above) ..
Yearly cash flows (see above) ..
Salvage value of equipment .....
Release of working capital .......
Net present value ...................
Amount of 14%
Year(s) Cash Flows Factor
Now
Now
1
2
3
4-12
12
12
$(315,000)
$(60,000)
$(170,000)
$(50,000)
$40,000
$130,000
$15,000
$60,000
Present
Value of
Cash
Flows
1.000 $(315,000)
1.000
(60,000)
0.877
(149,090)
0.769
(38,450)
0.675
27,000
3.338 * 433,940
0.208
3,120
0.208
12,480
$ (86,000)
* Present value factor for 12 periods ....................................... 5.660
Present value factor for 3 periods ......................................... 2.322
Present value factor for 9 periods, starting 4 periods in the
future .............................................................................. 3.338
Since the net present value is negative, the company should not accept
the device as a new product.
13-47
Chapter 13 - Capital Budgeting Decisions
Case 13-33 (60 minutes)
1. Rachel Arnett’s revision of her first proposal can be considered a
violation of the IMA’s Statement of Ethical Professional Practice. She
discarded her reasonable projections and estimates after she was
questioned by William Earle. She used figures that had a remote chance
of occurring. By doing this, she violated the requirements to
“Communicate information fairly and objectively” and “disclose all
relevant information that could reasonably be expected to influence an
intended user’s understanding of the reports, analyses, or
recommendations.” By altering her analysis, she also violated the
Integrity standard. She engaged in an activity that would prejudice her
ability to carry out her duties ethically. In addition, she violated the
Competence standard—“Provide decision support information and
recommendations that are accurate, clear, concise, and timely.”
2. Earle was clearly in violation of the Standards of Ethical Conduct for
Management Accountants because he tried to persuade a subordinate to
prepare a proposal with data that was false and misleading. Earle has
violated the standards of Competence (Provide decision support
information and recommendations that are accurate, clear, concise, and
timely.), Integrity (Mitigate actual conflicts of interest. Regularly
communicate with business associates to avoid apparent conflicts of
interest.), and Credibility (Communicate information fairly and
objectively. Disclose all relevant information that could reasonably be
expected to influence an intended user’s understanding of the reports,
analyses, or recommendations.).
13-48
Chapter 13 - Capital Budgeting Decisions
Case 13-33 (continued)
3. The internal controls Fore Corporation could implement to prevent
unethical behavior include:
 approval of all formal capital expenditure proposals by the Controller
and/or the Board of Directors.
 designating a non-accounting/finance manager to coordinate capital
expenditure requests and/or segregating duties during the preparation
and approval of capital expenditure requests.
 requiring that all capital expenditure proposals be reviewed by senior
operating management, which includes the Controller, before the
proposals are submitted for approval.
 requiring the internal audit staff to review all capital expenditure
proposals or contracting external auditors to review the proposal if the
corporation lacks manpower.
(Unofficial CMA Solution, adapted)
13-49
Chapter 13 - Capital Budgeting Decisions
Case 13-34 (60 minutes)
1. Perhaps the clearest approach to a solution is as follows:
Item
Purchase of facilities:
Initial payment—property .....
Annual payments—property ..
Annual cash operating costs..
Resale value of the property .
Net present value .................
Lease of facilities:
Initial deposit .......................
First lease payment ..............
Remaining lease payments ...
Annual cost of repairs, etc. ...
Return of deposit .................
Net present value .................
Amount of 16%
Year(s) Cash Flows Factor
Present
Value of
Cash Flows
Now
1-4
1-18
18
$(350,000)
$(175,000)
$(20,000)
$500,000
1.000
2.798
5.818
0.069
$(350,000)
(489,650)
(116,360)
34,500
$(921,510)
Now
Now
1-17
1-18
18
$(8,000)
$(120,000)
$(120,000)
$(4,500)
$8,000
1.000
1.000
5.749
5.818
0.069
$ (8,000)
(120,000)
(689,880)
(26,181)
552
$(843,509)
Net present value in favor of
leasing the facilities ..............
$ 78,001
This is a least-cost decision, and, as shown above, the total-cost
approach is the simplest way to handle the data. The problem with Sam
Watkin’s approach, in which he simply added up the payments, is that it
ignores the time value of money. The purchase option ties up large
amounts of funds that could be earning a return elsewhere.
13-50
Chapter 13 - Capital Budgeting Decisions
Case 13-34 (continued)
The incremental-cost-approach can also be used, although this approach
is harder to follow and would not be as clear in a presentation to the
executive committee. The data could be arranged as follows:
Buy rather than lease:
Item
Incremental initial
payment ($350,000 –
$120,000 = $230,000) ....
Deposit avoided by
purchasing .....................
Annual payments—
property .........................
Lease payments avoided ....
Additional cash operating
costs ($20,000 – $4,500
= $15,500) .....................
Difference between resale
value and deposit at
end ($500,000 – $8,000
= $492,000) ...................
Net present value ..............
Amount of 16%
Year(s) Cash Flows Factor
Now
Now
$(230,000)
$8,000
1.000
1.000
Present
Value of
Cash Flows
$(230,000)
8,000
1-4
1-17
$(175,000)
$120,000
2.798
5.749
(489,650)
689,880
1-18
$(15,500)
5.818
(90,179)
18
$492,000
0.069
33,948
$ (78,001)
2. If Sam Watkins brings up the issue of the building’s future sales value, it
should be pointed out that a property that can be sold for $500,000 in
18 years has a present value of only $34,500 if a company can invest
money at 16%. In other words, a high future sales value is often worth
very little in terms of present value when money can be invested at a
high rate of return, such as in the case of Top-Quality Stores. Note that
the building’s sale value could be three times as high in 18 years (i.e.,
$1,500,000) and the lease alternative would still be better than the
purchase alternative.
13-51
Chapter 13 - Capital Budgeting Decisions
Case 13-35 (90 minutes)
1. This least-cost problem can be worked either using the total-cost or the incremental-cost approach.
Both solutions are given below. Regardless of which approach is used, we must first compute the
annual production costs that would result from each of the machines. The computations are:
Units produced .......................................
Model 400: Total cost at $0.80 per unit...
Model 800: Total cost at $0.60 per unit...
1
40,000
$32,000
$24,000
2
Year
60,000
$48,000
$36,000
3
80,000
$64,000
$48,000
4-10
90,000
$72,000
$54,000
Using these data, the solution by the total-cost approach would be:
Item
Alternative 1: Purchase the Model 400 machine:
Cost of a new machine ....................................
Cost of a new machine ....................................
Market value of the replacement machine ........
Production costs (above) .................................
Production costs (above) .................................
Production costs (above) .................................
Production costs (above) .................................
Repairs and maintenance (maintenance for
two Model 400 machines @ $2,500 per
year) ...........................................................
Present value of cash flows .............................
*See the note on the next page.
13-52
Year(s)
Amount of
Cash Flows
Now
7
10
1
2
3
4-10
$(170,000)
$(200,000)
$140,000
$(32,000)
$(48,000)
$(64,000)
$(72,000)
1-10
$(5,000)
20%
Factor
Present
Value of
Cash Flows
1.000
$(170,000)
0.279
(55,800)
0.162
22,680
0.833
(26,656)
0.694
(33,312)
0.579
(37,056)
2.086 * (150,192)
4.192
(20,960)
$(471,296)
Chapter 13 - Capital Budgeting Decisions
Case 13-35 (continued)
Item
Alternative 2: Purchase the Model 800 machine:
Cost of a new machine ....................................
Production costs (above) .................................
Production costs (above) .................................
Production costs (above) .................................
Production costs (above) .................................
Repairs and maintenance ................................
Present value of cash flows .............................
Year(s)
Amount of
Cash Flows
20%
Factor
Now
1
2
3
4-10
1-10
$(300,000)
$(24,000)
$(36,000)
$(48,000)
$(54,000)
$(3,800)
1.000
0.833
0.694
0.579
2.086 *
4.192
Net present value in favor of purchasing the
model 400 machine .........................................
* Present value factor for 10 periods ...................................................
Present value factor for 3 periods .....................................................
Present value factor for 7 periods starting 4 periods in the future .......
Present
Value of
Cash Flows
$(300,000)
(19,992)
(24,984)
(27,792)
(112,644)
(15,930)
$(501,342)
$ 30,046
4.192
2.106
2.086
When doing an analysis by the incremental-cost approach, it is necessary to proceed from a
perspective of one of the two alternatives. Since the Model 800 is the more costly of the two, we will
proceed from the perspective of this alternative. The computations are provided on the following
page.
13-53
Chapter 13 - Capital Budgeting Decisions
Case 13-35 (continued)
The solution from an incremental-cost approach would be:
Item
Incremental cost of the Model 800 machine:
Cost avoided on a replacement Model 400 machine
Market value forgone on the replacement .............
Savings in production costs ..................................
Savings in production costs ..................................
Savings in production costs ..................................
Savings in production costs ..................................
Savings on repairs and maintenance costs ............
Net present value of purchasing a Model 800
machine rather than a second Model 400
machine ...........................................................
Year(s)
Now
7
10
1
2
3
4-10
1-10
Amount of
Cash
Flows
$(130,000)
$200,000
$(140,000)
$8,000
$12,000
$16,000
$18,000
$1,200
20%
Factor
1.000
0.279
0.162
0.833
0.694
0.579
2.086
4.192
Present
Value of
Cash Flows
$(130,000)
55,800
(22,680)
6,664
8,328
9,264
37,548
5,030
$(30,046)
Therefore, the company should purchase a second Model 400 machine rather than purchase the
Model 800 machine.
2. An increase in labor costs would make the Model 800 machine more desirable because the labor cost
per unit of product is only $0.16 on the Model 800 machine, as compared to $0.49 per unit on the
Model 400 machine.
3. An increase in materials cost would make the Model 800 machine less desirable because the
materials cost per unit of product is $0.40 on the Model 800 machine, as compared to only $0.25 per
unit on the Model 400 machine.
13-54
Chapter 13 - Capital Budgeting Decisions
Appendix 13A
The Concept of Present Value
Exercise 13A-1 (10 minutes)
1. From Exhibit 13B-1, the factor for 10% for 3 periods is 0.751. Therefore,
the present value of the required investment is:
$8,000 × 0.751 = $6,008
2. From Exhibit 13B-1, the factor for 14% for 3 periods is 0.675. Therefore,
the present value of the required investment is:
$8,000 × 0.675 = $5,400
13-55
Chapter 13 - Capital Budgeting Decisions
Exercise 13A-2 (10 minutes)
Amount of Cash Flows
Investment Investment
Year
A
B
1
2
3
4
$3,000
$6,000
$9,000
$12,000
$12,000
$9,000
$6,000
$3,000
18%
Factor
0.847
0.718
0.609
0.516
Investment project B is best.
13-56
Present Value of Cash
Flows
Investment Investment
A
B
$ 2,541
4,308
5,481
6,192
$18,522
$10,164
6,462
3,654
1,548
$21,828
Chapter 13 - Capital Budgeting Decisions
Exercise 13A-3 (10 minutes)
The present value of the first option is $150,000, since the entire amount
would be received immediately.
The present value of the second option is:
Annual annuity: $14,000 × 7.469 (Exhibit 13B-2) ........
Lump-sum payment: $60,000 × 0.104 (Exhibit 13B-1)
Total present value ....................................................
$104,566
6,240
$110,806
Thus, Julie should accept the first option, which has a much higher present
value.
On the surface, the second option appears to be a better choice because it
promises a total cash inflow of $340,000 over the 20-year period ($14,000
× 20 = $280,000; $280,000 + $60,000 = $340,000), whereas the first
option promises a cash inflow of only $150,000. However, the cash inflows
under the second option are spread out over 20 years, causing the present
value to be far less.
13-57
Chapter 13 - Capital Budgeting Decisions
Exercise 13A-4 (10 minutes)
1. From Exhibit 13B-2, the factor for 16% for 8 periods is 4.344. The
computer system should be purchased only if its net present value is
positive. This will occur only if the purchase price is less:
$7,000 × 4.344 = $30,408
2. From Exhibit 13B-2, the factor for 20% for 8 periods is 3.837. Therefore,
the maximum purchase price would be:
$7,000 × 3.837 = $26,859
13-58
Chapter 13 - Capital Budgeting Decisions
Exercise 13A-5 (10 minutes)
1. From Exhibit 13B-2, the factor for 12% for 20 periods is 7.469. Thus,
the present value of Mr. Ormsby’s winnings is:
$80,000 × 7.469 = $597,520
2. Whether or not it is correct to say that Mr. Ormsby is the state’s newest
millionaire depends on your point of view. He will receive more than a
million dollars over the next 20 years; however, he is not a millionaire as
shown by the present value computation above, nor will he ever be a
millionaire if he spends his winnings rather than investing them.
13-59
Chapter 13 - Capital Budgeting Decisions
Exercise 13A-6 (10 minutes)
1. From Exhibit 13B-1, the factor for 10% for 5 periods is 0.621. Therefore,
the company must invest:
$500,000 × 0.621 = $310,500
2. From Exhibit 13B-1, the factor for 14% for 5 periods is 0.519. Therefore,
the company must invest:
$500,000 × 0.519 = $259,500
13-60
Chapter 13 - Capital Budgeting Decisions
Appendix 13C
Income Taxes in Capital Budgeting Decisions
Exercise 13C-1 (10 minutes)
1. Management development program cost ..............
Multiply by 1 – 0.30 ............................................
After-tax cost......................................................
$100,000
× 70%
$ 70,000
2. Increased contribution margin .............................
Multiply by 1 – 0.30 ............................................
After-tax cash flow (benefit) ................................
$40,000
× 70%
$28,000
3. The depreciation deduction is $210,000 ÷ 7 years = $30,000 per year,
which has the effect of reducing taxes by 30% of that amount, or
$9,000 per year.
13-61
Chapter 13 - Capital Budgeting Decisions
Exercise 13C-2 (20 minutes)
1.
Annual cost of operating the present equipment.......
Annual cost of the new dishwashing machine:
Cost for wages of operators ..................................
Cost for maintenance ...........................................
Annual net cost savings (cash inflow) ......................
$85,000
$48,000
2,000
50,000
$35,000
2. The net present value analysis would be as follows:
Items and Computations
Year(s)
Cost of the new dishwashing machine .. Now
Annual net cost savings (above) .......... 1-12
Depreciation deductions* .................... 1-7
Cost of the new water jets ..................
6
Salvage value of the new machine ....... 12
Net present value ...............................
(1)
Amount
(2)
Tax Effect
$(140,000)
—
$35,000 1 – 0.30
$20,000
0.30
$(15,000) 1 – 0.30
$9,000 1 – 0.30
*$140,000 ÷ 7 years = $20,000 per year
Yes, the new dishwashing machine should be purchased.
13-62
(1)×(2)
After-Tax
Cash
Flows
$(140,000)
$24,500
$6,000
$(10,500)
$6,300
14%
Factor
Present
Value of
Cash
Flows
1.000 $(140,000)
5.660
138,670
4.288
25,728
0.456
(4,788)
0.208
1,310
$ 20,920
Chapter 13 - Capital Budgeting Decisions
Exercise 13C-3 (20 minutes)
Items and Computations
Project A:
Investment in heavy trucks ........
Annual net cash inflows .............
Depreciation deductions*...........
Salvage value of the trucks ........
Net present value ......................
Project B:
Investment in working capital ....
Annual net cash inflows .............
Release of working capital .........
Net present value ......................
Year(s)
(1)
Amount
(1)×(2)
Present
(2)
After-Tax
12%
Value of
Tax Effect Cash Flows Factor Cash Flows
Now
1-9
1-5
9
$(130,000)
—
$25,000 1 – 0.30
$26,000
0.30
$15,000 1 – 0.30
$(130,000)
$17,500
$7,800
$10,500
1.000
5.328
3.605
0.361
$(130,000)
93,240
28,119
3,791
$ (4,850)
Now
1-9
9
$(130,000)
—
$25,000 1 – 0.30
$130,000
—
$(130,000)
$17,500
$130,000
1.000
5.328
0.361
$(130,000)
93,240
46,930
$ 10,170
*$130,000 ÷ 5 years = $26,000 per year
13-63
Chapter 13 - Capital Budgeting Decisions
Problem 13C-4 (20 minutes)
Items and Computations
Investment in the new trucks ...........
Salvage from sale of the old trucks ...
Annual net cash receipts ..................
Depreciation deductions* .................
Replacement of motors ....................
Salvage from the new trucks ............
Net present value ............................
Year(s)
Now
Now
1-7
1-5
4
7
(1)
Amount
$(350,000)
$16,000
$105,000
$70,000
$(45,000)
$18,000
(2)
Tax Effect
1
1
1
1
—
– 0.30
– 0.30
0.30
– 0.30
– 0.30
(1)×(2)
After-Tax
Cash
Flows
$(350,000)
$11,200
$73,500
$21,000
$(31,500)
$12,600
16%
Factor
1.000 $(350,000)
1.000
11,200
4.039
296,867
3.274
68,754
0.552
(17,388)
0.354
4,460
$ 13,893
*$350,000 ÷ 5 years = $70,000 per year
Because the project has a positive net present value, the contract should be accepted.
13-64
Present
Value of
Cash
Flows
Chapter 13 - Capital Budgeting Decisions
Problem 13C-5 (60 minutes)
1.
Items
Buy the new trucks:
Investment in the trucks .....................
Cash from the sale of the old trucks:
Sale price received...........................
Tax savings from loss on sale* .........
Annual cash operating costs................
Depreciation deductions ($650,000 ÷
5 years = $130,000 per year) ...........
Salvage value of the new trucks ..........
Net present value ...............................
Year(s)
(1)
Amount
(2)
Tax
Effect
Now
$(650,000)
—
Now
1
1-7
$85,000
—
$35,000
0.30
$(110,000) 1 – 0.30
1-5
7
$130,000
0.30
$60,000 1 – 0.30
* Book value of old trucks .... $120,000
Less sale price (above) ......
85,000
Loss on the sale ................ $ 35,000
13-65
(1)×(2)
After-Tax
Cash
12%
Flows
Factor
Present
Value of
Cash
Flows
$(650,000) 1.000 $(650,000)
$85,000 1.000
$10,500 0.893
$(77,000) 4.564
$39,000
$42,000
3.605
0.452
85,000
9,377
(351,428)
140,595
18,984
$(747,472)
Chapter 13 - Capital Budgeting Decisions
Problem 13C-5 (continued)
Items and Computations
Keep the old trucks:
Repairs needed ....................................
Annual cash operating costs..................
Depreciation deductions .......................
Salvage value of the old trucks..............
Net present value .................................
Net present value in favor of keeping
the old trucks ....................................
Year(s)
1
1-7
1-2
7
(1)
Amount
(2)
Tax
Effect
(1)×(2)
After-Tax
Cash
12%
Flows
Factor
Present
Value of
Cash
Flows
$(170,000) 1 – 0.30 $(119,000) 0.893 $(106,267)
$(200,000) 1 – 0.30 $(140,000) 4.564 (638,960)
$60,000
0.30
$18,000 1.690
30,420
$15,000 1 – 0.30
$10,500 0.452
4,746
$(710,061)
$ 37,411
13-66
Chapter 13 - Capital Budgeting Decisions
Problem 13C-5 (continued)
2. The solution by the incremental-cost approach below computes the net advantage (or disadvantage)
of investing in the new trucks versus keeping the old trucks.
Items and Computations
Investment in the new trucks ................
Repairs avoided on the old truck ............
Cash from the sale of the old trucks:
Sale price received .............................
Tax savings from loss on sale ..............
Savings in annual cash operating costs
($200,000 – $110,000) .......................
Depreciation deductions:
Depreciation on new trucks.................
Depreciation forgone on old trucks ......
Difference in salvage value in seven
years ($60,000 – $15,000)..................
Net present value .................................
Year(s)
Now
1
(1)
Amount
(2)
Tax
Effect
$(650,000)
—
$170,000 1 – 0.30
Now
1
$85,000
$35,000
1-7
$90,000 1 – 0.30
1-5
1-2
7
$130,000
$(60,000)
—
0.30
0.30
0.30
$45,000 1 – 0.30
(1)×(2)
After-Tax
12%
Cash Flows Factor
$(650,000)
$119,000
Present
Value of
Cash
Flows
1.000 $(650,000)
0.893 106,267
$85,000
$10,500
1.000
0.893
85,000
9,377
$63,000
4.564
287,532
$39,000
$(18,000)
3.605
1.690
140,595
(30,420)
$31,500
0.452
14,238
$ (37,411)
Because the net present value of investing in the new trucks rather than keeping the old trucks is
negative, the new trucks should not be purchased.
13-67
Chapter 13 - Capital Budgeting Decisions
Problem 13C-6 (45 minutes)
Items and Computations
Alternative 1:
Investment in the bonds ..............
Interest on the bonds
(10% × $225,000) ...................
Maturity of the bonds ..................
Net present value ........................
(1)×(2)
After-Tax
8%
Cash Flows Factor
Year(s)
(1)
Amount
(2)
Tax
Effect
Now
$(225,000)
—
$(225,000)
1-12
12
$22,500
$225,000
1 – 0.40
—
$13,500
$225,000
13-68
Present
Value of
Cash
Flows
1.000 $(225,000)
7.536
0.397
101,736
89,325
$ (33,939)
Chapter 13 - Capital Budgeting Decisions
Problem 13C-6 (continued)
Items and Computations
Alternative 2:
Investment in the business .....................
Annual net cash receipts
($850,000 – $780,000 = $70,000) ..........
Depreciation deductions:
Year 1: 14.3% of $80,000 ....................
Year 2: 24.5% of $80,000 ....................
Year 3: 17.5% of $80,000 ....................
Year 4: 12.5% of $80,000 ....................
Year 5: 8.9% of $80,000 ....................
Year 6: 8.9% of $80,000 ....................
Year 7: 8.9% of $80,000 ....................
Year 8: 4.5% of $80,000 ....................
Payment to break the lease .......................
Recovery of working capital
($225,000 – $80,000 = $145,000) ...........
Net present value .......................................
Net present value in favor of alternative 2 ..
Year(s)
(1)
Amount
(2)
Tax
Effect
Now
$(225,000)
—
(1)×(2)
After-Tax
Cash
8%
Flows
Factor
$(225,000) 1.000 $(225,000)
1-12
$70,000 1 – 0.40
$42,000
7.536
1
2
3
4
5
6
7
8
12
$11,440 0.40
$19,600 0.40
$14,000 0.40
$10,000 0.40
$7,120 0.40
$7,120 0.40
$7,120 0.40
$3,600 0.40
$(2,000) 1 – 0.40
$4,576
$7,840
$5,600
$4,000
$2,848
$2,848
$2,848
$1,440
$(1,200)
0.926
0.857
0.794
0.735
0.681
0.630
0.583
0.540
0.397
12
$145,000
13-69
—
Present
Value of
Cash
Flows
$145,000
0.397
316,512
4,237
6,719
4,446
2,940
1,939
1,794
1,660
778
(476)
57,565
$173,114
$207,053