Chapter 16 Planning for Capital Investments
16-1
Answers to Questions
1. A capital investment is an investment in a long-term operational asset. Stocks and
bonds are not operational assets but rather intangible legal agreements of
ownership in another company or loans to another company. They are bought and
sold in organized free markets, such as the New York Stock Exchange where there
revenues, or cost savings, generated by the asset.
2. This concept applies for the following reasons: 1) the smaller present amount can
be invested to earn interest that increases its future worth, 2) there is risk associated
3. Yes, both statements mean that a dollar today has more value because it can be
invested to earn interest, it has less risk associated with its receipt, and there is less
risk of its decrease in buying power due to inflation. In the first statement, you
4. When a company invests in capital assets, it is giving
up present dollars in exchange for future dollars. Since present dollars have more value,
the company must be compensated for the exchange. This compensation is called the
you received a 10% return ($500/$5,000).
5. In order to obtain assets (capital) to make investments, businesses must pay owners
dividends and lenders interest. The return paid to investors and creditors is the
cost of capital establishes the minimum acceptable rate of return on investments.
6. To determine the amount to invest today solve the following equation:
Investment x (0.10) + Investment = $500,000
Investment x (0.10 + 1) = $500,000
Chapter 16 Planning for Capital Investments
16-2
7. Many times converting future values into their present value equivalents requires a
considerable amount of mathematical manipulation, particularly if the future values
future values into present values.
8. An annuity is a series of equal cash flows paid over equal time intervals at a
9. Some programs offer an efficient means of converting future values into present
value equivalents. The conversion power of the present value function available
10. The mathematical formula based on the present value of an annuity table factor
would be written as:
Annual payment x PV of an annuity factor @ 14% for 5 years = PV
11. The bank’s investment balance is declining each year. A part of the original
investment is recovered with each payment made by Ms. Espinosa. Since the
interest Ms. Espinosa pays is based on the investment balance, the amount of
12. The higher net present value does not necessarily imply the better investment
opportunity. Other factors such as the amount of the initial outlay and the
Chapter 16 Planning for Capital Investments
16-3
13. Projects that produce zero or positive net present values satisfy the desired rate of
14. The net present value method does not provide a measure of the rate of return. It
simply indicates whether or not a project meets the desired rate of return criterion.
15. The investment with the highest internal rate of return is not always the best
investment even when risk is relatively equal. Firms have a limited supply of capital
16. Pursuing the highest rate of return does not guarantee the maximum profit for
companies. As long as an investment results in a return greater than the company’s
cost of capital, the investment will contribute additional profit to the company. If
17. The desired rate of return represents the level of return that management seeks to
attain on all investments. The internal rate of return is the actual return from a
18. Inflow items include incremental revenue, operating cost savings, salvage values,
19. The strategy is not sound because it does not take into account the limitations of the
20. The payback method can be used when cash flows are unequal. A cumulative
technique or an averaging technique can be employed.
21. The primary advantages of the unadjusted rate of return are simplicity and ease of
16-4
22. Capital investments involve major commitments of resources that are recovered
over extended future periods via increases in revenue or decreases in expenses.
23. A postaudit consists of using the same analytical techniques used for evaluating a
capital investment proposal in evaluating its success. A postaudit is conducted at
Exercise 16-1
Item
Type of Cash Flow
a. Initial investment
Outflow
b. Salvage value
Inflow
c. Recovery of working capital
Inflow
d. Incremental expenses
Outflow
e. Working capital commitments
Outflow
f. Cost savings
Inflow
g. Incremental revenue
Inflow
Exercise 16-2
a.
Present value
Present value
=
Future value
x
Table Factor*
Present value
=
$80,000
x
0.943396
Present value
=
$75,472
b.
Investment + (0.06 x Investment) = $80,000
Exercise 16-3
Chapter 16 Planning for Capital Investments
16-5
a.
Present value
Present value
=
Future value
x
Table Factor*
Present value
=
$600,000
x
0.680583
Present value
=
$408,350
*Table 1, n = 5, r = 8%
Ms. Long should not accept her employer’s offer of $360,000 because this amount is less
Exercise 16-4
a.
Present Value
Present Value
=
Future Value
x
Table Factor
=
Present Value
Present value
=
$20,000
x
0.925926(1)
=
$18,518.52
Present value
=
$20,000
x
0.857339(2)
=
17,146.78
Present value
=
$20,000
x
0.793832(3)
=
15,876.64
Total present value
$51,541.94
(1)Table 1, n = 1, r = 8%
b.
Present Value
Present Value
=
Future Value
x
Table Factor
=
Present Value
Present value
=
$20,000
x
2.577097(1)
=
$51,541.94
c. The present values are the same because the present value factor of Table 2 is
simply the sum of the three values from Table 1.
Exercise 16-5
a.
Chapter 16 Planning for Capital Investments
16-6
Present Value
Present Value
=
Future Value
x
Table Factor
=
Present Value
Present value
=
$28,000
x
3.387211*
=
$ 94,841.91
Present value
=
$42,000
x
0.762895**
=
32,041.59
Total present value
=
126,883.50
Cost of vans
=
(91,000.00)
Net present value
=
$35,883.50
*Table 2, n = 4, r = 7%
b. Since the net present value is positive, the investment opportunity can be
Exercise 16-6
a.
Year
Cash
Inflow
−
Cash
Outflow
=
Net Cash
Flows
x
Present Value
Table Factor
=
Present
Value
2015
$16,000
−
$10,000
=
$6,000
x
0.925926
=
$5,555.56
2016
20,000
−
15,600*
=
4,400
x
0.857339
=
3,772.29
2017
21,000
−
12,600
=
8,400
x
0.793832
=
6,668.19
2018
22,500**
−
12,600
=
9,900
x
0.735030
=
7,276.80
Present value
23,272.84
Cost of equipment
21,000.00
Net present value
$ 2,272.84
* $12,000 + $3,600
** $21,000 + $1,500
b. The positive net present value indicates that the investment is earning a return that is
Exercise 16-7
a.
Alternative 1
Present value – Cash inflows
$100,000
Present value – Cash outflows
(80,000)
Net present value
$ 20,000
Alternative 2
Present value – Cash inflows
$240,000
Chapter 16 Planning for Capital Investments
16-7
Present value – Cash outflows
(210,000)
Net present value
$ 30,000
Exercise 16-7 (continued)
b.
Present value
index
Present value of cash
inflows
$100,000
for
=
————————
=
————
=
1.25
Alternative 1
Present value of cash
outflows
$80,000
Present value
index
Present value of cash
inflows
$240,000
for
=
————————
=
————–
=
1.14
Alternative 2
Present value of cash
outflows
$210,000
Exercise 16-8
Revenues
$ 400,000
Operating expenses
(210,000)
Depreciation expense
(90,000)
($360,000 – $0) 4
Income before taxes
100,000
Tax expense
(30,000)
($100,000 x 0.30)
Net income
70,000
Add back depreciation
90,000
Net cash flows
$ 160,000
(For years 2 to 4)
Because the cash expenditure for equipment will be $360,000, the first year’s operations
Chapter 16 Planning for Capital Investments
16-8
Exercise 16-9
a.
Present value table factor x $1,280,000 = $7,865,045.76
Looking at table 2, at row 10, we find the factor 6.144567 under the rate of return column
marked 10%. Accordingly, 10% represents the internal rate of return.
Exercise 16-10
a. Determination of the annuity table values can be accomplished by dividing the
cost of the investment by the annuity:
First investment: $9,840.48 ÷ $2,400 = 4.1002. Locating this value in Table 2
b. Since the second investment has a higher internal rate of return it should be
accepted.
(1) The life of the investments. The second investment has a three-year useful life.
below the return generated by the first investment.
Exercise 16-10 (continued)
(2) The size of the investment. If the company has $9,840.48 (i.e., amount of the first
investment opportunity) of funds available to invest and only invests $6,442.74
Chapter 16 Planning for Capital Investments
16-9
(3) Confidence in the accuracy of projected cash flows. Uncertainty is just another
Exercise 16-11
Mr. Lyte does have a point. The company should evaluate the results of capital budget
decisions through the practice of conducting postaudits. A postaudit should be
conducted at the end of each capital investment project. The postaudit should repeat
the analytical technique that was used to justify the original investment. For example,
Exercise 16-12
a.
Cash cost of investment Annual cash inflow = Payback period
Alternative 1
$9,000,000 $3,000,000 = 3 years
Alternative 2
b. The payback method does not consider the life of the investment. In this case,
Exercise 16-13
a.
Year
Nature of Item
Cash Flows
Chapter 16 Planning for Capital Investments
16-10
2015
Revenue
$30,000
2016
Revenue
30,000
2017
Revenue
21,000
2017
Major overhaul
(9,000)
Total
$72,000
The payback occurs at the end of 3 years.
b. Average cash inflow is computed as follows:
($30,000 + $30,000 + $21,000 − $9,000 + $18,000 + $14,400 + $9,600) ÷ 5 = $22,800
average per year
Exercise 16-14
a.
Incremental increase in net income Average cost of original investment
Exercise 16-15
a. $45,000 ÷ $25,000 = 1.8 years
b. Depreciation expense = $45,000 ÷ 3 = $15,000 per year
Problem 16-16
a.
Alternative 1
Cash Inflows
Table Value
Present Value
Annual cash inflows
$260,000
x
3.1698651
=
$824,164.90
Salvage value
80,000
x
0.6830132
=
54,641.04
Working capital recovery
40,000
x
0.6830132
=
27,320.52
Total cash inflow
906,126.46
Cash outflows
Chapter 16 Planning for Capital Investments
16-11
Cost of vans
(720,000.00)
Working capital increase
(40,000.00)
Net present value
$146,126.46
1Table 2, n= 4, r = 10%
2Table 1, n= 4, r = 10%
Problem 16-16 (continued)
Alternative 2
Cash Inflows
Table Value
Present Value
Year 1
$140,000
x
0.9090911
=
$127,272.74
Year 2
300,000
x
0.8264462
=
247,933.80
Year 3
360,000
x
0.7513153
=
270,473.40
Year 4
400,000
x
0.6830134
=
273,205.20
Salvage value
65,000
x
0.6830134
=
44,395.85
Total cash inflow
963,280.99
Cash outflows
Cost of trucks
(800,000.00)
Training cost
(16,000.00)
Net present value
$147,280.99
1Table 1, n=1, r=10% 3Table 1, n=3, r=16%
2Table 1, n=2, r=10% 4Table 1, n=4, r=16%
b.
Alternative 1:
Present value of cash inflows
$906,126.46
––––––––––––––––––––––––––––––––
=
––––––––––––––
=
1.19
Present value of cash outflows
$760,000
Alternative 2
Present value of cash inflows
$963,280.99
––––––––––––––––––––––––––––––––
=
––––––––––––
=
1.18
Present value of cash outflows
$816,000
c. Alternative 1 will provide the higher rate of return, but alternative 2 results in a
greater net present value. With Alternative 1 there is only $760,000 invested while