Q4 Review - Spring 2008 savannahstate.edu/misc/dowlingw/3155/Practice%20Exams/q4_-_review_-_spring_2008.htm
1.
The largest number of firms is partnerships.
ANSWER:
F
POINTS:
0/1
FEEDBACK: REF:
2.
One major advantage of incorporating is permanence.
ANSWER:
T
POINTS:
0/1
FEEDBACK: REF:
3.
If a firm needs additional equity financing through the retention of earnings, it may be advantageous to incorporate.
ANSWER:
T
POINTS:
0/1
FEEDBACK: REF:
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4.
The corporate income tax rates increase as earnings increase.
ANSWER:
T
POINTS:
0/1
FEEDBACK: REF:
5.
If a corporation operates at a loss, the loss is initially carried forward to offset future income.
ANSWER:
F
POINTS:
0/1
FEEDBACK: REF:
6.
Corporate losses are carried back to offset income for up to three prior years.
ANSWER:
T
POINTS:
0/1
FEEDBACK: REF:
2/47
7.
The straight-line total revenue function suggests the firm may sell additional output without having to lower the price of the product.
ANSWER:
T
POINTS:
0/1
FEEDBACK: REF:
8.
If a firm has a large amount of operating leverage, that suggests its earnings may be volatile.
ANSWER:
T
POINTS:
0/1
FEEDBACK: REF:
9.
A recession will cause earnings to fall more rapidly for more highly financially leveraged firms.
ANSWER:
T
POINTS:
0/1
FEEDBACK: REF:
3/47
10.
Since high use of financial financial leverage is is associated associated with with less risk, higher financial financial leverage may also result in in higher stock prices.
ANSWER:
F
POINTS:
0/1
FEEDBACK: REF:
11.
If a company company calls calls a bond and retires it, the use of financial leverage is reduced.
ANSWER:
T
POINTS:
0/1
FEEDBACK: REF:
12.
The weighted cost of capital capital includes the cost cost of debt and the cost of equity equity..
ANSWER:
T
POINTS:
0/1
FEEDBACK: REF:
4/47
13.
If the firm issues debentures instead of preferred stock to raise additional funds, the cost of capital rises.
ANSWER:
F
POINTS:
0/1
FEEDBACK: REF:
14.
If the cost of capital exceeds the internal rate of return, the firm should not make the investment.
ANSWER:
T
POINTS:
0/1
FEEDBACK: REF:
15.
If two investments are mutually exclusive, the firm cannot make both investments.
ANSWER:
T
POINTS:
0/1
FEEDBACK: REF:
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16.
A high cost of capital favors investments with large initial cash inflows.
ANSWER:
T
POINTS:
0/1
FEEDBACK: REF:
17.
If two investments are not mutually exclusive, the firm can make only one of them.
ANSWER:
F
POINTS:
0/1
FEEDBACK: REF:
18.
Analyzing an investment from a stand-alone perspective avoids considering portfolio effects.
ANSWER:
T
POINTS:
0/1
FEEDBACK: REF:
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19.
A higher standard deviation for an investment's cash inflows is associated with greater risk.
ANSWER:
T
POINTS:
0/1
FEEDBACK: REF:
20.
If an investment is riskier, using a higher beta coefficient to analyze the alternative reduces the investment's internal rate of return.
ANSWER:
F
POINTS:
0/1
FEEDBACK: REF:
Multiple Choice Identify the choice that best completes the statement or answers the question.
7/47
21.
Owners in which of the following forms of business have unlimited liability? a.
LLCs
b.
corporations
c.
sole proprietorships
d.
limited partnerships
ANSWER:
C
POINTS:
0/1
FEEDBACK: REF:
22.
Corporate losses a.
offset other losses from prior years
b.
are carried forward to future years
c.
are carried forward three years and then carried back
d.
are carried back three years and then carried forward
ANSWER:
D
POINTS:
0/1
FEEDBACK: REF:
8/47
23.
To determine the break-even level of output, management must know 1.
fixed costs of operation
2.
per unit variable costs of output
3.
total sales
a.
1 and 2
b.
1 and 3
c.
2 and 3
d.
all three
ANSWER:
D
POINTS:
0/1
FEEDBACK: REF:
24.
A union contract suggests that labor costs may be a.
variable
b.
fixed
c.
a non-cash expense
d.
undetermined
ANSWER:
B
POINTS:
0/1
FEEDBACK: REF:
9/47
25.
Business risk refers to 1.
use of accelerated depreciation
2.
the risk inherent in the nature of the business
3.
the sources of the firm's finances
a.
1 and 2
b.
1 and 3
c.
2 and 3
d.
only 2
ANSWER:
D
POINTS:
0/1
FEEDBACK: REF:
26.
The payback period is not concerned with a.
earnings
b.
cash inflows
c.
the cost of an investment
d.
selecting investments
ANSWER: POINTS:
A 0/1
FEEDBACK: REF:
10/47
27.
The lower the debt ratio, a.
the higher is the use of financial leverage
b.
the lower is the use of financial leverage
c.
the lower are the firm's total assets
d.
the higher are the firm's total assets
ANSWER:
B
POINTS:
0/1
FEEDBACK: REF:
11/47
28.
Higher fixed costs are associated with 1.
higher operating leverage
2.
lower operating leverage
3.
increased risk
4.
lower risk
a.
1 and 3
b.
1 and 4
c.
2 and 3
d.
2 and 4
ANSWER: POINTS:
A 0/1
FEEDBACK: REF:
12/47
29.
Operating leverage a.
is affected by the demand for the product
b.
results from use of fixed instead of variable costs
c.
is the result of using debt financing
d.
is associated with less risk and more certainty
ANSWER:
B
POINTS:
0/1
FEEDBACK: REF:
30.
A firm does not obtain financial leverage by a.
issuing bonds
b.
borrowing from a bank
c.
issuing preferred stock
d.
issuing common stock
ANSWER:
D
POINTS:
0/1
FEEDBACK: REF:
13/47
31.
The greater the usage of financial leverage, the larger is the variability of a.
revenues
b.
gross profits
c.
operating earnings
d.
net earnings
ANSWER:
D
POINTS:
0/1
FEEDBACK: REF:
32.
The effective cost of debt depends on 1.
the firm's total assets
2.
the firm's tax rate
3.
the stated interest rate
a.
1 and 2
b.
1 and 3
c.
2 and 3
d.
1, 2, and 3
ANSWER:
C
POINTS:
0/1
FEEDBACK: REF:
14/47
33.
Debt financing 1.
increases stockholders' return more than an equal dollar amount of preferred stock
2.
increases stockholders' return less than an equal dollar amount of preferred stock
3.
is less risky to the investor than preferred stock
4.
is more risky to the investor than preferred stock
a.
1 and 3
b.
1 and 4
c.
2 and 3
d.
2 and 4
ANSWER: POINTS:
A 0/1
FEEDBACK: REF:
15/47
34.
The cost of equity 1.
is less than the cost of debt
2.
is greater than the cost of debt
3.
depends on the riskiness of the firm
4.
depends on the firm's current ratio
a.
1 and 3
b.
1 and 4
c.
2 and 3
d.
2 and 4
ANSWER:
C
POINTS:
0/1
FEEDBACK: REF:
16/47
35.
If the capital asset pricing model is used, the cost of equity depends on 1.
the firm's earnings growth rate
2.
the firm's beta
3.
the return on the market
a.
1 and 2
b.
1 and 3
c.
2 and 3
d.
1, 2, and 3
ANSWER:
C
POINTS:
0/1
FEEDBACK: REF:
36.
The optimal capital structure involves a.
maximizing the cost of all funds
b.
minimizing the cost of all funds
c.
using no financial leverage
d.
minimizing the weighted average of the cost of funds
ANSWER:
D
POINTS:
0/1
FEEDBACK: REF:
17/47
37.
The effective cost of debt is reduced because a.
interest is a tax-deductible expense
b.
interest is not a tax deducible expense
c.
interest is paid before preferred dividends
d.
interest is paid after common stock dividends
ANSWER: POINTS:
A 0/1
FEEDBACK: REF:
38.
The marginal cost of capital a.
is the firm's cost of debt and equity finance
b.
is constant given an optimal capital structure
c.
declines as flotation costs alter equity financing
d.
refers to the cost of additional financing
ANSWER:
D
POINTS:
0/1
FEEDBACK: REF:
18/47
39.
The net present value method considers 1.
the timing of the cash inflows from an investment
2.
the cost of an investment
3.
the firm's cost of capital
a.
1 and 2
b.
1 and 3
c.
2 and 3
d.
1, 2, and 3
ANSWER:
D
POINTS:
0/1
FEEDBACK: REF:
40.
The internal rate of return will be higher if a.
the cost of capital is lower
b.
the cost of capital is higher
c.
the cost of the investment is lower
d.
the cost of the investment is higher
ANSWER:
C
POINTS:
0/1
FEEDBACK: REF:
19/47
41.
A firm should not make an investment if 1.
its net present value is positive
2.
its net present value is negative
3.
the internal rate of return exceeds the cost of capital
4.
the internal rate of return is less than the cost of capital
a.
1 and 3
b.
1 and 4
c.
2 and 3
d.
2 and 4
ANSWER:
D
POINTS:
0/1
FEEDBACK: REF:
42.
An increase in the cost of capital will a.
increase an investment's internal rate of return
b.
decrease an investment's internal rate of return
c.
increase an investment's net present value
d.
decrease an investment's net present value
ANSWER:
D
POINTS:
0/1
FEEDBACK: REF:
20/47
43.
If the internal rates of return of two mutually exclusive investments exceed the firm's cost of capital, the firm should a.
make both investments
b.
make neither investment
c.
make the investment with the lower internal rate of return
d.
make the investment with the higher internal rate of return
ANSWER:
D
POINTS:
0/1
FEEDBACK: REF:
44.
The internal rate of return and net present value methods of capital budgeting assume the cash flows are reinvested at a.
the cost of capital
b.
the internal rate of return
c.
the cost of capital for IRR and the internal rate of return for NPV
d.
the cost of capital for NPV and the internal rate of return for IRR
ANSWER:
D
POINTS:
0/1
FEEDBACK: REF:
21/47
45.
NPV may be preferred to IRR because a.
IRR makes the more conservative assumption concerning reinvestment
b.
NPV makes the more conservative assumption concerning reinvestment
c.
IRR excludes salvage value
d.
NPV includes salvage value
ANSWER:
B
POINTS:
0/1
FEEDBACK: REF:
46.
A firm should not make an investment if the internal rate of return is a.
greater than the cost of capital
b.
less than the cost of capital
c.
greater than the interest rate
d.
less than the interest rate
ANSWER:
B
POINTS:
0/1
FEEDBACK: REF:
22/47
47.
A stand-alone perspective for capital budgeting suggests a.
an investment has no risk
b.
cash flows are independent of the firm's other investments
c.
portfolio effects are ignored
d.
the investment has a low beta
ANSWER:
C
POINTS:
0/1
FEEDBACK: REF:
48.
The lack of correlation between an investment's return and the firm's other investments suggests a.
the investment has little risk
b.
portfolio effects may exist
c.
the investment's beta coefficient is low
d.
the investment's net present value is negative
ANSWER:
B
POINTS:
0/1
FEEDBACK: REF:
23/47
49.
Small standard deviations for cash inflows a.
reduces an investment's net present value
b.
increases an investment's internal rate of return
c.
increases the firm's cost of capital
d.
implies more certainty
ANSWER:
D
POINTS:
0/1
FEEDBACK: REF:
50.
The use of certainty equivalents means a.
the investment's cash inflows are certain
b.
an investment's cash inflows are expressed as if they were certain
c.
the cost of capital is known
d.
the probability of occurrence is certain
ANSWER:
B
POINTS:
0/1
FEEDBACK: REF:
Problem
51.
Using the corporate tax rates given in the text (p. 345), what is the corporate income tax paid on earnings of (a) $1,000, (b) $10,000, (c) $100,000, (d) 1,000,000, and (e) 10,000,000?
RESPONSE:
24/47
ANSWER:
a.
for $1,000: ($1,000)0.15 = $150
b.
for $10,000: ($10,000)0.15 = $1,500
c.
for $100,000: ($50,000).15 + (25,000).25 + 25,000(.34) = $22,250
d.
for $1,000,000: ($50,000).15 + (25,000).25 + 25,000(.34) + (235,000).39 + (665,000).34 = $340,000
e.
for $10,000,000: ($50,000).15 + (25,000).25 + 25,000(.34) + (335,000).39 + (665,000).34 + (9,000,000)x.34 =
POINTS:
$3,400,000
-- / 1
REF:
25/47
52.
The price of a product is $1 a unit. A firm can produce this good with variable costs of $0.50 per unit and total fixed costs of $100. a.
What is the break-even level of output?
b.
What is the break-even level of output if fixed costs increase to $180 and variable costs decline to $0.40 per unit?
RESPONSE: ANSWER:
a.
break-even level of output: $100/($1 - $0.50) = 200 units
b.
break-even level of output: $180/($1 - $0.40) = 300 units
POINTS:
-- / 1
REF:
26/47
53.
You want to start a firm whose output you believe you can sell for $25 per unit. The operation will require fixed costs of $10,000, and the variable costs are expected to be $18 a unit. What will be the break-even level of output?
RESPONSE: ANSWER:
Break-even level of output: $100,000/($25 - 18) = 14,286 units
POINTS:
-- / 1
REF:
54.
Which of the following $1,000 investments would the payback method select? Cash flows:
Year
A
B
C
1
$200
$250
$400
2
250
250
350
3
300
250
200
4
350
250
150
5
400
250
100
RESPONSE: ANSWER:
Payback for A is approximately 3.5 years Payback for B is 4 years Payback for C is 3.3 years Since C recoups the $1,000 cost the fastest, it will be selected.
POINTS:
-- / 1
REF:
55.
(This is a simple problem that replicates the example in the chapter.) A firm needs $100 to start and expects
Sales
$200
Expenses
$185
27/47
Tax rate
33% of earnings
a.
What are earnings if the owners invest the $100?
b.
If the firm borrows $40 of the $100 at any interest rate of 10%, what are the firm's net earnings?
c.
What is the return on the owners' investment in each case? Why do the returns differ?
d.
If expenses rise to $194, what will be the returns in each case?
e.
In which case did the returns decline more?
f.
What generalization can you draw form the above?
RESPONSE: ANSWER:
a.
and b.
Sales
a
b
no financial
with financial
leverage
leverage
$200
$200
185
185
Expenses EBIT
15
15
Interest
-
4
EBT
15
11
Taxes Net earnings
5 $
10
3.63 $
7.37
28/47
c.
Return on equity
$10/$100 = 10%
$7.37/$60 = 12.28%
The return for b is higher because of the successful use of financial leverage. (Point out that operating income is 15% of assets versus the 10% interest rate and the reduction in taxes that results from the interest expense.)
d.
Sales
no financial
with financial
leverage
leverage
$200
$200
194
194
Expenses
POINTS:
EBIT
6
6
Interest
-
4
EBT
6
2
Taxes
2
0.66
Net earnings
$
Return on equity
$4/$100 = 4%
4
$
1.34
$1.34/$60 = 2.23%
e.
The return on equity fell more for the firm that was financially leveraged.
f.
The generalization is that the use of financial leverage to increase the return on equity works both ways. If revenues fall and/or expenses rise, the use of financial leverage will magnify the swing in the firm's return on equity.
-- / 1
REF:
29/47
. a.
Given the following schedules,
cost of
cost of
debt/assets s
debt
equity
0%
7%
14%
10
7
14
20
7
14
30
8
14
40
8
16
50
10
18
60
12
20
What is firm's cost of capital at the various combinations of debt and equity?
b.
What is the firm's optimal capital structure? Construct a balance sheet showing that combination of debt and equity financing.
Balance Sheet for Firm ´ as of XX/XX/XX Assets
$100
Debt Equity $100
c.
If the firm earns $10 on every $100 of assets, will the stockholders receive more or less than their required rate of return if the firm uses its optimal combination of debt and equity financing?
d.
If the above cost of equity is the cost of retained earnings, what happens to the cost of capital if the cost of new shares is one percentage point higher at the firm's optimal capital structure?
e.
If the firm has retained earnings of $1,500,000, what is the cost of capital at the optimal capital structure if the firm needs $2,000,000?
30/47
RESPONSE: ANSWER:
a.
Determination of cost of capital:
k
= weight ´ cost of debt + weight ´ cost of equity = .0(.07) + 1(.14) = 14.00% = .1(.07) + .9(.14) = 13.30 = .2(.07) + .8(.14) = 12.60 = .3(.08) + .7(.14) = 12.20 = .4(.08) + .6(.16) = 12.80 = .5(.10) + .5(.18) = 14.00 = .6(.12) + .4(.20) = 15.20
b.
The optimal capital structure is 30% debt and 70% equity. The balance sheet is
Balance Sheet for Firm ´ as of XX/XX/XX Assets
$100
Liabilities Equity
c.
$ 30 70 $100
If the firm earns $10 on every $100 of assets (i.e., 10% on assets), the stockholders will not receive their required return of 14%. With 30% debt financing, $2.40 must go to creditors ($30 ´ .08 = $2.40), which leaves $7.60 for stockholders ($10 - 2.40). Since the stockholders have invested $70, they earn a return of 10.86% ($7.60/$70).
31/47
For the stockholders to earn their required return, the firm must earn at 12.2%. Then the firm can pay the creditors $2.40 and have sufficient left over ($9.80) so that the stockholders earn the 14% required rate of return (i.e., $9.80/$70 = 14%).
d.
If the cost of new equity rises to 15 percent, the cost of capital at the optimal capital structure becomes: .3(.08) + .7(.15) = 12.90.
e.
If the firm has retained earnings of $1,500,000, the breakpoint in the marginal cost of capital schedule is $1,500,000/.7 = $2,142,857.
The cost of capital from $0 - $2,142,857 is 12.2%. The cost of capital above $2,142,857 is 12.9%.
The cost of $2,000,000 is 12.2 percent. The cost of the next $2,000,000 is $142,857 at 12.2 percent and $1,857,143 at 12.7 percent. POINTS:
-- / 1
REF:
57.
Given the following information:
a.
interest rate
8%
tax rate
30%
dividend
$ 1
price of the common stock
$50
growth rate of dividends
7%
debt ratio
40%
Determine the firm's cost of capital.
32/47
b.
If the debt ratio rises to 50 percent and the cost of funds remains the same, what is the new cost of capital?
c.
If the debt ratio rises to 60 percent, the interest rate rises to 9 percent, and the price of the stock falls to $30, what is the cost of capital? Why is this cost different?
RESPONSE:
33/47
ANSWER:
a.
Cost of debt: .08(1 - .3) = .056 = 5.6% Cost of equity: $1(1 + .07)/$50 + .07 = 9.1% Cost of capital:
weights
´
costs
.4
´
.056
=
.0224
.6
´
.091
=
.0546 .0770 = 7.7%
b.
The cost of debt and equity are unchanged. Only the weights are changed. Cost of capital:
weights
´
costs
.5
´
.056
=
.0280
.5
´
.091
=
.0455 .0735 = 7.35%
c.
Both the cost of debt and equity are changed. Cost of capital:
weights
´
costs
.6
´
.063
=
.0378
.4
´
.106
=
.0424 .0802 = 8.02%
The cost of capital changes as any of the components are changed. As the firm initially substitutes cheaper debt financing, the cost of capital declines (7.7% to 7.35%). However, as the firm uses more debt financing and becomes more financial leveraged, it becomes riskier, and the cost of capital rises (7.35% to 8.02%).
34/47
-- / 1
POINTS: REF:
58.
Fill in the table using the following information. Assets required for operation: $2,000 Case A
- firm uses only equity financing
Case B
- firm uses 30% debt with a 10% interest rate and 70% equity
Case C
- firm uses 50% debt with a 12% interest rate and 50% equity
Debt outstanding
A
B
C
$
$
$
300
300
300
%
%
%
Stockholders' equity Earnings before interest and taxes Interest expense Earnings before taxes Taxes (40% of earnings) Net earnings Return on stockholders'
investment
What happens to the rate of return on the stockholders' investment as the amount of debt increases? Why did the rate of interest increase in case C?
RESPONSE:
35/47
ANSWER:
A
B
C
$ 600
$1,000
Debt outstanding
$
0
Stockholders' equity
2,000
1,400
1,000
Earnings before
300
300
300
Interest expense
0
60
120
Earnings before taxes
300
240
180
Taxes (40% of earnings)
120
96
72
Net earnings
$ 180
$ 144
$ 108
Return on stockholders'
9%
10.3%
10.8%
interest and taxes
investment
The rate of return to stockholders rises because the after tax cost of debt in B is .1(1 .4) = 6%. The after tax cost of debt in C is .12(1 - .4) = 7.2%. These costs are less than the 9 percent the firm earns after taxes on its assets ($180/$2,000). The interest rate increases because the firm becomes riskier when it uses more financial leverage.
POINTS:
59.
-- / 1
The firm's cost of debt is 8 percent, and the cost of retained earnings is 14 percent. However, if the firm REF: its retained earnings of $23,678, the cost of equity rises to 14.9 percent. Currently management exhausts believes that the firm's current combination of 35 percent debt and 65 percent equity is the optimal capital structure. a.
What is the firm's cost of capital if it uses only retained earnings?
b.
What is the firm's cost of capital if it uses new equity?
c.
How much total financing may the firm have before the marginal cost of capital rises?
RESPONSE:
36/47
ANSWER:
a.
The cost of capital using retained earnings: (.35)(.08) + (.65)(.14) = 11.9%
b.
The cost of capital using new equity: (.35)(.08) + (.65)(.149) = 12.485%
Notice that the marginal cost of capital rises after the firm exhausts its retained earnings and must start using more expensive new equity.
c.
The break-point in the marginal cost of capital schedule: $23,678/.65 = $36,428
The retained earnings can support up to $36,428 in total financing and still maintain the optimal combination of debt and equity financing. However, after $36,428 of total financing, the retained earnings are exhausted, and the firm must start using more expensive new equity.
POINTS:
-- / 1
REF:
60.
An investment costs $10,000 and will generate annual cash inflows of $1,770 for ten years. According to the net present value and internal rate of return methods of capital budgeting, should the firm make this investment if its cost of capital is (a) 10% or (b) 14%?
RESPONSE:
37/47
ANSWER:
Internal rate of return: $10,000 = (PVAIF x%, 10y)$1,770 $10,000 = $1,770X X = $10,000/$1,770 = 5.650 r = 12% (PV = -10000; N= 10; I = ?; PMT = 1770, and FV = 0. I = 12.) Net present value at 10%: NPV
= $1,770(PVAIF 10%, 10y) = $1,770(6.145) - $10,000 = $10,876.65 - $10,000 = $876.65
(PV = ?; N = 10; I = 10; PMT = 1770, and FV = 0. PV = -10876.) Net present value at 14%: NPV
= $1,770(PVAIF 14%, 10y) = $1,770(5.216) - $10,000 = ($767.68)
(PV = ?; N = 14; I = 10; PMT = 1770, and FV = 0. PV = -9233.) At k = 10% the firm should make the investment. (NPV is positive and IRR exceeds the firm's cost of capital.) At k = 14% the firm should not make the investment. (NPV is negative and IRR is less than the firm's cost of capital.)
POINTS:
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REF:
61.
A firm with the following investment opportunities has a capital budget of $10,000. According to the net present value technique, which investment(s) should the firm make if the firm's cost of capital is 10%?
Investment
Cost
A
B
C
$10,000
$7,000
$3,000
$12 000
$8 600
$4 000
Cash inflow
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RESPONSE: ANSWER:
The firm should select that combination of investments which uses the available funds and maximizes the combined net present value. NPV A
= $12,000(PVIF 10% 1y) - $10,000 = $12,000/(1 + .1) - 10,000 = $12,000(.909) - $10,000 = $908
NPVB
= $8,600/(1 + .1) - $7,000 = $8,600(.909) - $7,000 = $817
NPVC
= $4,000/(1 + .1) - $3,000 = $4,000(.909) - $3,000 = $636
NPV A is less than NPV B + NPV C. Therefore, select B + C over A even though A has the highest individual NPV.
POINTS:
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REF:
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.
A firm has two $1,000, mutually exclusive investment alternatives with the following cash inflows. The cost of capital is 6 percent. Year
Cash Inflow A
B
1
$175
$1,100
2
175
-
3
175
-
4
175
-
5
175
-
6
175
-
7
175
-
8
175
-
a.
What is the internal rate of return on each investment? Which investment should the firm make?
b.
What is the net present value of each investment? Which investment should the firm make?
c.
If the cash inflows can be reinvested at 8 percent, which investment should be made?
RESPONSE: ANSWER:
a.
Determination of the internal rates of return: A:
$175(PVAIF x%, 8y) = $1,000 Interest factor = $1,000/$175 = 5.174 r A = approximately 8% (PV = -1000; N = 8; I = ?; PMT = 175, and FV = 0. I = 8.15.)
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B:
$1,100/(1 + r B ) = $1,000 Interest factor = $1,000/$1,100 = .909 r B = 10%
Since the investments are mutually exclusive, the firm should select B because it has the higher internal rate of return.
b.
Determination of the net present values:
A:
Net present value A: $175(PVAIF 6%, 8y) - $1,000 = $175(6.210) - $1,000 = $87
B:
Net present value B: $1,100/(1 + .06) - $1,000 = $1,100(.943) - $1,000 = $37
Since the investments are mutually exclusive, the firm should select A because it has the higher net present value.(This contradicts part a, which selected investment B.)
c.
If the firm is able to reinvest the annual payments of $175, the terminal value of A is $175(10.637) = $1,861.48 (10.637 is the interest factor for the future value of an ordinary annuity at 8% for eight years.)
If the firm selects B, it receives $1,100 in year one, which is reinvested at 8% for seven years. The terminal value is $1,100(1.714) = $1,885.40. This is higher than the terminal value for A, so the firm should make investment B.
POINTS:
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REF:
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63.
A firm has three investment opportunities. Each costs $1,000, and the firm's cost of capital is 10 percent. The cash inflow of each investment is as follows: cash inflow
A
B
C
1
$300
500
100
2
300
400
200
3
300
200
400
4
300
100
500
year
a.
If the net present value method is used, which investment(s) should the firm make?
b.
What is the internal rate of return of investment A? The internal rate of return of investment B is 10.22% and 6.15% for investment C. Which investment(s) should the firm make?
c.
What is the payback period for each investment?
RESPONSE: ANSWER:
A.
Discount the cash inflows by the cost of capital. For each investment, that is
A
B
$300 ´ .909
=
$272.70
$500 ´ .909
=
$ 454.50
300 ´ .826
=
247.80
400 ´ .826
=
330.40
300 ´ .751
=
225.30
200 ´ .751
=
150.20
300 ´ .683
=
100 ´ .683
=
204.90 $950.70
68.30 $1,003.40
C
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$100 ´ .909
=
$ 90.90
200 ´ .826
=
165.20
400 ´ .751
=
300.40
500 ´ .683
=
341.50 $898.00.
Since investment A is an annuity, the present value could be determined by using the interest table for the present value of an annuity. That is, $300 ´ 3.170 = $951, which is essentially the same answer except for rounding.
Next subtract the cost from the present value to determine the net present value:
A:
$950.70 - $1,000 = ($49.30)
B:
$1,003.40 - $1,000 = $3.40
C:
$898.00 - $1,000 = ($102.00).
Since only B has a net present value that is positive, it is the only investment that covers the firm's cost of capital and hence is the only one that should be selected.
b.
Internal rate of return for A:
Since investment A is an annuity, the annuity table for the present value of an annuity may be used to solve the problem. Restated the equation is $1,000 = $300X X = $1,000/$300 = 3.33.
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3.33 is the interest factor for the present value of an annuity for four years. Find this interest factor in the table to determine the internal rate of return. In this case the internal rate of return is approximately 8 percent, which is less than the firm's cost of capital. (The IRR is 7.7 percent using a financial calculator.) Therefore, the investment should not be made. (This answer is consistent with the answer given by the net present value in the previous question.) The internal rates of return for investments B and C were given. Only the internal rate of return of B exceeds the cost of capital; thus it is the only investment the firm should make.
c.
The payback periods for the investments are A
three and one-third years
B
two and one-half years
C
three and two-thirds years.
Notice that in this case the payback method gives the same ranking of investments as the net present value. However, the payback method does not tell if any of the investments should be made. POINTS:
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REF:
64.
Investments A and B are mutually exclusive and cost $2,000 each. The firm's cost of capital is 9%, and the investments' estimated cash inflows are cash inflow
A
B
1
$2,320
---
2
---
---
3
---
$2,810
year
a.
What investment(s) should the firm make according to net present value?
b.
What investment(s) should the firm make according to internal rate of return?
c.
If the firm can reinvest funds earned in year 1 at 10%, which investment(s) should the firm make?
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RESPONSE: ANSWER:
a.
Net present value of A: $2,320/(1 + .09) - 2,000 = $128
Net present value of B: $2,810/(1 + .09) 3 - 2,000 = $170
Since the investments are mutually exclusive, the firm cannot make both and will select B since it has the higher NPV.
b.
Internal rate of return of A: $2,000 = $2,320/(1 + r) PVIF = .862 r = 16%
Internal rate of return of B: $2,000 = $2810/(1 + r) 3 PVIF = .712 r = 12%
Since the investments are mutually exclusive, the firm cannot make both and will select A since it has the higher IRR.
c.
There is an obvious conflict in the rankings. The purpose of this question is to help reconcile the conflict. If the $2,320 grow annually at 10 percent, then the future value is
$2,320(1 + .1) 2 = $2,320(1.210) = $2,807.20.
Investment B is now clearly preferred to A because the terminal value of S is $2,807.20, which is less than $2810.
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POINTS:
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REF:
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