Problem 1
a. What is the after-tax cost of debt?
8.5%(1 - tax rate) = 8.5(1 - .30) = 5.95%
b. What is the cost of preferred stock?
Dividend/Price of the stock = $9/$91 = 9.9%
c. What is the cost of the common stock?
Dividend (1 + g)/Price of the stock + growth rate =$0.75(1 + .06)/$15 + 6% = 11.3%
d. What is the firm’s weighted average cost of capital?
k = (weight)*(cost of debt) + (weight)*(cost of preferred) + weight*(cost of common stock)
= (.35)*(5.95%) + (.05)*(9.9%) + (.60)*(11.3%) = 9.3575%
Problem 2
Cost of retained earnings: $2.10(1 + .06)/$34 + 6% = 5.565%
Cost of new stock:
= Dividend(1 + g)/(stock price minus any flotation costs)+ growth rate
= $2.10(1 + .06)/($34 - $2.70) + .06 = 7.09%
Problem 3
The cost of capital (k) is a weighted average:
k = (weight)(cost of debt) + weight(cost of equity)
Debt/ Weight x + Weight x = Cost of
Assets Cost Cost Capital
of Debt of Equity
0% (.0)(.08) + (1.0)(.12) = .120
10 (.1)(.08) + (.9)(.12) = .116
20 (.2)(.08) + (.8)(.12) = .112
30 (.3)(.08) + (.7)(.13) = .115
40 (.4)(.09) + (.6)(.14) = .120
50 (.5)(.10) + (.5)(.15) = .125
60 (.6)(.12) + (.4)(.16) = .136
b. Pro Forma Balance Sheet
| Pro forma Balance Sheet at Optimal Capital Structure | |||
| Assets | $100 | Debt | $20 |
| Equity | $80 |
When compared with the current balance sheet the firm currently employs less debt by $10 and excess equity by $10. In order to obtain optimal levels, the firm must increase its debt and reduce its equity obtaining a debt/equity ratio of 20:80.
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c. As the firm employs more of the cheaper debt, the weighted cost of capital declines. This happens because of the use of debt that has a lower cost compared to the equity the weighted cost of capital declines initially.
d. Initially the weighted cost will decline because of the cheaper cost of debt which reduces the overall cost, however, this cost does not continue indefinitely. After reaching the minimum level the cost will begin to rise as cost of debt and equity both begin to increase. The reason being that
creditors and investors increase the cost and debt the financial leverage will also increase which is considered very risky.
Chapter 22 Problem Set: 465–469
Problem 1
a. What is the investment’s internal rate of return? Based on the internal rate of return, should the firm make the investment?
NPV = 6000*pvifa(10%, 5) – 23958
= (6000*3.7908)-23958
= -1213.2 Not equal to zero
Based on internal rate of return, firm should not make the investment as the IRR is less than Cost of Capita
b. What is the net present value? Based on the net present value, should the firm make the investment?
Calculation of Net Present Value (NPV)
NPV = 66000*pvifa(10%, 5) – 23958
NPV = -1213.2
Based on NPV present value, firm should not make the investment as NPV is zero.
Problem 3
a. Based only on visual inspection, which investment is to be preferred and why? Based on visual inspection alone, Cash Inflow B is to be preferred because it is steady and consistent at $200 for all three years. Cash Inflow A declines from year to year for the duration of the time period.
b. Based on each investment’s net present value, which investment(s) should the firm make?
Net present value of Project A = -$480 + $300/1.1 + $200/1.1^2 + $100/1.1^3 = $33.14800902
Net present value of Project B = -$480 + $200/1.1 + $200/1.1^2 + $200/1.1^3 =$17.3703982
Investment A is the better choice with a higher NPV of $33.15 compared to the NPV of $17.36 for investment option B.
c. Based on each investment’s internal rate of return, which investment(s) should the firm make? Is this the same answer you obtained in part b?
Project A:
-$480 + $300/(1+r) + $200/(1+r)^2 + $100/(1+r)^3 = 0
r = 14.68%
Project B:
-$480 + $200/(1+r) + $200/(1+r)^2 + $200/(1+r)^3 = 0
r = 12.04%
Yes, investment A yields a higher rate of return and is the same choice from part b.
d. If the cost of capital were to increase to 14 percent, which investment(s) should the firm make?
Project A
-$480 + $300/1.14 + $200/1.14^2 + $100/1.14^3 = $4.548552051
Project B
-$480 + $200/1.14 + $200/1.14^2 + $200/1.14^3= -$15.67359457
According to the net present value, the firm should invest in Project A
Problem 4
a. What is the net present value of each investment?
Project A:
NPV = $254.91 (3,254.91-Total Cost)
| Year |
A |
PVF @ 8% |
NPV |
|
1 |
$1,100 |
0.9901 |
1,089.11 |
|
2 |
1,100 |
0.98852 |
1,087.37 |
|
3 |
1,100 |
0.98039 |
1,078.43 |
Project B:
NPV = $564.36 (3,564.36 -Total Cost)
|
Year |
B |
PVF @ 8% |
NPV |
|
1 |
$3,600 |
0.9901 |
3,564.36 |
|
2 |
- |
0.98852 |
- |
|
3 |
- |
0.98039 |
- |
Project C:
NPV = $1,472.54 (4,472.54-Total Cost)
|
Year |
C |
PVF @ 8% |
NPV |
|
1 |
- |
0.9901 |
- |
|
2 |
- |
0.98852 |
- |
|
3 |
$4,562 |
0.98039 |
4,472.54 |
b. According to the net present values, which investment(s) should the firm make? Why?
Investment C because C offers the highest rate of NPV
c) What is the internal rate of return on each investment?
Investment A:
$1,100/(1 + rA)t= $3,000
interest factor = $3,000/$1,100 = 2.727
rA= approximately 5%
(PV = -3000; N = 3; I = ?; PMT = 1100, and FV = 0. I = 4.92.)
Investment B:
$3,600/(1 + rB) = $3,000
interest factor = $3,000/$3,600 = .833
rB= 20%
(PV = -3000; N = 1; I = ?; PMT = 0, and FV = 3600. I = 20.)
Investment C:
$4,562/(1 + rC)3= $3,00
interest factor = $3,000/$4,562 = .6575rC= 15%
(PV = -3000; N = 3; I = ?; PMT = 0, and FV = 4562.I = 14.99.)
Investment A is not acceptable because its internal rate of return is less than the cost of capital. Since B and C are mutually exclusive, the firm should select B since it has the higher internal rate of return.
d. According to the internal rates of return, which investment(s) should the firm make? Why?
Investments B & C because t he cost of capital is less that rate of return.
e. According to both the net present values and internal rates of return, which investments should the firm make?
Investment C because it offers a favorable combination of NPV and IRR .
f. If the firm could reinvest the $3,600 earned in year one from investment B at 10 percent, what effect would that information have on your answer to part e?
No, the answer will remain the same
Project B: IRR = 20%
|
Year |
Inflows |
PVF @ 10% |
NPV |
|
0 |
-3,000 | ||
|
1 |
3,600 |
0.909 |
3,272.40 |
Would the answer be different if the rate were 14 percent? No
Project B: IRR = 20%
| Year |
Inflows |
PVF @ 14% |
NPV |
|
| 0 | -3,000 | |||
| 1 | 3,600 | 0.8772 | 3,157.92 | |
g. If the firm's cost of capital had been 10 percent, what would be investment A's internal rate of return?
Project A: IRR = 5%
| Year | Inflows | PVF @ 10% |
| 0 | -3,000 | |
| 1 | 1,100 | 0.909 |
| 2 | 1,100 | 0.8264 |
| 3 | 1,100 | 0.7513 |
h) The payback method of capital budgeting selects which investment? Why?
The payback method considers the period of time necessary to recoup the cost of an investment. The payback period may also be used to rank alternative investments. The more rapidly the initial cash outflow is recovered the more preferred the investment is. If the payback method is used, option B would be the preferred investment.
Problem 5
a) Which investment(s) should the firm make according to the net present value? Why?
Net present value investment A:
NPV=$395/(1+0.12)-$1000
=352.68-1000
= -647.32
FV=395; PMT=0;I=12,N=1;PV=? =-647.32
Net present value investment B:
NVP=$1749/(1+0.12^4-$1000=$747.43
=$1749/(0.636)-$1000 = $112.364
FV = $1749; PMT=0; I=12 N=4; PV?=$1861.64
Internal rate return investment A:
$1000=$1749/(1+r)
PVIF = $1000/$1749=.806 SO IRP = 24%
FV = $1749; PMT =0; N=1; PV=1000; I=?=24
Internal rate of return investment B:
$1000=$1749/(1+r)^4
PVIF = 1000/$1749= 0.515 SI IRP =18%
PV =1,749; PMT=0’ M=4’ [V=1000; I=?=18
b) Which investment(s) should the firm make according to the internal rates of return? Why?
Investment A because rate of return on investment is higher.
Problem 7
An investment with total costs of $10,000 will generate total revenues of $11,000 for one year. Management thinks that since the investment is profitable, it should be made. Do you agree?
The investment will provide a positive return and I would agree with management.
What additional information would you want?
It would be helpful to also know: If the project will be analyzed solely, what is the risk associated with the investment, what is the cost of debt ratio for the company, and what is the cost of the fund.
If funds cost 12 percent, what would be your advice to management?
My advice would be not to purchase because the net present value is negative.
Net present value = -177
11000(.893)-10000 = -177
Would your answer be different if the cost of capital is 8 percent?
If the cost of capital was 8%, my advice would be to purchase because the net present value would be positive.
11000(.926)-10000 =186
Net present value = 186
Problem 10
Determine the firm's optimal capital structure.
40% debt ratio
Construct a simple pro forma balance sheet that shows the firm's optimal combination of debt and equity for its current level of assets.
Current Balance Sheet |
|||
| Assets | $500 | Debt | $200 |
| Equity | $300 | ||
| Total | $500 | ||
c. An investment costs $400 and offers annual cash inflows of $133 for five years. Should the firm make the investment?
Yes, the investment has potential to yield 20%
d. If the firm makes this additional investment, how should its balance sheet appear?
Current Balance Sheet |
|||
| Assets | $500 | Debt | $600 |
| Liabilities | $360 | Equity | $433 |
| Total | $860 | $1,033 | |
e. If the firm is operating with its optimal capital structure and a $400 asset yields 20.0 percent, what return will the stockholders earn on their investment in the asset?
The stockholder will earn 30%.
Problem 11
a. According to the net present value method of capital budgeting, which investment(s) should the firm make?
S because its net present value is higher and the investments are mutually exclusive therefore, the firm can only make one.
|
NPV |
|
| Q |
S |
|
NPVS = $1,300/(1 +.1) $1,000= $1,181.70 $1,000 = $181.70 |
$386(PVAIF 10I, 4N) $1,000 = $386(3.170) $1,000= $223.62 |
b. According to the internal rate of return method of capital budgeting, which investment(s) should the firm make?
Contrary to answer a, Q should be selected because its internal rate of return is higher.
|
IRR |
|
|
Q |
S |
|
$1,000 = $1,300/(1 + rQ)= (1 + rQ) = $1,000/$1,300 = .769 rQ = 30% |
$386(PVAIF ?I, 4N) = $1,000 Interest factor = $1,000/386 = 2.591 rS = 20% |
c. If Q is chosen, the $1,300 can be reinvested and earn 12 percent. Does this information alter your conclusions concerning investing in Q and S? To answer, assume that S's cash flows can be reinvested at its internal rate of return. Would your answer be different if S's cash flows were reinvested at the cost of capital (10 percent)?
| Terminal Value | |
| Q@ 12% |
S@ 20% |
|
$1,300 (1 + .12)^t $1,300(1.405) =$1,826.50 |
$386 (FVAIF 20I, 4N) $386(5.386) = $2,072.05 |
| S@ 10% | |
| $386(4.641) = $1,791.42 | |
The terminal value of S is larger, and is preferred to Q. However, if the reinvestment rate of S had been 10%, then terminal value of S would not be and investment Q would be best to select
