BA 340
Final review questions’ solutions
1. Degnan Dance Company, Inc., a manufacturer of dance and exercise apparel, is considering replacing an
existing piece of equipment with a more sophisticated machine. The following information is given.
Existing Machine
Proposed Machine
_________________________________________________________________
Cost = $100,000
Cost = $150,000
Purchased 2 years ago
Installation = $20,000
Depreciation using MACRS over
Depreciation--the MACRS
a 5-year recover schedule
5-year recovery schedule will be used.
Current market value = $105,000
Five year usable life remaining
Five year usable life expected
Earnings Before Depreciation and Taxes
Existing Machine
Proposed Machine
________________________________________________________________
Year
1
$160,000
Year 1
$170,000
2
150,000
2
170,000
3
140,000
3
170,000
4
140,000
4
170,000
5
140,000
5
170,000
The proposed machine would be sold at book value at the end of the fifth year. The existing machine would
be discarded after its remaining useful life if it was maintained. No working capital investment is required.
The firm’s cost of capital is 10% and its tax rate is 40%. Should the new machine be purchased?
Solution: Since we are evaluating just one project, we can use NPV.
The required rate of return is 10%
Incremental cash flows:
Proposed machine:
Initial cash flows: Purchase price + installation = $170,000
Operating cash flows:
Using a 5-yr MACRS schedule, depreciation for the proposed machine for 5 years is:
Yr.
1:
170000 * 0.2
= 34000
2:
170000 * 0.32 = 54400
3:
32640
4:
19580
5:
19580
OCFs:
Yr
1
2
3
4
5
EBDepr
- Depr
170000
34000
170000
54400
170000
32640
170000
19580
170000
19580
EBIT
-taxes
+Depr
136000
54400
34000
115600
46240
54400
137360
54948
32640
150420
60168
19580
150420
60168
19580
OCF
115600
123760
115052
109832
109832
Terminal cash flow:
Sale of proposed machine (at book value):
Book value = 170000 – 34000 – 54400 – 32640 – 19580 – 19580 = 9800
Existing machine:
Sale of existing machine (included in initial cash flows):
Book value = 100000 – (100000 * 0.2) – (100000 * 0.32) = 48000
Cash flow from sale: 105000 – (105000 – 48000) * 0.4 = 82200
Operating cash flows lost:
The existing machine is to be used for 5 more years:
Depreciation:
Yr.
1:
2:
3:
4:
5:
OCFs:
Yr
100000 * 0.192 = 19200
100000 * 0.1152 = 11520
100000 * 0.1152 = 11520
100000 * 0.0576 = 5760
0
1
2
3
4
5
EBDepr
- Depr
160000
19200
150000
11520
140000
11520
140000
5760
140000
0
EBIT
-taxes
+Depr
140800
56320
19200
138480
55392
11520
128480
51392
11520
134240
53696
5760
140000
56000
0
OCF
103680
94608
88608
86304
84000
NPV:
(-170000 + 82200)
+
(115600 – 103680)/1.1
+ (123760 – 94608)/1.1^2 +
(115052 – 88608) / 1.1^3
+
+ (109832 + 9800 – 84000) / 1.1^5
=
5191
ACCEPT.
(109832 – 86304)/1.1^4
2. Galaxy Satellite Co. is attempting to select the best group of independent projects competing for the
firm's fixed capital budget of $10,000,000. All four projects have conventional cash flows. The firm’s cost
of capital is 20%. A summary of key data about the proposed projects follows.
Project
-------
Initial Investment
------------------
IRR
---
PV of Inflows
at 20%
-------------
A
B
C
D
E
F
$3,000,000
9,000,000
1,000,000
7,000,000
4,000,000
6,000,000
21%
25
24
23
19%
21%
$3,150,000
9,320,000
1,040,000
7,350,000
3,875,000
6,500,000
What should the firm do?
Solution: For this question we can use either the profitability index or NPV of a combination of projects
such that the total investment is 10 million (budget) or less. Since PI is the present value of benefits divided
by the present value of costs, we can simply divide PV of inflows by the initial investment to obtain PI for
each project:
PI for
A:
B:
C:
D:
E:
F:
3150000 / 3000000 = 1.05
9320000 / 9000000 = 1.036
1040000 / 1000000 = 1.04
7350000 / 7000000 = 1.05
3875000 / 4000000 = 0.969
6500000 / 6000000 = 1.08
All but project E is acceptable. Ranks: F, A and D (tied), C, B. We will have used up our 10 million dollar
budget exactly by investing in projects F, A and C. Although D is ranked ahead of C we do not have the
capital to invest in D.
3. Cuda Marine Engines, Inc. must decide whether a capital investment (new equipment) proposal is
worthwhile. The firm has spent $15,000 developing the technology that will be applied to the new
equipment. The proposed asset costs $50,000 and has installation costs of $3,000. The equipment will be
housed in a facility that is owned by the firm but that is currently not being used. This facility is currently
worth $10,000. The new equipment will be depreciated using a five-year recovery schedule, is expected to
be used for 3 years after which it will be sold for $20,000. The new equipment is expected to generate
revenues of $25,000 and operating expenses of $10,000 annually. It also requires an investment in
inventory of $10,000. No other current accounts are expected to be affected. The firm has a 40 percent tax
rate. If the required rate of return for this proposal is 15%, should Cuda go through with it?
Solution: Done in class.
4. A corporation is considering a capital project for the coming year. The project has an internal rate of
return of 14 percent. If the firm has the following target capital structure and costs, what should their
decision be and why?
Source of Capital
Proportion
After-tax cost
__________________________________________________
Long-term debt
.40
10 %
Preferred stock
.10
15 %
Common stock equity
.50
20%
Solution: We need to compare the IRR of the project to the WACC. The WACC is:
0.4 * 10% + 0.1 * 15% + 0.5 * 20% = 15.5%.
Since IRR < WACC, we would reject the project.
5. Kottinger's Kamp Supplies is considering an investment in new manufacturing equipment. The
equipment costs $220,000 and will provide annual aftertax inflows of $80,000 at the end of each of the next
four years. No terminal cash flows are expected. The firm's proportion of its capital structure that is debt is
25%. The remainder is common equity. The firm’s beta is 1.4, and its pretax cost of debt is based on the
firm’s outstanding debt: Current price = $1040, Maturity = 15 years, Annual coupon rate = 7% (paid semiannually). The current risk-free rate is 4% and the market return is 8%.
1.
2.
Assume the project is of approximately the same risk as the firm's existing operations. Should the
firm invest?
Assume instead that KK is a multi-division firm with operations in Manufacturing, Travel
Services, Retail Stores Rentals. Use the following information to determine whether the project
should be accepted.
Firm
Stanton
Xenox
Trail Mix
Industry
Retail
Travel Services
Manufacturing
Beta
1.3
0.7
2.2
Each of the firms above only operates in the industry indicated.
Solution: I did not provide you with a tax rate for this question. One is needed. Assume it is 35%.
1.
For the first question, we can use the firm WACC to assess the project
Re = 4% + 1.4 * (8% - 4% ) = 9.6%
We can come up with an approximate value for the before-tax cost of debt using the firms
outstanding debt information:
1000  1040
15
 6.6%
1000  1040
2
70 
Rd =
WACC = 0.75 * 9.6% + 0.25 * 6.6% * (1 – 0.35) = 8.27%
The NPV of the project is:
NPV = -220 – 80/1.0827 - 80/1.0827^2
- 80/1.0827^3
- 80/1.0827^4 = 43,485
Project is acceptable.
2.
For the second question, we need to determine a project-specific WACC. Since the project is in
manufacturing, we can use Trail Mix’s beta to compute a cost of equity and WACC for the
project. Trail Mix represents a pure play firm for evaluating the project.
Re for project: 4% + 2.2 * (8% - 4%) = 12.8%
WACC = 0.75 * 12.8% + 0.25 * 6.6% * (1-0.35) = 10.67%
NPV = -220 – 80/1.1067 - 80/1.1067^2
- 80/1.1067^3
- 80/1.1067^4 = 29955
Project is still acceptable.
6. Which of the following firms will benefit from an increase in debt in their capital structure? The firms’
tax rate is 35%
Firm
A
B
C
D
E
Beta
1.3
1.1
2.1
0.8
0.5
Cost of equity
11.5
10.5
15.5
9.0
7.5
Return on Equity Before Tax cost of debt
20%
7%
15%
13%
13%
10%
7%
8%
6%
10%
Solution: Firms will benefit by adding debt if their return on equity is greater than their after-tax cost of
debt.
Firm
A
B
C
D
E
ROE
20%
15%
13%
7%
6%
AT cost of debt
7% * (1-0.35) = 4.55%
13% * (1-0.35) = 8.45%
10% * (1-0.35) = 6.5%
8% * (1-0.35) = 5.2%
10% * (1-0.35) = 6.5%
BENEFIT
BENEFIT
BENEFIT
BENEFIT
WILL NOT BENEFIT