BA 654 Finance Midterm, Fall 2009
Name ____________________________
Label all answers, and show your calculations in problems 3 and 4.
1. (12 points) You have estimated the following cash flows for Project X:
Year
0
1
2
3
CFX
(125,000)
80,000
40,000
20,000
The cost of capital for the project is 12%.
a. Calculate the internal rate of return for the project.
b. Calculate the NPV for the project.
IRR = 7.57%
NPV = -$7,448
2. (12 points) Shown below are the cash flows for two mutually exclusive projects, A and B, as
well as an excel worksheet showing analysis of those cash flows.
Year
0
1
2
3
CFA
($1,200)
$800
$500
$200
CFB
($200)
$120
$100
$80
CF
($1,000)
$680
$400
$120
IRR
15.3%
25.3%
12.9%
r
0
10
14
20
25
NPVA
$300.00
$90.76
$21.48
($70.37)
($137.60)
NPVB
$100.00
$51.84
$36.21
$15.74
$0.96
$350.00
$300.00
$250.00
$200.00
$150.00
$100.00
NPVA
$50.00
NPVB
$0.00
($50.00)
0
5
10
15
20
25
30
($100.00)
($150.00)
($200.00)
Use the information above to answer the questions on the next page.
Problem 2, continued.
As stated above, the two projects are mutually exclusive.
a. If the cost of capital is 10%, which project(s) should be selected? State what your decision is
based on.
b. What is the third column of cash flows (CF) and what is the significance of its IRR?
a. If the cost of capital (r) is 10 percent, choose A. It has a higher NPV than B.
b. CFis the difference in cash flows, that is CF CFA – CFB. The IRR of CF represents the cost
of capital (r) at which the decision is reversed. If r < 12.9%, choose A. If r > 12.9%, choose B.
3. (28 points) A firm’s target weights for its capital structure are that 40 percent of financing will
come from long-term debt and 60 percent of financing will come from common equity. It can
sell 20 year bonds with $1,000 par and a coupon rate of 8% paid annually for $950.
a. (8 points) Calculate the before-tax interest rate on new debt financing and the after-tax
interest rate on new debt financing if the firm’s tax rate is .40.
To solve rd: -950 = PV, 1000 = FV, pmt = 80, n = 20, I/Y = rd = 8.53%
ATrd = rd ( 1-T) = 8.53 (.6) = 5.12%
b. (4 points) The risk-free rate is 4% and the expected return on the market is 10%. The
common stock has a beta of 1.25. Calculate the required return on the firm’s stock.
Rs = rf + B (ERM – rf) = 4 + 1.25 (6) = 11.5%
c. (4 points) Calculate the firm’s weighted average cost of capital (WACC), assuming that new
common equity is from retained earnings. (If you are unable to do part (a) or (b), assume values
you believe are reasonable for the cost of debt and/or the required return on equity and clearly
state them.)
WACC = Wd (ATrd) + Wce (rs) = .4 (5.1) + .6 ( 11.5) = 2.04 + 6.9 = 8.94%
Problem 3, continued.
d. (12 points) Suppose all financing in the first quarter for the firm in this problem will come
from internally generated cash flows (i.e., retained earnings) and all financing in the second
quarter will come from debt. Should the firm use the weighted average cost of capital as the
required return on a project of average risk in both periods, or should it use the required return
on equity (rs) in the first quarter and the after-tax cost of debt (AT rd) in the second quarter as
the required return on projects of average risk? Explain your answer.
The firm should use the WACC as the hurdle rate (required return) in both periods. The WACC is
based on the firm’s target weights. In this case, the firm plans, on average, to get 40% of its
financing from debt and 60% from equity. As pointed out in your text on p. 359, all investors
have a claim on future cash flows of every project, and it is management’s responsibility to
insure that the cash flows are sufficient to satisfy those investors. In addition, it only makes
sense that there should be some consistency from period to period. If the firm uses r s (11.5%)
as the hurdle rate in the first quarter and the after-tax interest rate (5.1%) in the hurdle rate in
the second quarter, it will reject projects with an IRR of 10% in the first quarter and invest in
projects with an IRR of 6% in the second quarter.
4. (30 points) Pasta and Pizza, Inc. owns a chain of restaurants. It is considering ting its own
brand of pasta in grocery stores. It will require purchasing equipment with a cost of $2.4
million. Delivery and installation of the equipment will cost an additional $300,000. The project
will require an increase in net working capital of $200,000 at the beginning of the project. The
project is expected to generate sales revenue of $3 million per year, based on the expected
sales price in year 1. Cash expenses are 45 percent of sales revenue. The sale price and cash
expenses are expected to increase at 4 percent annually due to inflation. Depreciation for tax
purposes will be straight line to zero over the three year life of the equipment. The firm’s tax
rate is 40 percent. At the end of 3 years the equipment will be sold for an estimated $800,000
and funds invested in net working capital will be recovered.
a. (6 points) Calculate the initial investment for the project.
Price
Delivery & installation
Change in net WC
Initial investment
2,400
300
200
2,900
b. (4 points) Calculate annual depreciation expense for the project.
Depr Exp = 2,700 / 3 = 900
c. (4 points) Calculate the after-tax salvage value of the equipment, assuming the expected
salvage value of the equipment is not affected by inflation.
Salvage value
-Book Vale
Recap Depr
xT
Tax
800
0
800
.4
320
Salvage value
-Tax
AT Salvage value
800
320
480
Problem 4, continued.
d. (4 points) Calculate the terminal cash flows associated with the project.
AT salvage value
Change in Net WC
Terminal CF
480
200
680
e. (12 points) Calculate the annual operating cash flows for each year of the project, taking into
consideration the effects of inflation on sales revenue and cash expenses.
Op CF1 = (Sales Rev – Cash Exp) (1 – T) + Depr Exp) (T)
(3,000 – 1350) (.6) + (900) (.4) = 990 + 360 = 1,350
Op CF2 = (3,120 – 1,404) (.6) + 360 = 1,389.6
Op CF3 = (3,244.8 – 1,460.16) (.6) + 360 = 1,430.78
5. (18 points) Flagstaff Mfg. has a corporate WACC of 12 percent. You are evaluating two
mutually exclusive projects, X and Y, each of which has a lifetime of 6 years. Use the
information provided to answer the questions below.
Project X:
Initial investment
Expected NPV @ 12%
Standard deviation of NPV
$126,700
17,321
15,112
Project Y:
Initial investment
Expected NPV @ 12%
Standard deviation of NPV
$126,700
17,321
15,112
The cash flows from project X are positively correlated with the firm’s existing cash flows,
however, the cash flows of Y are negatively correlated with the firm’s existing cash flows.
a. What type of risk does the standard deviation measure(circle one)?
stand-alone risk
within-firm risk
market risk Answer: stand-alone risk
b. What type of risk do the correlations affect (circle one)?
stand-alone risk
within-firm risk
market risk
Answer: within-firm risk
c. Briefly explain your answer to (b).
Within firm refers to the effect of the project on the variability of the firm’s cash flows. It views
the firm’s assets as a portfolio and considers the diversification effects of adding another asset
to that portfolio. Diversification (and the resulting risk reduction) is greater if the correlation is
negative.
d. Based on the information provided, which project should be selected and why?
Choose Y; it has lower within firm risk than X and based on the information, it is identical in all
other respects.