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Practice Problems for the Final Exam
Managerial Finance - 2320
Professor Brian Clark
Fall 2021
1
MGMT 2320 Practice Problems for Final Exam
PROBLEMS
Problems
Chapter 8
1.
Company X is considering investment in a new project that is projected to generate $2 million in sales
each of the next 4 years. Manufacturing closts are expected to be 60% of revenues. The project will
also require annual sales and marketing expenses of $200 thousand each year, starting immediately
and continuing each year of the 4 years of the project life. The project will require an upfront capital
expenditure of $1 million, depreciated on a straight-line to zero over the 4-year life. The project will
require $100 thousand in cash, deposited immediately and returned after the life of the project. Find
the NPV if Company X has an appropriate cost of capital of 10%. Assume a marginal tax rate of 35%.
2.
Your company purchased a new manufacturing machine one year ago for $100,000. You just learned
that a new machine is available that is superior to the old one. It costs $150,000. It will have a useful
life of 5 years and be depreciated on a straight-line. No salvage value is expected. The new machine is
expected to produce an EBIT of $80,000 a year for the next 5 years. Your current machine is expected
to produce an EBIT of $40,000 a year. The depreciation expense for the current machine is $20,000 per
year and will remain the same for the next five years, at which time it can be scrapped for no cost.
All other expenses associated with the machines are identical. The current market value of the old
machine is $40,000. If your company’s marginal tax rate is 30% and the appropriate cost of captial for
the machine is 12%, should you invest in the new machine?
3.
Your firm is considering a project that will require a purchase of $10 million in new equipment. Assume
a cost of capital of 10% and determine the present value of the depreciation tax shield if the firm’s
marginal tax rate is 30% and the equipment can be depreciated
(a) Over an eight-year period, with the first deduction starting in one year.
(b) Over a four-year period, with the first deduction starting in one year.
4.
Your firm is considering expanding and starting a new division.
Your marketing department has
provided you with the following pro-forma income statement. After year 5, you expect free cash flow to
grow at a constant rate of 3% forever. If the new division has an appropriate cost of capital of 10%,
what is the present value of the division?
5.
Rensselaer Manufacturing recently spent $100 million to invest in some manufacturing equipment.
The company expects that the equipment will have a useful life of four years and the company has a
marginal tax rate of 26%. What is the present value of the depreciation tax shield assuming a discount
rate of 10%?
Fall 2021
2
Chapter 9
MGMT 2320 Practice Problems for Final Exam
PROBLEMS
Chapter 9
1.
Consider a company that just paid a
quarterly
divendend of $2.00 per share and has an equity beta of
1.2. You expect the market to return 8.0% above the risk-free rate of 2%.
(a)
What is the fair value of the stock if the quarterly dividend is expected to remain constant for the
foreseeable future?
(b)
What is the fair value of the stock if the dividend is expected to grow at a rate of 3%
per year
forever?
2.
AT&T paid an annual dividend of $2.08 per share over the past year and their common stock is currently
trading at $28.00 per share. Assuming that the dividends will continue to grow at a constant rate
forever, use the divident discount model to find the implied growth rate for the dividends. Assume that
AT&T has an equity beta of 1.4, the risk-free rate is 1%, and the expected market risk premium is 7%.
3.
Company X expects to have earnings this coming year of $4.50 per share. Company X plans to retain
all of its earnings for the next three years. For the subsequent two years, the firm will retain 75% of its
earnings. It will then retain 25% of its earnings from that point onward. Each year, retained earnings
will be invested in new projects with an expected return of 25% per year. Any earnings that are not
retained will be paid out as dividends. Assume Company X’s share count remains constant and all
earnings growth comes from the investment of retained earnings. If Company X’s equity cost of capital
is 10%, what price would you estimate for Company X stock?
4.
A Wall St. Analyst has forecast startup company First One’s free cash flows for the next five years to
be the following: -$100, $12, $24, $28, and $120. After that, the free cash flows are expected to grow at
a rate of 3% forever. If the appropriate cost of captial for First One is 18%, what is the present value of
the company?
5.
(HW problem 23) KCP was acquired in 2012 for a price of $15.25 per share. KCP had 18.5 million
shares outstanding, $45 million in cash, and no debt at the time of the acuisition.
(a)
Given a WACC of 11%, and assuming no future growth, what level of annual free cash flow would
justify the acquisition price?
(b)
If KCP’s current annual sales are $480 million, assuming no net CAPEX or increases in NWC,
and a tax rate of 35%, what EBIT margin does your answer in part (a) require?
6.
Company X paid an annual dividend of $5.00 per share last year.
They are expected to increase
dividends by 5% per year for the next three years and then level off to a steady-state long-run growth
rate of 2% per year thereafter. If the company has a cost of equity of 12%, would you be willing to buy
shares at a price of $55.00? Why or why not?
7.
(HW problem 9.14) Based on the dividend-discount model, what is the value of a firm with an initial
dividend
D
0
, growing for
n
years (i.e., until year
n
+ 1
) at rate
g
1
and after that rate
g
2
forever, when
the equity cost of capital is
r
?
8.
Fall 2021
3
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Chapters 10-12 Problems
MGMT 2320 Practice Problems for Final Exam
PROBLEMS
Chapters 10-12 Problems
1.
Your friend asks for investment advice. Currently, she has $10 million invested in a portfolio that has
an expected return of 5.0% and a volatility of 7.0%. Suppose the risk-free rate is 1.0%, and the market
(tangent) portfolio has an expected return of 10.0% and a volatility of 9.5%. Assume that the CAPM
holds and she can only invest in the market portfolio and/or US Treasuries (i.e., the risk-free asset).
(a)
To maximize her expected return without increasing her volatility, which portfolio would you
recommend? Specifically, how much money would you recommend her to invest in Treasuries and
how much in the market portfolio?
(b)
To minimize her expected volatility without decreasing her expected return, which portfolio would
you recommend? Specifically, how much money would you recommend her to invest in Treasuries
and how much in the market portfolio?
2.
(HW Problem 11.33) Suppose you have $100,000 to invest in cash, and you decide to borrow another
$15,000 at a 4% annual interest rate to invest in the stock market. You invest the entire $115,000 in a
diversified portfolio
M
with a 15% expected return and 25% volatility.
(a) What is the expected return and volatility of your investment?
(b) What is your realized return if the portfolio
M
goes up by 25% over the year?
(c) What return do you realize if
M
falls by 20% over the year?
3.
(HW Problem 46) Your investment portfolio consists of $15,000 invested in only one stock - MSFT.
Suppose the risk-free rate is 5%, MSFT has an expected return of 12% and volatility of 40%, and the
market portfolio has an expected return of 10% and a volatility of 18%. Under the CAPM assumptions,
(a)
What alternative investment has the lowest possible volatility while having the same expected
return as MSFT? What is the volatility of this investment?
(b)
What investment has the highest possible expected return while having the same volatility as
MSFT? What is the expected return of this investment?
4.
You currently have $100,000 invested in AAPL stock and want to add another stock to your portfolio.
You expect the S&P 500 to return 8% above the risk-free rate of 1% next year. You are considering
adding either of the two following stocks to your current investment in AAPL by selling some AAPL
shares and investing in one other stock so you maintain a $100,000 investment portfolio. If you want
to target the expected market return in your two stock protfolio, which stock should you add to your
investment?
Figure 1: alt text here
Fall 2021
4
Chapters 14-15 Problems
MGMT 2320 Practice Problems for Final Exam
PROBLEMS
Chapters 14-15 Problems
1.
Assume perfect capital markets and no taxes. Suppose Visa Inc. (V) has no debt and an equity cost of
capital of 9.2%. The average debt-tovalue ratio for the credit services industry is 13%. What would its
cost of equity be if it took on the average amount of debt for its industry at a cost of debt of 6%?
2.
(HW 14.18) In mid-2015, Qualcomm Inc. had $11 billion in debt, total equity capitalization of $89
billion, and an equity beta of 1.43 (as reported on Yahoo! Finance). Included in Qualcomm’s assets
was $21 billion in cash and risk-free securities. Assume that the risk-free rate of interest is 3% and the
market risk premium is 4%. Assume perfect capital markets and no tax.
(a) What is Qualcom’s enterprise value?
(b) What is the beta of Qualcom’s assets?
(c) What is Qualcom’s WACC?
3.
Consider a project with free cash flows in one year of $500 or $800, with each outcome equally likely
and fully dependent on the overall state of the economy. The initial investment for the project is $400
and the appropriate cost of capital is 20%. Assume that the risk-free rate of interest is 10%.
(a) What is the NPV of the project?
(b)
Suppose that to raise the funds for the initial investment, the project is sold to investors as an
all-equity firm. The equity holders will receive the cash flows of the project in one year. How much
money can be raised in this way—that is, what is the initial market value of the unlevered equity?
(c) What are the expected returns on equity in each state?
(d)
Suppose instead that the entrepreneur raises half of the initial funds (from part a) by issuing debt.
What is the new market value of the equity? Market value of the debt?
(e) What are the expected returns on equity now?
4.
The common stock of TWO, Inc. has a beta of 0.90. The short term U.S. Treasury bill rate is 4% and
the market risk premium is estimated at 8%. TWO, Inc. is financed with 30% debt and 70% equity
and pays 40% in taxes. Assume the debt is risk free.
(a)
What is TWO, Inc.’s weighted average cost of capital asssuming that interest paymnets on debt
are tax-deductible and the firm is profitable.
(b)
You are provided with the following forecasts (in millions of dollars) of TWO, Inc.’s profits and of
its future investment in new property, plant and equitment (i.e., CAPEX). After year 4, EBITDA,
depreciation, EBIT, and investment are expected to grow at a constant rate of 5% from their
respective year 4 levels indefinitely. The company also plans on maintaining a capital structure
of 30% debt and 70% equity indefintiely. Based on this information and your answer to part a,
estimate TWO, Inc.’s total value and the separate values of equity and debt [HINT: You need to
find the total free cash flows]
Table 1:
TWO, Inc.
Year 1
Year 2
Year 3
Year 4
EBITDA
80
100
115
120
Depreciation
20
30
35
40
Pretax Profit (EBIT)
60
70
80
80
Net Investment (CAPEX)
12
15
18
20
Fall 2021
5
Chapters 14-15 Problems
MGMT 2320 Practice Problems for Final Exam
PROBLEMS
5.
Company Three, Inc. is considering entering in to a new business and therefore needs to estimate the
WACC for projects associated with the new venture. Their lead analyst has compiled the following list
of comparable firms in the new industry. You note that all of the firms have different capital structures
and that should be taken into account. Assume that the current Treasury bill rate is 1.0% and the
market risk premium is 7%.
Table 2:
TWO, Inc.
Company
Equity Beta
Market Value of Debt
Market Value of Equity
A
1.2
100
50
B
1.4
100
45
C
0.8
100
90
D
0.4
100
200
(a)
Assuming Three, Inc. will be subject to a marginal tax rate of 35% in the new venture, find an
appropriate WACC that you should use for this new venture if it is funded with 100% equity.
Assume the debt of each of the comparable companies is risk-free.
(b)
Now, assuming that Three, Inc. will be subject to a marginal tax rate of 35% in the new venture,
find an appropriate WACC that you should use for this new venture if it is financed with 50%
debt and 50% equity. Assume the debt is risk-free.
(c)
Finally, assuming there is a negligible risk of bankruptcy with 50% debt, would you recommend
using debt financing for the new venture or all equity?
6.
Four, Inc. is a clothing retailer with a current share price of $10.00 per share and has 25 million shares
outstanding. Suppose that Four, Inc. announces plans to lower its corporate taxes by borrowing $100
million and using the proceeds to repurchase shares.
(a)
Assuming perfect capital markets (including no income tax), find Four Inc.’s expected share price
after the announcement.
(b)
Find the new share price after the announcement if Four, Inc. pays 35% in corporate tax and
shareholders expect the change in capital structure to be permanent. Also assume that corporate
taxes are the only market imperfection. [Assume that the $10 share price already reflects the 35%
tax rate for the unlevered firm].
7.
Consider the following two companies, U and L. They are exactly the same in every way (i.e., the
expected future cash flows are exactly the same). The only difference is that company U is all equity
financed whereas company L is financed by 30% debt and 70% equity. Company L’s debt is risk free
and equity has a beta of 1.6. The market value of company U is $100 million. Assume the risk free rate
is 5% and the expected return on the market is 12%.
(a) Assuming perfect capital markets including no taxes, find each company’s WACC.
(b)
Suppose you are prohibited from investing directly in company L due to a conflict of interest and
can only invest in company U. If you have the ability to borrow and lend at the risk fee rate, show
how you could replicate the returns of company L using only company U’s equity and the risk free
asset.
(c)
Suppose you are prohibited from investing directly in company U due to a conflict of interest and
can only invest in company L. If you have the ability to borrow and lend at the risk fee rate, show
how you could replicate the returns of company U’s equity using only company L’s equity and the
risk free asset.
Fall 2021
6
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MGMT 2320 Practice Problems for Final Exam
QUIZ 2 PROBLEMS
Quiz 2 Problems
1.
Stihl is considering investing in a new project to manufacture a new electric chainsaw. The project
will require an up-front research and development (R&D) expense of $10 million and require an intial
capital expenditure of another $45 million to build out new machinery. The capital expenditure will be
depreciated in a straight-line over the three year life of the project and scrapped at no cost at the end
of the project. Stihl expects to sell 300,000 chainsaws each year at a price of $400 each. The cost to
manufacture each saw is expected to be $200 per unit. Given it is a new venture for the firm, Stihl
expects to spend $20 million in advertising during the current year (year 0) and then and $10 million
each year of the three year life of the project (years 1-3). Assume Stihl has a marginal tax rate of 25%
and the project has an appropriate cost of capital of 10%. Find the NPV of the project. Should Stihl
invest?
[20 points]
Fall 2021
7
MGMT 2320 Practice Problems for Final Exam
QUIZ 2 PROBLEMS
2.
Consider the new project proposal in question 1. After analyzing the above projections, Stihl’s CFO
realized that the new chainsaw project would tie up some capital. In particular, she notes that 1) the
project will require an initial cash infusion of $5 million which will increase to $10 million for the life
of the project and then be returned after the project’s 3 year life; 2) Stihl will be able to pay their
suppliers with a 2 month lag; and 3) Stihl will have to carry 25% of units sold as inventory. Find the
net present value of the cash flows from net working capital.
[10 points]
Fall 2021
8
MGMT 2320 Practice Problems for Final Exam
QUIZ 2 PROBLEMS
3.
An industry analyst projects that Consolidated Edison (ED) will pay an annual dividend of $3.10 per
share in the coming year and that the dividend will grow by 1.0% annually forever. Based on the
dividend discout model, what is ED’s cost of equity if the stock is currently trading at $78.00 per share?
[10 points]
4.
IBM expects to have earnings this coming year of $8.00 per share. It plans to retain all earnings for
the next three years. After that, it will then retain 25% of its earnings from that point onward. Each
year, retained earnings will be invested in new projects with an expected return of 15.0% per year.
Any earnings that are not retained will be paid out as dividends. Assume IBM’s share count remains
constant and all earnings growth comes from the investment of retained earnings. If IBM’s equity cost
of capital is 9.5%, what price would you estimate for IBM’s stock according to the dividend discount
model?
[10 points]
Fall 2021
9
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MGMT 2320 Practice Problems for Final Exam
QUIZ 2 PROBLEMS
5.
A Wall St. Analyst has forecast Company X’s free cash flow to be $100 million next year and grow by
50% per year for the subsequest three years. After that, the free cash flows are expected to grow at
a constant rate of 3% forever. If the appropriate cost of captial for Compamy X is 15%, what is the
present value of the company?
[10 points]
Fall 2021
10
MGMT 2320 Practice Problems for Final Exam
QUIZ 2 PROBLEMS
Use the information in Figure 1 to answer the following questions (it is attached as the last page of this exam
- feel free to tear it off). The upper plot on the left shows a scatter plot of the monthly excess returns of
Exxon Mobil (XOM) versus the S&P 500 Index (SPY). The results of a linear regression through the data
are depicted by the equation on the plot. The bottom plot shows the same thing but for Amazon (AMZN)
vs. SPY. The right panel shows the correlation and covariance matrices for the monthly returns of four stocks
(AAPL, AMZN, ED, XOM) and an ETF that tracks the S&P 500 (SPY). The monthly volatility of each
stock is given at the bottom along with the expected annual market return and risk-free rate.
6.
Based on the information in Figure 1, what are the expected returns of Exxon Mobil (XOM) and
Amazon (AMZN) based on the CAPM?
[10 points]
7.
Suppose you have $1 million to invest but can only invest in the above two stocks (XOM and AMZN).
How much money should you allocate to each stock in order to achieve an expected return of 9.0%?
[10
points]
Fall 2021
11
MGMT 2320 Practice Problems for Final Exam
QUIZ 2 PROBLEMS
8. What is the expected volatility of the two-stock portfolio in the above question?
[10 points]
9.
Would you be better off investing in the portfolio constructed above or in an index fund that tracks the
S&P 500 (i.e., SPY)? Provide a quantitative justification for your answer. (Ignore transactions costs
and taxes).
[10 points]
Fall 2021
12
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MGMT 2320 Practice Problems for Final Exam
QUIZ 2 PROBLEMS
10.
BONUS (all or nothing):
Repeat questions 6-9 for Consolidated Edison (ED) and Apple (AAPL).
[5 points]
Fall 2021
13
MGMT 2320 Practice Problems for Final Exam
USEFUL EQUATIONS
Useful Equations
The following equations will be useful as you complete the exam.
1. Present value of a future cash flow:
PV
=
CF
(1 +
r
)
k
(1)
2. Future value of a cash flow:
FV
=
CF
(1 +
r
)
k
(2)
3. Simple Perpetuity that pays a series of period cash flows (
CF
) forever:
PV
P
=
CF
r
(3)
4. Simple Annuity with
k
equal payments of
CF
:
PV
A
=
CF
r
1
-
1
(1 +
r
)
k
(4)
5.
A Growing Perpetuity that pays a growing series cash flows starting at
CF
and growing at a rate of
g
:
PV
P.grow
=
CF
r
-
g
(5)
6. A Growing Annuity that pays a growing periodic stream of
k
cash flows (
CF
) that grow at a rate
g
:
PV
A.grow
=
CF
r
-
g
1
-
(1 +
g
)
k
(1 +
r
)
k
(6)
where,
PV
is the present value,
FV
is future value,
CF
is a cash flow,
r
is the discount rate,
k
is the
number of periods to discount, and
g
is the growth rate of the cash flow in an annuity or perpetuity.
1. Capital Asset Pricing Model (CAPM) expected return:
R
i
=
R
f
+
β
i
(
R
M
-
R
f
)
(7)
2. Expected return on a portfolio:
R
pf
=
n
i
=1
R
i
x
i
(8)
3. Volatility (standard deviation) of a two-asset portfolio:
σ
pf
=
x
2
i
σ
2
i
+
x
2
j
σ
2
j
+ 2
ρ
ij
σ
i
σ
j
x
i
x
j
(9)
4. Relation between covariance and correlation:
Cov
ij
=
ρ
ij
σ
i
σ
j
(10)
where,
R
i
is the return on asset
i
,
R
f
is the risk-free rate of return,
R
M
is the expected return on the
market,
R
pf
is the return of a portfolio of
n
assets,
x
i
is the weight on asset
i
,
j
is the weight on asset
j
,
σ
pf
is the standard deviation of a two asset portfolio,
σ
i
and
σ
j
are the volatilities of assets
i
and
j
,
ρ
ij
is the correlation coefficient between the returns of assets
i
and
j
, and
Cov
ij
is the covariance
between assets
i
and
j
.
Fall 2021
14
MGMT 2320 Practice Problems for Final Exam
USEFUL EQUATIONS
Figure 2: Data for Questions 6 - 10
Fall 2021
15
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a. What is the initial investment in the product? Remember working capital.
b. If the plant and equipment are depreciated over 4 years to a salvage value of zero using straight-line depreciation, and the firm’s tax rate is 40%, what are the project cash flows in each year? Assume the plant and equipment are worthless at the end of 4 years.
c. If the opportunity cost of capital is 10%, what is the project's NPV?
d. What is project IRR?
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QUESTION 13
A project requires an initial investment in equipment of $81,000 and then requires an initial investment in working capital of $19,000 (at t = 0).
You expect the project to produce sales revenue of $100,000 per year for three years. You estimate manufacturing costs at 60% of revenues.
(Assume all revenues and costs occur at year-end, i.e., t-1, t-2, and t= 3.) The equipment depreciates using straight-line depreciation over
three years. At the end of the project, the firm can sell the equipment for $20,000 and recover the investment in net working capital. The
corporate tax rate is 30% and the cost of capital is 15%. Calculate the NPV of the project:
O $3,840.
$4,122.46.
$-2,735.
$7,342.
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Revenues generated by a new fad product are forecast as follows:
Year
Revenues
1
$60,000
2
40,000
3
30,000
4
20,000
Thereafter
0
Expenses are expected to be 40% of revenues, and working capital required in each year is expected to be 30% of revenues in the following year. The product requires an immediate investment of $70,000 in plant and equipment.
Required:
a. What is the initial investment in the product? Remember working capital.
b. If the plant and equipment are depreciated over 4 years to a salvage value of zero using straight-line depreciation, and the firm’s tax rate is 20%, what are the project cash flows in each year? Assume the plant and equipment are worthless at the end of 4 years.
c. If the opportunity cost of capital is 10%, what is the project's NPV? A negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.)
d. What is project IRR? (Do not round intermediate calculations. Enter…
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Revenues generated by a new fad product are forecast as follows:
Year
Revenues
1
$40,000
2
30,000
3
20,000
4
5,000
Thereafter
0
Expenses are expected to be 40% of revenues, and working capital required in each year is expected to be 20% of revenues in the following year. The product requires an immediate investment of $49,000 in plant and equipment.
Required:
a. What is the initial investment in the product? Remember working capital.
b. If the plant and equipment are depreciated over 4 years to a salvage value of zero using straight-line depreciation, and the firm’s tax rate is 20%, what are the project cash flows in each year? Assume the plant and equipment are worthless at the end of 4 years.
c. If the opportunity cost of capital is 10%, what is the project's NPV?
d. What is project IRR?
Req A
What is the initial investment in the product? Remember working capital.
Req B
If the plant and equipment are depreciated over 4 years to a salvage value of zero…
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6.7 Project Evaluation Your firm is contemplating the purchase of a new $575,000 com-puter based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $60,000 at the end of that time. You will save $176,000 before taxes per year in order processing costs, and you will be able to reduce working capital by $80,000 (this is a one-time reduction). If the tax rate is 23 percent, what is the IRR for this project?
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QUESTION 5
A company is thinking about marketing a new product. Up-front costs to market and develop the product are $14.56 Million. The product is
expected to generate profits of $1.39 million per year for 26 years. The company will have to provide product support expected to cost
$294051 per year in perpetuity. Furthermore, the company expects to invest $40821 per year for 11 years for renovations on the product.
This investing would start at the end of year 7. Assume all profits and expenses occur at the end of the year. Calculate the NPV of this
project if the interest rate is 7.45%.
NOTE: Answer in $. If your answer is 220M, you must answer 220000000.0000.
HINT. Compute the present value of all cash flows and then combine them.
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