Corporate Finance Assignment

Please can you assist with this assignment

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Executives – Pro

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lem Set #

3

Name:

Robert Whitelaw

Score:

Q

1 rf

2

%

Excess Returns rM 6

%

Month MMM-rF rM-rF

S

D

[rM] 1

5

% 1

1

0

.3

8

% 9

.5

4

%

2

-2.88% 3.88% a

beta

r 3

0.

33

% 0.6

0% I 1.4

4

2.

7 5%

6.8

2% ii

0.6 5

1.8

7% 1.99% iii -0.2

6

5.

52

% 3.

49

% 7

1.

37

% 0.

45

% b beta r 8

3.97% 2.90% I

10%

9

-2.3

4% -1.

27

% ii 5% 10

0.

50

% -1.75% iii

-1% 11 -8.

13

% -2.3

6% 12 -4.

14

% -5.99% c r

w(rf) w(rM)

13

-13.49% -7.

59

% I 4% 14

10.07% 11.

35

% ii 5%

15 3.

28

% -0.28% iii 7%

16 0.8

5% 0.74% 17 6.09% 5.05% d

sd[r]

w(rf) w(rM)

18 1.71% 4.

42

% I 6%

19 1.84% 3.11% ii

15% 20 0.17% -0.85% iii

21

%

21

-4.90% -6.19% 22 6.15% 3.89% e

P0

50

23 1.82% 0.79% P1 53 24 2.14% 2.

55

% D1

0

25 -0.20% 2.7

3% 26 -5.23% -1.76% beta

alpha

27

4.50% 0.78% i

1.0

28

2.0

8% 1.1

8% ii 2.0

29 8.29% 5.

57

% 30 4.07% 1.2

9% Q2

beta

mkt cap 31 2.22% 4.03% 1.1

100 32 -1.50% 1.55% 1.2

200

33

5.91% 2.80% 1.4

300 34 -0.83% -1.20% 35

7.

39

% 5.65% a

EW beta 36 -2.74% -2.71% 37

5.13% 3.77% b

VW beta 38 5.39% 4.18% 39

6.61% 3.12% Q3

a

beta(1)

0.8

40

5.05%

2.81% beta(2) 1.3 41 -8.

60

% -3.32% firm beta

42

5.79% 4.65% 43 0.69% 0.43% b beta(1) 0.8

44 2.53% -0.19% beta(2) 45 3.11%

2.06% firm beta 1.0

46 0.

48

% 2.61% 47 -1.64% -2.04% c beta 48 2.81%

4.24% 49

-1.61% -1.97% Q4

a beta 50

8.53% 2.52% 51 4.67%

2.55%
b alpha 52

2.64% -0.06% 53

-1.23% -3.11% c

% sys 54 4.

56

% 6.13% 55

-2.19% -1.12% Q5

rf 2% 56

-5.19% 0.59% rM 6% 57

2.36% 1.36% SD[rM]

15%

58 -3.00% -1.53% beta 1 59

-1.92% 1.54% SD[rStock] 30%

60

-5.42% -6.04% a

SD[sys] b

SD[idio] c % sys
Q6 E1 2.00 b

40% beta 2.00
rf 2%
rM-rf

4%
a r
b

g

4%
i

V0 ii r
c P0

16.00 g
Q7 D1-D5

0
D6

1
g7-15

10%
g(perpetual)

3%
beta

1.00

rf 2%
rM-rf 4%

a r

b

V15 c

V5 d V0
Q8 Time

0 1 2 3 4

C

F

-100

0

70

0 70

beta

0.50

rf 2%
rM-rf 4%

a r

b

NPV

1
2
3
4
5

A

B

C
D

Finance for Executives – Problem Set #3

Name:
Robert Whitelaw

Q1

rf
2%
rM
6%

1

FINANCE FOR EXECUTIVES: PART

2

Professor Robert F. Whitelaw

e-mail: rwhitelaw@triumemba.org

Problem Set #3: The CAPM and Equity Valuation

This problem set is due on Monday, 28 February 2022, 23:55 (GMT). This problem set is an

individual assignment, and you should NOT consult or collaborate with your classmates in its

completion. However, feel free to email me if you have any questions. Please answer the

problems in Excel and submit the Excel spreadsheet. A template Excel file “Finance for

Executives – Problem Set #3” that contains the relevant data is provided for your convenience.

Please type your name in the blue highlighted cell at the top (my name is currently there) and put

your answers in the yellow highlighted cells that correspond to each question. These cells have

been formatted to display the correct number of decimal places. No rounding is necessary. You

can add additional calculations elsewhere in the spreadsheet, but please put your answers in the

highlighted cells.

Because your solutions will be computer-graded it is very important to follow the instructions:

• Please do NOT reformat the file or move the yellow cells. Do NOT add rows or columns
to the worksheet. However, you can add additional calculations in non-highlighted cells if

you wish. Everything in non-highlighted cells will be ignored for grading purposes. You

can either enter the formula to calculate your answer in the yellow cells, or enter these

formulas elsewhere and just put references to these answers in the yellow cells.

• Please do NOT round your answers or intermediate calculations. Excel will display
rounded answers based on the formatting of the cells, but it will retain the unrounded

numbers.

• Please do NOT add a new worksheet to the file. Do all of your calculations in the “Results”
worksheet and submit a file with only a single worksheet.

2

1. Assume the risk-free rate is 2% (rf = 2%), the expected return on the market portfolio is 6%
(rM = 6%) and the standard deviation of the return on the market portfolio is 15% (σM =

15%). (All numbers are annual.) Assume the CAPM holds. (1 point each)

a. What are the expected returns on securities with the following betas:
(i) β = 1.

4

(ii) β = 0.6

(iii) β = -0.2

b. What are the betas of securities with the following expect returns:
(i) 10%

(ii) 5%

(iii) -1%

c. What are the portfolio weights (in the risk-free asset and the market portfolio) for
efficient portfolios (portfolios on the efficient frontier/CML) with expected returns of

(i) 4%

(ii) 5%

(iii) 7%

d. What are the portfolio weights (in the risk-free asset and the market portfolio) for
efficient portfolios (portfolios on the efficient frontier/CML) with standard deviations of

(i) 6%

(ii) 15%

(iii) 21%

e. For a moment (but just a moment) assume that the CAPM may not hold. A non-dividend
paying stock has a current price of $50/share and an expected price in 1 year of $53/share

(based on your personal analysis of the company’s prospects).

(i) If the stock has a beta of 1 (β = 1.0), what is its alpha (α)?

(ii) What is the alpha (α) if the beta is 2 (β = 2.0)?

2. Assume that there are 3 firms in an industry for which you wish to compute an industry beta.
The betas of these 3 firms are 1.1, 1.2, and 1.4.

(2 points each)

a. What is the beta of an equal-weighted portfolio of the 3 firms?
b. If the market capitalizations of the 3 firms are $100 million (beta 1.1), $200 million (beta

1.2), $300 million (beta 1.4), what is the beta of a market capitalization, value-weighted

industry portfolio?

3. Consider a firm with two equally sized divisions (in terms of their value) that engage in
completely different lines of business with different risks. (2 points each)

a. If these 2 divisions have betas of 0.8 and 1.3, what is the beta of the firm?
b. If one division has a beta of 0.8, and the beta of the firm is 1.0, what is the beta of the

second division?

c. For the firm in part (b), what beta should be used to compute the cost of capital for the
low risk division, i.e., should it be the firm beta (1.0) or the divisional beta (0.8)?

3

4. The spreadsheet contains 60 months of monthly data on the excess returns on 3M (the maker
of Post-it Notes among many other things) and the US stock market. Run a linear regression

(SCL regression) of the returns on 3M on the returns on the market portfolio, using the

regression tool in Excel. (There is a video and associated Excel file illustrating how to do this

using data on Apple. Put the regression results elsewhere in the spreadsheet, and put

references to the cells with the correct answers in the highlighted cells.) (2 points each)

a. What is 3M’s beta from this regression?
b. What is 3M’s monthly alpha?
c. What percentage of 3M’s total risk (variance) is systematic?

5. Assume the risk-free rate is 2% (rf = 2%), the expected return on the market portfolio is 6%
(rM = 6%) and the standard deviation of the return on the market portfolio is 15% (σM =

15%). Assume the CAPM holds. A stock with a beta of 1 has a return standard deviation

(volatility) of 30%. (2 points each)

a. What is the standard deviation (volatility) of the systematic component of the stock’s
return?

b. What is the standard deviation (volatility) of the idiosyncratic component of the stock’s
return?

c. What percentage of the stock’s return variance is systematic?

6. XYZ Inc., an all equity company, has expected earnings over the next year of $2/share (E1 =
2). The company is expected to maintain an earnings retention rate of 40% (b = 0.4), i.e.,

60% of earnings are expected to be paid out as dividends every year. The company has an

equity beta of 2, the risk-free rate is 2% (rf = 2%), and the market risk premium is 4% (rM-rf =

4%). (2 points each)

a. What is the required return on XYZ’s equity?
b. If the growth rate in earnings is expected to be 4% in perpetuity

(i) What is the value of the stock?
(ii) What is the expected return over the next year?

c. If the current price of the stock is $16/share, what is the implied growth rate of earnings
(and dividends)?

7. XYZ Inc. is expected to pay no dividends for the next 5 years. However, at the end of the
sixth year (at time 6), the company is expected to pay a dividend of $1/share. Dividends are

expected to grow at 10% per year for the following 9 years (through the end of the 15th year,

i.e., time 15), then to grow at 3% every year thereafter (forever). The company has an equity

beta of 1, the risk-free rate is 2% (rf = 2%), and the market risk premium is 4% (rM-rf = 4%).

(2 points each)

a. What is the required return on XYZ’s equity?
b. What is the expected value of the stock at time 15 (not including the time 15 dividend)?
c. What is the expected value of the stock at time 5?
d. What is the value of the stock today?

4

8. XYZ Inc., an all equity company, is considering undertaking an average risk, 4-year project
with the following annual cash flows:

0 1 2 3 4

-100 0 70 0 70

The company has an equity beta of 0.5, the risk-free rate is 2% (rf = 2%), and the market risk

premium is 4% (rM-rf = 4%). (2 points each)

a. What is the required return on XYZ’s equity?
b. What is the net present value (NPV) of this project?