Assignment 2
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San Diego State University *
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Finance
Date
Apr 3, 2024
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1 STOCK VALUATION
1)
FM corporation earns a ROE of 12%. It reinvests one-half its earning and pays out the
other half as cash dividends. The cost of capital is 12%
(a) Given this ROE and dividend payout ratio, what is the growth rate of FM dividends?
-
Growth rate= ROE * Retention Ratio
-
0.12 * 0.5= 6%
-
Growth rate= 6%
(b) Assume this growth rate is expected to continue in perpetuity. What is the present value of
FM shares? Assume that book value per share is $10 and the first payment of dividends
happens at the end of the current year.
-
Share price= D1/r-g
-
D1= $10 X (1+0.06)= $10.60
-
Share price= $10.60/0.12-0.06= $176.76
(c) Suppose FM decides to pay out all its earnings as cash dividends. Therefore it does not
grow. What is the present value of FM shares?
-
Present value= $10
2. IF corporation expects to pay a dividend of $1 per share next year, which will grow at 10% for
the following 5 years. Afterwards, the growth becomes 2%. The cost of capital for FM is 8%.
What is today’s share price of FM?
-
Input into dividend growth calculator
-
21.74
3. Firm XYZ has two lines of business, organized as two divisions, A and B. Division A
generates a risk-free cash flow. It will produce $2 million in free cash flow next year and it will
grow at 2% each year thereafter forever. The second line of business, run by Division B, is risky.
It expects to generate a cash flow of $2 million next year and will grow at a rate of 4%. Currently,
the total market value of XYZ is $87 million. The risk-free rate is 5%. What is the cost of capital
for the second line of business?
-
Cost of Capital (K) = Risk-Free Rate (Rf) + Beta (B) * (Market Risk Premium)
-
Rf= 5%, B= 1.2, Market Risk Premium= 5%
-
5% + 1.2*5%= 11
-
Cost of capital= 11%
2 Capital Budgeting
1. Table 1 gives investments, NPVs, IRRs and the first three years’ cash flow for several capital
investment projects. The cost of capital is 12% for all projects. Project A and B are mutually
exclusive. The projects are discrete – you cannot make partial investments in any project.
(a) Suppose the firm rejects all projects with payback periods greater than 3 years. What is the
NPV from following this policy
-
Cash flows of projects C and F are higher than the investment amount, so we will use
these values and add them to solve for NPV.
-
NPV= 41+5.5= 46.5
(b) Which project would you choose, A or B?
-
Both projects are profitable but they are mutually exclusive so only one can be
accepted. Since they are both profitable you can choose either one.
(c) Suppose the firm has only $200 million to invest – a fixed capital constraint. Which projects
would you undertake?
-
I would pick the projects with the best cash flows so in this case, C and F.
3 Risk and Return
1. What is the beta of a portfolio with the expected return of 18%, if the risk-free rate is 6% and
the risk premium of the market portfolio is 8%?
-
CAPM= Rf + B(Rm-Rf)
-
18 = 6 + B(8)
-
8B = 12
-
Beta = 1.5
2. Assume that the risk-free rate of interest is 6% and the expected rate of return on the market
is 16%. A share of stock sells for $50 today. It will pay a dividend of $6 per share at the end of
the year. Its beta is 1.2. What do investors expect the stock to sell for at the end of the year?
-
Expected return = risk free rate+beta*(market rate-risk free rate)
-
6+(16-6)*1.2
-
18% = Expected return
-
Expected return=(D1/Current price)+Growth rate
-
0.18=(6/50)+Growth rate
-
Growth Rate= 0.18 - (6/50)
-
6%
-
Expected price = Current price*(1+Growth rate)
-
50 * 1.06
-
$53
3. Assume that the risk-free rate of interest is 6% and the expected rate of return on the market
is 16%. A stock has an expected rate of return of 4%. What is its beta? Why would anyone
consider buying this risky asset which provides an expected return less than the risk-free rate?
-
Expected Return=
-
0.04 = 0.06 + beta(0.16 - 0.06)
-
0.04 = 0.06 + beta(0.10)
-
-0.02 = beta(.10)
-
Beta = -0.2
4. The rate of return on short-term government securities (perceived to be risk-free) was about
5%. Suppose the expected rate of return required by the market for a portfolio with a beta
measure of 1 is 12%. According to the capital asset pricing model:
(a) What is the expected rate of return on the market portfolio?
-
Rf = 5%
-
Rm = 12%
-
Beta = 1
-
Expected Return = 5 + 1(12-5)
-
12%
(b) What would be the expected rate of return on a stock with b = 0?
-
5 + 0(12-5)
-
5%
(c) Suppose you consider buying a share of stock at $40. The stock is expected to pay $3
dividends next year and you expect it to sell then for $41. The stock risk has been evaluated by
b = −0.5. Is the stock overpriced or underpriced?
-
The stock is underpriced because it’s valued at $40 and is expected to rise
-
Rf + Beta (Rm - Rf)
-
= 5 + [ - 0.5 ( 12 - 5) ]
-
= 5 + (- 0.5 x 7 )
-
= 5 - 3.5
-
Cost of capital = 1.5%
-
PV = 3/1.015 + 41/1.015= 43.35
-
$40 is underpriced because the actual value should be 43.35
5. If we regress the stocks’ average return on their betas, what should be the slope and the
intercept according to the CAPM?
-
the slope of the regression line should be the market risk premium.
-
The intercept of this regression should be the risk-free rate.
6. If we regress a stock’s returns on returns of the market portfolio, what should be the slope
according to the CAPM?
-
the slope of the regression line should be the stock's beta
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