1. Company JJ gives you the following information for its operation. The expected net income is $28 million next year. Suppose there is 20% income tax imposed on the company. There are 5 million shares of common stocks outstanding. Let the current market price for the stock be $51 per share. Suppose that there is no expansion plan for the company to either spend on working capital vs. long-term investment or to apply the accumulated retained earnings. Answer the following questions:
a) Suppose that Company JJ wants to issue some 15-year coupon bonds issued. The bond carries 6% coupon with $1,000 par value, paid semiannually. Let the current bond price be $860 per bond, what is the yield to maturity for this bond? What are the assumptions you make here? Is there any limitation for this model?
YIELD TO MATURITY (YTM)
=INTEREST (1-TAX) + (MV-BO) / N) / (MV + BO) /2
WHERE INTEREST = 1000 * 6% / 2 =30
TAX RATE = 20%
MV = MATURITY VALUE = 1000
LET ASSUME BOND MATURE AT PAR VALUE
BO=CURRENT PRICE = 860
N = NUMBER OF YEARS = 15 YEARS * 2 =30
YTM= (30 (1-0.20) + (1000-860)/30] + (1000 + 860) / 2
= 28.67 / 930
= 3.08 %
b) Let Company JJ’s total debts on coupon bond be $15 million in market value with the coupon rate given in a). How much will be the value of stockholders’ equities under Modigliani and Miller’s Proposition 2?
USING MM APPROACH
PO = P1 + D1 / (1+K)
WHERE PO = LAST PRICE
P1 = CURRENT PRICE
51=P1+5.6/ (1+0.107)
P1=50.857 PER SHARE
VALUE OF EQUITY=50.857 * 5 MILLION SHARES =254.285 MILLION
c) What is the cost of equity for Company JJ, if there’s no preferred stock issued for this company?
COST OF EQUITY = DPS/MPS
TOTAL EARNING =28MILLION
EPS = 28MILLION / 5 MILLION
= 5.6 PER SHARE
CONSIDERING WHOLE EARNING IS DISTRIBUTED AS DIVIDEND-
COST OF EQUITY = 5.6 / 51
= 10.98%
d) What is the “beta” of the firm’s stock after debt if the risk-free rate is 2% and the market index rate of return is 15%? What is the weighted average cost of capital after debt? Show your work!
VALUE OF EQUITY = 5 MILLION * 51 = 255 MILLION
VALUE OF DEBT = 15 MILLION
TOTAL VALUE = 255 + 15 = 270
WACC=WE * KE + WD * KD = 255 /270 8 10.98% + 15/270 * 6% =10.7%
NOW K = RF +B (RM-RF)
10.7= 2+B (15-2)
B OR BETA = 0.67
e) What is the emphasis of the M&M Proposition 1?
THAT THE FIRMS CAPITAL STRUCTURE DOES NOT AFFECT ITS VALUE.
2. You are given with the following information about 4 asset returns in Table 1. The (subjective) probability distribution is shown that the asset returns may result from different states of the economy. For instance, Ra represents the rate of return of Asset a. Answer the following questions.
a) Is this probability distribution well-defined? If not, when is it well-defined? What is the difference between “risk” and “uncertainty”? Why do we need the definition of risk in determining the asset returns?
Yes, the table shows the possible outcomes of probability for the different states the economy can be in.
b) Does this probability distribution determine the investors’ expectations? Why or why not?
Yes. This table shows the rate of return for the investors depending on which state the economy is in.
c) Explain the reasons why we can apply these statistics for representations as risk.
This representation shows the probable rate of return during the different stages of the economy. These statistics are helpful in determining risk for investors.
d) Can we directly apply these expected rates of return for asset pricing such as using these rates as the discount rates for the expected cash flows in holding these assets? Why or why not?
No. These figures are only predictions and not an accurate representation of the outcomes given specific variables.
e) Suppose that you are given with the following data:
What are the required rates of return for these assets according to CAPM, where E(Rm)=12%, risk-free rate is 3%? Why do you call them the required rates of returns?
Table 1:
States of the economy
Probability
Ra
Rb
Rc
Rd
Recession
1/6
-30%
-25%
15%
2%
Recovery
1/3
12%
6%
6%
2%
Boom
?
60%
30%
15%
2%
