Question

Question 1

(a)         Suppose that you can invest with a continuously compounded rate of 5.25% per annum.

(i)           If you invest $50,000 today, how many years will it take for your investment to be worth $1 million?

(ii)         If you want your investment to grow to be $1 million in 10 years, how much do you need to invest today?

(iii)        Compute the equivalent effective 1-year rate.

(b)            Consider two stocks, Stock A and Stock B, where the CAPM betas of the Stock A and Stock B are 1.3 and 0.86, respectively. The cost-of-capitals of Stock A and Stock B are 19.25% and 13.75%, respectively. Find the risk-free rate and the expected return on the market portfolio.

Answer 1

1 a.i) PV =50000
FV =1000000
FV =PV*e^(r*t)
1000000=50000*e^(5.25%*t)
20=e^(5.25%*t)
Applying log on both sides
t =ln(20)/5.25% =57.06 years

ii). FV =1000000
Time =10 years
PV =FV/e^(R*t) =1000000/e^(5.25%*10) =591555.36

iii. Effective Rate=e^(rt)-1 =e^(5.25%*1)-1 =5.39%

b. Cost of Equity =Risk free Rate+Beta*(Market Return-Risk free Rate)
19.25% =Rf+1.3*(Rm-Rf)
13.75% =Rf+0.86*(Rm-Rf)
Subtracting both equations
5.5% =0.44*(Rm-Rf)
Rm-Rf =5.5%/0.44 =12.5%

19.25% =Rf+1.3*(Rm-Rf)
19.25% =Risk free Rate+1.3*12.5%
Risk free Rate =19.25%-1.3*12.5% =3%
Expected Return =12.5%+3% =15.5%