In: Accounting
(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.
(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.
a) | ||
1) | ||
Present Value | 50,000.00 | |
Future Value | 1,000,000.00 | |
Rate | 5.25% | |
PMT | 0.00% | |
Period | 58.55 | Years |
2) | ||
Future Value | 1,000,000.00 | |
Rate | 5.25% | |
Period | 10.00 | |
PMT | 0.00 | |
Present Value | $599,485.88 | |
c) | ||
Nominal Interest | 5.25% | |
Compounding (annual) | 1 | |
Effective Interest | 5.250% | |
b) | ||
A | B | |
Beta | 1.3 | 0.86 |
Cost of equity | 19.25% | 13.75% |
Cost of equity = Rf + Beta x (Rm -Rf) | ||
Putting numbers in the above equation subtracting eq 2 from eq 1 | ||
19.25% = Rf + 1.3 x (Rm - Rf) | ||
13.75% = Rf + .86 x (Rm - Rf) | ||
risk-free rate be X and the expected return on the market be Y | ||
5.50% =0 + .44 x (Rm - Rf) | ||
By solving this | ||
Rm-rf = 5.50%/.44 | 12.50% | |
19.25% = Rf + 1.3 x 12.50% | ||
Rf = | 3% | |
Rm= 12.50% + 3% | 15.500% | |