Question

In: Accounting

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

(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.

Solutions

Expert Solution

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%


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