Question

Assume you are 35 years old, and have salary of $65,000 per year. you are in search of a good investment that can cover future goals which include a car, emergency fund, and child education. you want invest 30% of annual salary for the purpose of investment. For this, you making an investment of 30% in equity, 70% in Debt. The return on Debt is 15%. The risk-free return is 4%, the beta of the market is 1.25, and the market return is 11%. What will be the E(R) of the stock using CAPM? If you wants an investment return of $100,000 at the age of 65 what will be the yearly investment you needs to make? Calculate the WACC.

Answer 1

1)

Using CAPM Formula, Expected return of the stock, E(R) = R_f + β X (R_m - R_f)

Risk free return, R_f = 4%

Market return, Rm= 11%

Beta of the market, β = 1.25

E(R) = 4% + 1.25 X (11%-4%)

= 4% + 1.25 X 7%

= 4% + 8.75%

= 12.75%

2)

Let Y be the annual investment to be made

Investment in Equity = 30% of Y = 0.3Y

Investment in Debt = 70% of Y = 0.7Y

Investment Period = 30 years

The future value of investments can be calculated using the FV formula in spreadsheet

FV(rate, number of periods, payment amount, present value, when-due)

Where, rate = annual return

number of periods = 30

payment amount = yearly investment

present value = present value of investments = 0

when-due = when is the investment made each year = beginning = 1

In the formula the payment amount is taken as 0.3 instead of 0.3Y

FV for Equity Investments = FV(12.75%, 30,0.3, 0,1) = 94.45Y

In the formula the payment amount is taken as 0.7 instead of 0.7Y

FV for Debt Investments = FV(15%, 30,0.7, 0,1) = 349.97Y

Total Investment Value after 30 years = FV of Equity + Fv of Debt = 94.45Y + 349.97Y = 444.42Y

This is equal to $100,000

Implies, 444.42Y = $100,000

Y = 100,000/444.42 = $225.01

Hence a yearly investment of $225.01 has to be made

3)

Assuming zero tax,

WACC = Weight of Equity X R_e + Weight of Debt X R_d

Where R_e = return for equity and R_d = return for debt

implies, WACC = 0.3 X 12.75% + 0.7 X 15% = 3.825% + 10.50% = 14.325%