Question 1
Multiple ChoiceA USD40 million equity portfolio is financed 25 percent with debt at a cost of 5 percent annually. If the total portfolio generates a 9 percent return, the leveraged return is closest to:
Explanation
To calculate the leveraged return, use the formula:
R_{L}=R_{p}+(\frac{V_{D}}{V_{E}})(R_{p}-R_{D})
Where:
R_{L} = leveraged return
R_{p} = return on the portfolio = 9%
R_{D}= cost of debt = 5%
V_{D} = value of debt = 25% of USD40 million = USD10 million
V_{E} = value of equity = 75% of USD40 million = USD30 million.
R_{L}=0.09+(\frac{10}{30})(0.09-0.05)
Question 2
Multiple ChoiceAt the beginning of the year, an investor allocates USD15,000 to a hedge fund investment. To finance this, she borrows 30 percent of the purchase price at an annual interest rate of 5%. She expects to pay a 25% tax on the return earned. At year-end, the hedge fund reports the following:
Hedge Fund Performance
Metric | Value
Gross return | 9.10%
Trading expenses | 1.20%
Managerial & administrative fees | 1.80%
The investor’s after-tax return on the hedge fund investment is closest to:
Explanation
Step 1: Compute net return on the investment (excluding trading costs, already in gross)
Net return = 9.10% − 1.80% = 7.30%
Step 2: Compute leveraged return
Investor borrows 30% = USD4,500
Equity = USD10,500
R_{L}=0.73+(\frac{4,500}{10,500})(0.73-0.05) = 8.29%
Step 3: Compute after-tax return
Now apply the investor’s 25% tax rate to the leveraged return of 8.29%:
After-tax return = 8.29% × (1 − 0.25) =8.29% ×0.75 = 6.2175%