A new business opportunity has a 70% chance of being worth $500,000 next year and a 30% chance of being worth $100,000. The appropriate expected rate of return is 10%.
-Refer to the information above. Assume that the new opportunity will be financed with a $150,000 bank loan. What rate of return will the levered equity holder earn if the business
Pays off $500,000 in one year?
A)57.1%
B)52.2%
C)45.7%
D)13.6%

Question

Quizplus · Accepted Answer

The levered equity holder will earn a return equal to the internal rate of return (IRR) of the investment, which takes into account the cash flows from both the equity and the debt financing.

To calculate the levered return, we need to first determine the cash flows to equity:

- If the business is worth $500,000 in one year, the equity holders will receive $500,000 - $150,000 (repayment of the loan) = $350,000
- If the business is worth $100,000 in one year, the equity holders will receive $100,000 - $150,000 (repayment of the loan) = -$50,000 (i.e. a loss)

The expected cash flow to equity is therefore: 
Expected cash flow = 0.7 * $350,000 + 0.3 * (-$50,000)
Expected cash flow = $235,000

Now we can calculate the levered return using the IRR function in Excel or a financial calculator:

- PV = -$150,000 (investment)
- FV = $235,000 (expected cash flow)
- N = 1 (one year)
- CPT IRR = 57.1%

Therefore, the levered equity holder will earn a return of 57.1%.

A New Business Opportunity Has a 70% Chance of Being