Question

______     1.      Assume a firm would like to borrow $125 from a bank to invest in a project with the following possible cash flows at time 1:

Probability	70% chance	30% chance
Project cash flows	$20	$250

The firm has no “assets-in-place,” and therefore will only be able to use the cash flows from the project (given above) to make payment on the loan. Assume the bank sets the interest rate on a one-year loan to this firm at 40%. Based on this 40% interest rate, what is the bank’s expected return on the loan?

______     2.      Assume a firm would like to borrow $900 from a bank for one year to invest in a project with the following possible cash flows at time 1:

Probability	40% chance	60% chance
Project cash flows	$375	$2000

The firm has no “assets-in-place,” and therefore will only be able to use the cash flows from the project (given above) to make payment on the loan. What interest rate will the bank need to charge on this one-year loan to earn an expected return of 7%?

Answer 1

1.

Given loan amount = P = CF0 = $125

Expected Value of Cash flow in Period 1 = CF1 = 0.70*20 + 0.30*250 = 89

Interest Rate r = 40%

NPV = -CF0 + CF1/(1+r) = -125 + 89/1.40 = -$61.42

=> Expected Return = -61.42/125 *100% = -49.14%

2.

Given CF0 = $900

Cash Flow in Year 1 CF1 = Σp_iC_i = 0.40*375 + 0.60*2000 = $1350

Let Interest rate = r

NPV = -CF0 + CF1/(1+r) = -900 + 1350/(1+r)

Expected Return = 7%

NPV required = 900*1.07 = 963

=> 963 = -900 + 1350/(1+r)

=> r = 0.38 or 38%