Question

Bill Guerin, an entrepreneur, has a project available for investment with two pro-duction techniques, Safe and Risky, both requiring an initial investment of $100. Next year, the Safe technique provides a payoff of $120 with certainty, and the Risky technique pays $124 if successful, but only $94 if unsuccessful, where the risk-neutral probability of success is ½. The risk-free rate is 5%.

Can Guerin obtain a $100 loan to be repaid next year to finance the project at the risk-free rate?

What is the NPV for the bank if it charges 15% interest on the loan?

What is the NPV for the bank if it charges 17% interest on the loan?

(1 mark) Suppose the bank has a monopoly on providing financing. Discuss how parts b) and c) relate to the bank’s decision about what interest rate to charge.

Answer 1

pay off or cash inflow available from safe technique= $120

pay off or cashflow available from risky technique (using expected value) is 124x 0.50 + 94 x 0.50   = $109

answer 1

payment of $100 as principal + interest of 5% of $100 that is $5 = 100 + 5= $105 is the loan repayment to be made

Yes .Guerin can obtain the loan since his repayment amount is less than the cash inflows he can get whether he chooses the safe technique or risky technique

answer 2

NPV FOR THE BANK

estimated cash recovery/inflows for the bank = principal of $100 + interest $15= $115 which is the future value after 1 year

we discount this future value using present value interest factor at 5% for 1 yr which is 0.952

present value of cash inflows for the bank = 115x 0.952= 109.48

So NPV of loan = present value of cash inflows - present value of cash outflows

= 109.48-100 = $9.48

answer 3

estimated cash recovery or inflows for the vank = $100 +$17= $117

present value of cash inflows at 5% discount rate = 117x 0.952= $111.38

NPV = 111.38-100= $11.38

answer 4

since NPV is higher at 17% interest rate , bank will charge 17% , if it has a monopoly on providing financing