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

safe project cash inflow = $ 120

risky project cash inflow = 0.5*$124 + 0.5*$94 = $ 62 + $ 47 = $ 109

investment = $ 100

risk free rate = 5%

return on safe project = ($ 120 - $100) / $ 100 = $20 / $100 = 0.2 = 20%

return on risky project = ($ 109 - $100) / $ 100 = $ 9 / $100 = 0.09 = 9%

A) So, Guerin can obtain a $100 loan to be repaid next year to finance the project at the risk-free rate

B) NPV (safe project) = $120/1.15 - $100 = $104.348 - $100 = $ 4.348 ( ACCEPATABLE)

NPV (RISKY project) = $109/1.15 - $100 = $94.783 - $100 = -$ 5.271 (REJECTED)

C) NPV (safe project) = $120/1.17 - $100 = $102.564 - $100 = $ 2.564 ( ACCEPATABLE)

NPV (RISKY project) = $109/1.17 - $100 = $93.162 - $100 = -$ 6.838 (REJECTED)

D) IF BANK HAS MONOPOLY, AMONG B AND C OPTIONS, BANK WOULD CHOOSE TO OPT FOR 17% INTEREST ON THE LOAN AS THE BANK GETS TWO PERCENT EXTRA WITH AN ACCEPTABLE PROJECT i.e. Safe production techniques.