Question

34. Spacely Sprockets is considering investing in a new sprocket factory. A new sprocket factory requires an immediate payment $200 million. However, at the end of 20 years the sprocket factory will yield $600 million.

Part 1: Assume the prevailing interest rate is 5%. Should Spacely Sprockets invest in the new sprocket factory? Show your work and explain your answer.

Part 2: Assume the prevailing interest rate is 7%. Should Spacely Sprockets invest in the new sprocket factory? Show your work and explain your answer

Answer 1

Cost of new sprocket factory=PV=$200 million

Expected value of sprocket factory=P=$600 million

Number of years=i=20

Let interest rate be i

FV=PV*(1+i)^n

Part 1

Given i=5%

FV=200*(1+0.05)²⁰=$530.66 million

Expected value of sprocket factory is higher than the FV at 5% interest rate. So, it is advisable to invest.

Part 2

Given i=7%

FV=200*(1+0.07)²⁰=$773.94 million

Expected value of sprocket factory is less than the FV at 7% interest rate. So, it is not advisable to invest.