Question

FastTrack​ Bikes, Inc. is thinking of developing a new composite road bike. Development will take six years and the cost is $207,500 per year. Once in​ production, the bike is expected to make $290,728 per year for 10 years. The cash inflows begin at the end of year 7.

For parts​ a-c, assume the cost of capital is 9.7 %.

a. Calculate the NPV of this investment opportunity. Should the company make the​ investment?

b. Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

c. How long must development last to change the​ decision?

For parts​ d-f, assume the cost of capital is 14.9%.

d. Calculate the NPV of this investment opportunity. Should the company make the​ investment?

e. How much must this cost of capital estimate deviate to change the​ decision?

f. How long must development last to change the​ decision?

Answer 1

1.
=-207500/9.7%*(1-1/1.097^6)+290728/1.097^6*1/9.7%*(1-1/1.097^10)
=126661.485695

Make the investment

2.
-207500/x*(1-1/(1+x)^6)+290728/(1+x)^6*1/x*(1-1/(1+x)^10)=0
=>IRR=x=11.6265%

Maximum deviation=11.6265%-9.7%=1.92650%

3.
-207500/9.7%*(1-1/1.097^x)+290728/1.097^x*1/9.7%*(1-1/1.097^10)=0
=>x=6.621347

4.
NPV=-207500/14.9%*(1-1/1.149^6)+290728/1.149^6*1/14.9%*(1-1/1.149^10)
=-150866.410217

Do not make the investment

5.
-207500/x*(1-1/(1+x)^6)+290728/(1+x)^6*1/x*(1-1/(1+x)^10)=0
=>IRR=x=11.6265%

Maximum deviation=11.6265%-14.9%=-3.27350%

6.
-207500/14.9%*(1-1/1.149^x)+290728/1.149^x*1/14.9%*(1-1/1.149^10)=0

=>x=5.174448