Question

FastTrack​ Bikes, Inc. is thinking of developing a new composite road bike. Development will take six years and the cost is $198,000 per year. Once in​ production, the bike is expected to make $289,572 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 10.4%.

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 13.3%.

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.
If the cost of capital is 10.4%​, the NPV is ​
=-198000/10.4%*(1-1/1.104^6)+289572/10.4%*(1-1/1.104^10)*1/1.104^6
=113739.52

2.
Should the company make this​ investment? 
Accept the investment because the NPV is equal to or greater than zero ($0)

3.
The IRR is

-198000/x*(1-1/(1+x)^6)+289572/x*(1-1/(1+x)^10)*1/(1+x)^6=0

=>IRR=x=12.2740%

If the cost of capital is 10.4%​, the maximum deviation is

Maximum deviation=12.2740%-10.4%=1.8740%

4.
-198000/10.4%*(1-1/1.104^n)+289572/10.4%*(1-1/1.104^10)*1/1.104^n=0

=>n=6.586471

5.
If the cost of capital is 13.3%​, the NPV is

=-198000/13.3%*(1-1/1.133^6)+289572/13.3%*(1-1/1.133^10)*1/1.133^6
=-50960.30

6.
Reject the investment because the NPV is less than zero ($0)

7.
The IRR is

-198000/x*(1-1/(1+x)^6)+289572/x*(1-1/(1+x)^10)*1/(1+x)^6=0

=>IRR=x=12.2740%

If the cost of capital is 13.3%​, the maximum deviation is

Maximum deviation=12.2740%-13.3%=-1.0260%

8.
-198000/13.3%*(1-1/1.133^n)+289572/13.3%*(1-1/1.133^10)*1/1.133^n=0

=>n=5.721064