Question

FastTrack​ Bikes, Inc. is thinking of developing a new composite road bike. Development will take six years and the cost is $198,100 per year. Once in​ production, the bike is expected to make $301,477 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 9.9%.

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 14.6%.

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?

a. Calculate the NPV of this investment opportunity.

If the cost of capital is 9.9%​, the NPV is $ ___ . (Round to the nearest​ dollar.)

Should the company make this​ investment?  ​(Select the best choice​ below.)

A. Accept the investment because the NPV is equal to or less than zero​ ($0).

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

C. Accept the investment because the NPV is equal to or greater than zero ($0).

D. Reject the investment because the NPV is equal to or greater than zero​ ($0).

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

The IRR is ___ ​%. (Round to two decimal​ places.)

If the cost of capital is 9.9%​, the maximum deviation is ___ ​%. (Round to two decimal​ places.)

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

For the decision to​ change, development must last ___ years, or longer. ​ (Round to two decimal​ places.)

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

If the cost of capital is 14.6%​, the NPV is $ ___ . (Round to the nearest​ dollar.)

Should the company make the​ investment?  ​(Select the best choice​ below.)

A. Accept the investment because the NPV is equal to or greater than zero ($0)

B. Accept the investment because the NPV is equal to or less than zero​ ($0).

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

D. Reject the investment because the NPV is equal to or greater than zero​ ($0).

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

The maximum deviation is __ ​%. (Round to two decimal​ places.)

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

For the decision to​ change, development must last no longer than __ years

Answer 1

a.NPV of this investment opportunity

-(198100*4.36085)+(301477*(7.87051-4.36805))=

192027

P/A,198100,6 yrs.,9.9%=4.36805

P/A,301477,16 yrs.,9.9%=7.87051

Yes. The company should make this invetsment as the NPV is POSITIVE.

If the cost of capital is 9.9%​, the NPV is $ 192027

C. Accept the investment because the NPV is equal to or greater than zero ($0).

b.IRR

Seting the NPV to 0,we get the IRR as,

0=-(198100*(1-(1+r)^-6)/r))+(301477*((1-(1+r)^-16)/r)-(1-(1+r)^-6)/r)))

Solving for r,

IRR= 12.88%

So, the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged

is

12.88%-9.9%=

2.98%

or 3%

The IRR is 12.88 ​%

If the cost of capital is 9.9%​, the maximum deviation is 2.98%

d.NPV of this investment opportunity

-(198100*3.82561)+(301477*(6.07450-3.82561))=

-79865

P/A,198100,6 yrs.,14.6%=3.82561

P/A,301477,16 yrs.,14.6%=6.07540

No. The company should make this invetsment as the NPV is NEGATIVE.

If the cost of capital is 14.6%​, the NPV is $ -79865

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

b.IRR

Seting the NPV to 0,we get the IRR as,

0=-(198100*(1-(1+r)^-6)/r))+(301477*((1-(1+r)^-16)/r)-(1-(1+r)^-6)/r)))

Solving for r,

IRR= 12.88%

So, the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged

is

12.88%-14.6%=

-1.72%

or -2%

The maximum deviation is -1.72%