Question

FastTrack Bikes, Inc. is thinking of developing a new composite road bike. Development will take six years and the costs is $196,200 per year. Once in production, the bike is expected to make $293,055 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 10.7%

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 13.9%

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

(a)

Tenure of Development = 6 Years

Total accumulated development cost at the end of Year 6 **=$200000*1.107^5+$200000*1.107^4+$200,000*1.107^3+$200000*1.107^2+$200000*1.107+ $200000 = $1,570631

Total expected income as Present Value at the year 6 for the expected income for next 10 years

=$300000/1.107^10+ $300000/1.107^9+ $300000/1.107^8+ $300000/1.107^7+$300000/1.107^6+ $300000/1.107^5+ $300000/1.107^4+ $300,000/1.107^3 + $300000/1.107^2+ $300000/1.107^1

=$1,843370

NPV at the end of Year 6 = Value of expected income at Year 6 - Value of expected cost at Year 6 =$1,843370- $1,570631 = $272739

NPV at Year 0 = $272739/1.107^6 = $148227

(B)

IRR is the discount rate where the NPV of the Project will be = Zero, of Present Value of the Cost = Present value of the income

If R is the discount rate, then,

Present Value of income at year 6 =$300000/(1+ R)^10+ $300000/(1+ R)^9+ $300000/(1+ R)^8+ $300000/(1+ R)^7+$300000/(1+ R)^6+ $300000/(1+ R)^5+ $300000/(1+ R)^4+ $300000/(1+ R)^3 + $300000/(1+ R)^2+ $300000/(1+ R)^1 ................................................(1)

Similarly Future value of the cost at Year 6 = $200000*(1+ R)^5+$200000*(1+ R)^4+$200000*(1+ R)^3+$200000*(1+ R)^2+$200000*(1+ R)+ $200000....................................................(2)

as per the condition (1) = (2)

solving for R in the equation (1) = (2) we get,

R = 12.17%

(C)

We consider the development will last for n Years

Total accumulated development cost at the end of Year n

FV = ($200000/10.70%)*(1.107^n -1)

But this cost will be at least equal to the expected income at year 6

So, ($200,000/10.70%)*(1.107^n -1) = $1,843370

So, (1.107^n -1)= $1,843370/{($200,000/10.70%)} = 0.9862

So, 1.107^n = 0.9862 +1 = 1.9862

Considering the logarithmic values, n = Log (1.9862)/ Log (1.107)= 6.75 years

So the development tenure should be at least 7 Years (rounding off next year) to change the decision.

(d)

Present Value of Income at year 6 =$300000/1.139^10+ $300000/1.139^9+ $300000/1.139^8+ $300000/1.139^7+$300000/1.139^6+ $300000/1.139^5+ $300000/1.139^4+ $300000/1.139^3 + $300000/1.139^2+ $300000/1.139^1 = $1,570960

Similarly Future value of the cost at Year 6 = $200000*(1.139)^5+$200000*(1.139)^4+$200000*(1.139)^3+$200000*(1.139)^2+$200,000*(1.139)+ $200,000 = $1702799

NPV at year 6 = $1,570960- $1,702799 = -$131839

NPV at Year 0 = -$131839/1.139^6 = -$60381

(e)

The cost of capital must he lower from the IRR of the project.

So the cost of capital must deviate for 13.9% - 12.17% = 1.73%

(f)

We consider the development will last for N years

We consider the development will last for n Years

Total accumulated development cost at the end of Year n

FV = ($200000/13.90%)*(1.139^n -1)

But this cost will be at least equal to the expected income at year 6

So, ($200,000/13.90%)*(1.139^n -1) = $1,570960

So, (1.139^n -1)= $1,570960/{($200,000/13.90%)} = 1.0919

So, 1.139^n = 1.0919+1 = 2.0919

Considering the logarithmic values, n = Log (2.0919)/ Log (1.139)= 5.67

So the development tenure should be maximum 6 Years (rounding off next year) to change the decision.