Math Problem Statement

astTrack​ Bikes, Inc. is thinking of developing a new composite road bike. Development will take

66

years and the cost is

$ 182 comma 000$182,000

per year. Once in​ production, the bike is expected to make

​$273 comma 000273,000

per year for

1010

years. Assume the cost of capital is

9 %9%.

a. Calculate the NPV of this investment​ opportunity, assuming all cash flows occur at the end of each year. Should the company make the​ investment?

b. By how much must the cost of capital estimate deviate to change the​ decision?**

​(Hint​:

Use Excel to calculate the​ IRR.)

c. What is the NPV of the investment if the cost of capital is

14 %14%​?

Note​:

Assume that all cash flows occur at the end of the appropriate year and that the inflows do not start until year

Question content area bottom

Part 1

a. Calculate the NPV of this investment​ opportunity, assuming all cash flows occur at the end of each year. Should the company make the​ investment?

The present value of the costs is

​$816,437.18816,437.18.

​ (Round to the nearest​ dollar.)

Part 2

The present value of the benefits is

​$1,044,6731,044,673.

​(Round to the nearest​ dollar.)

Part 3

The NPV of the investment opportunity is

​$228,236228,236.

​(Round to the nearest​ dollar.)

Part 4

You should

accept

the investment because the NPV is

positive

.

​(Select from the​ drop-down menus.)

Part 5

b. By how much must the cost of capital estimate deviate to change the​ decision?

​(Hint​:

Use Excel to calculate the​ IRR.)

The IRR of the investment opportunity is

enter your response here​%.

​ (Round to two decimal​ places.)

Solution

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Math Problem Analysis

Mathematical Concepts

Net Present Value (NPV)
Internal Rate of Return (IRR)
Time Value of Money
Discount Rate

Formulas

NPV = (Present Value of Benefits) - (Present Value of Costs)
IRR is the discount rate where NPV = 0
Present Value formula: PV = CF / (1 + r)^n

Theorems

Net Present Value (NPV) Theorem
Internal Rate of Return (IRR) Theorem

Suitable Grade Level

Undergraduate Business/Finance