Question

FastTrack Bikes, Inc. is thinking of developing a new composite road bike. Development will take six years and the cost is $200,000 per year. Once in production, the bike is expected to make $300,000 (after expenses) per year for 10 years. The cash inflows begin at the end of year 7.

At FastTrack, there is a difference of opinion as to the "best" decision rule to use. The four rules under consideration are NPV, IRR, Payback Period and Profitability Index (PI).                         

Additional Info: The firm's president has set a maximum acceptable payback period of 8 years for projects and the cost of capital appropriate for this project is 10%.

Using the end of year cash flows as shown in the table (see below), answer each of the following:

Year	Cash Flows
0	$0
1	-$200,000
2	-$200,000
3	-$200,000
4	-$200,000
5	-$200,000
6	-$200,000
7	$300,000
8	$300,000
9	$300,000
10	$300,000
11	$300,000
12	$300,000
13	$300,000
14	$300,000
15	$300,000
16	$300,000

1a        What is the NPV of the project if the firm's cost of capital is 10%?

1b        Should the project be accepted or rejected based on NPV and why?

Note that while at first you may think that IRR isn't appropriate, note that there is only one sign change, when the cash flows go from negative 200,000 to positive 300,000. This means there is only 1 sign change and 1 IRR.                                        

2a        What is the IRR of the project?

2b        Should the project be accepted or rejected based on IRR and why?

3a        What is the Payback period of the project?   

3b        Should the project be accepted or rejected based on Payback and why?   

4a        What is the profitability index or PI of the project?   

4b       Should the project be accepted or rejected based on PI and why?

5         If the firm's required rate of return increased, what would be the impact on each of the values?                                                    

5a Effect on NPV and why:                                                        

5b Effect on IRR and why:                                                          

5c Effect on Payback period and why:                                                    

5d Effect on PI and why:                                                 

Answer 1

1]

a]

NPV is the sum of the present values of cash flows. Present value = cash flow / (1 + discount rate)^year

At 10% cost of capital, NPV is $169,482

b]

The project should be accepted as the NPV is postiive

2]

a]

IRR is 12.66%

b]

Project should be accepted as the IRR is higher than the cost of capital