Stephenson

Week 3 Homework questions – Solutions

Chapter 5

1. a. The payback period is the time that it takes for the cumulative undiscounted cash inflows to equal the initial investment.

Project A:

Cumulative cash flows Year 1 = $9,500 = $9,500

Cumulative cash flows Year 2 = $9,500 + 6,000 = $15,500

Companies can calculate a more precise value using fractional years. To calculate the fractional payback period, find the fraction of year 2’s cash flows that is needed for the company to have cumulative undiscounted cash flows of $15,000. Divide the difference between the initial investment and the cumulative undiscounted cash flows as of year 1 by the undiscounted cash flow of year 2.

Payback period = 1 + ($15,000 – 9,500) / $6,000

Payback period = 1.917 years

Project B:

Cumulative cash flows Year 1 = $10,500 = $10,500

Cumulative cash flows Year 2 = $10,500 + 7,000 = $17,500

Cumulative cash flows Year 3 = $10,500 + 7,000 + 6,000 = $23,500

To calculate the fractional payback period, find the fraction of year 3’s cash flows that is needed for the company to have cumulative undiscounted cash flows of $18,000. Divide the difference between the initial investment and the cumulative undiscounted cash flows as of year 2 by the undiscounted cash flow of year 3.

Payback period = 2 + ($18,000 – 10,500 – 7,000) / $6,000

Payback period = 2.083 years

Since project A has a shorter payback period than project B has, the company should choose project A.

b. Discount each project’s cash flows at 15 percent. Choose the project with the highest NPV.

Project A:

NPV = –$15,000 + $9,500 / 1.15 + $6,000 / 1.152 + $2,400 / 1.153

NPV = –$624.23

Project B:

NPV = –$18,000 + $10,500 / 1.15 + $7,000 / 1.152 + $6,000 / 1.153

NPV = $368.54

The firm should choose Project B since it has a higher NPV than Project A has.

2. To calculate the payback period, we need to find the time...