Question

P10-21 (similar to)

All​ techniques, conflicting rankings   Nicholson Roofing​ Materials, Inc., is considering two mutually exclusive​ projects, each with an initial investment of

​$150,000.

The​ company's board of directors has set a​ 4-year payback requirement and has set its cost of capital at

7​%.

The cash inflows associated with the two projects are shown in the following​ table:

LOADING...

.

a. Calculate the payback period for each project. Rank the projects by payback period.

b.  Calculate the NPV of each project. Rank the project by NPV.

c.  Calculate the IRR of each project. Rank the project by IRR.

d.  Make a recommendation.

a.  The payback period of project A is

nothing

years. 

Cash inflows ​(CFt​)
Year	Project A		Project B
1	​$50,000		​$65,000
2	​$50,000		​$60,000
3	​$50,000		​$40,000
4	​$50,000		​$40,000
5	​$50,000		​$40,000
6	​$50,000		​$40,000

Answer 1

a)

Payback period:

Project A:

Payback period of project A = Initial investment / cash flow

Payback period of project A = 150,000 / 50,000

Payback period of project A = 3.00 years

Project B:

Cumulative cash flow for year 0 = -150,000

Cumulative cash flow for year 1 = -150,000 + 65,000 = -85,000

Cumulative cash flow for year 2 = -85,000 + 60,000 = -25,000

Cumulative cash flow for year 3 = -25,000 + 40,000 = 15,000

25,000 /  40,000 = 0.63

Payback period of project B = 2 + 0.63 = 2.63 years

Project B has a better payback period

b)

NPV:

Project A:

NPV = Present value of cash inflows - present value of cash outflows

NPV = Annuity * [1 - 1 / (1 + r)ⁿ] / r - Initial investment

NPV = 50,000 * [1 - 1 / (1 + 0.07)⁶] / 0.07 - 150,000

NPV = 50,000 * [1 - 0.666342] / 0.07 - 150,000

NPV = 50,000 * 4.76654 - 150,000

NPV = $88,326.98

Project B:

NPV = Present value of cash inflows - present value of cash outflows

NPV = -150,000 + 65,000 / (1 + 0.07)¹ + 60,000 / (1 + 0.07)² + 40,000 / (1 + 0.07)³ + 40,000 / (1 + 0.07)⁴ + 40,000 / (1 + 0.07)⁵ + 40,000 / (1 + 0.07)⁶

NPV = $81,494.85

Project A has a higher NPV

c)

IRR:

Project A:

IRR is the rate of return that makes NPV equal to 0:

NPV = 50,000 * [1 - 1 / (1 + R)⁶] / R - 150,000

Using trial and error method, i.e., after trying various values for R, lets try R as 24.29%

NPV = 50,000 * [1 - 1 / (1 + 0.2429)⁶] / 0.2429 - 150,000

NPV = 50,000 * [1 - 0.271258] / 0.2429 - 150,000

NPV = 50,000 * 3.000172 - 150,000

NPV = 0

Therefore, IRR of project A is 24.29%

Project B:

IRR is the rate of return that makes NPV equal to 0:

NPV = -150,000 + 65,000 / (1 + R)¹ + 60,000 / (1 + R)² + 40,000 / (1 + R)³ + 40,000 / (1 + R)⁴ + 40,000 / (1 + R)⁵ + 40,000 / (1 + R)⁶

Using trial and error method, i.e.e, after trying various values for R, lets try R as 25.28%

NPV = -150,000 + 65,000 / (1 + 0.2528)¹ + 60,000 / (1 + 0.2528)² + 40,000 / (1 + 0.2528)³ + 40,000 / (1 + 0.2528)⁴ + 40,000 / (1 + 0.2528)⁵ + 40,000 / (1 + 0.2528)⁶

NPV = 0

Therefore, IRR of project B is 25.28%

Project B has a higher IRR

d)

We would recommend project B as it has the higher NPV. When projects are mutually exclusive, we choose the project with the higher NPV.