Question

You are considering the following two mutually exclusive projects. Which project(s) should be recommended?

Project A                                      Project B   

Year       Cash Flow                Year    Cash Flow

0     -$75,000 0       -$70,000

1     $19,000 1       $10,000

2     $48,000 2       $16,000

3     $12,000 3       $72,000

Required rate of return:   

10 percent (for A) 13 percent (for B)

Answer 1

For mutually exclusive projects we need to select only one of them. When Net Present Value (NPV) of both the projects is positive then such project will be selected whose NPV is greater.

Generally while using NPV for decision making such project should be selected whose NPV is greater than zero. In case of negative NPV such project shall be rejected.

NPV = Present value of cash inflows - Initial Investment

Calculation of Net Present Value - Project A Cash inflows Discounting Factor Years ($) @ 10% Present Value($) 19,000 0.909090909 17,272.727272727 2 48,000 0.826446281 39,669.421487603 3 12,000 0.751314801 9,015.777610819 Total Present Value (A) 65,957.926371150 Initial Investment (B) 75,000.00 Net Present Value (A-B) Rounding to two decimal places (9042.073628851) (9042.07) Calculation of Net Present Value - Project B Cash inflows Discounting Factor Years ($) @ 13% Present Value($) 10,000 0.884955752 8,849.557522124 2 16,000 0.783146683 12,530.346933981 3 72,000 0.693050162 49,899.611683994 1 Total Present Value (A) 71,279.51614010 Initial Investment (B) 70,000.00 Net Present Value (A-B). Rounding to two decimal places 1,279.516140099 1279.52

Since the NPV of Project B is greater, it should be selected over project A.

Note - How did we calculate discounting factors @10%

Year 1 - 1/1.10

= 0.909090909

Year 2 - 0.909090909 / 1.10

= 0.826446281

Year 3 - 0.826446281 / 1.10

= 0.751314801

How did we calculate discounting factors @13%

Year 1 - 1/1.13

= 0.884955752

Year 2 -0.884955752 / 1.13

= 0.783146683

Year 3 - 0.783146683 / 1.13

= 0.693050162