Question

Consolidated Inc. uses a weighted average cost of capital of 12% to evaluate average-risk projects and adds/subtracts two percentage points to evaluate projects of greater/lesser risk. Currently, two mutually exclusive projects are under consideration. Both have a cost of $200,000 and last four years. Project A, which is riskier than average, will produce annual after-tax cash flows of $71,000. Project B, which has less-than-average risk, will produce after-tax cash flows of $146,000 in Years 3 and 4 only. What should Consolidated do?

a. Accept neither project since both NPVs are less than zero.

b. Accept Project A with an NPV of $15,652.

c. Accept both projects since both NPVs are greater than zero.

d. Accept Project A with an NPV of $6,874.

e. Accept Project B with an NPV of $9,412.

Answer 1

First of all we shall calculate the NPV of project A which is riskier than average project by using the below function:

= (Initial Investment) + Present value of Annual after tax cash flows for 4 years at a discount rate of 14% i.e. (12% + 2% since we need to add 2 percentage points to the weighted average cost of capital because it is a riskier project as compared with the average project).

= (200,000) + 71,000 / 1.14¹ + 71,000 / 1.14² + 71,000 / 1.14³ + 71,000 / 1.14⁴

= $ 6,873.57 or $ 6,874 Approximately.

Now we shall calculate the NPV of project B which is a less than average risk project:

= (Initial Investment) + Present value of Annual after tax cash flows for 4 years at a discount rate of 10% i.e. (12% - 2%, since we need to subtract 2 percentage points to the weighted average cost of capital because it is a less than riskier project as compared with the average project).

= (200,000) + 0 / 1.10¹ + 0 / 1.10² + 146,000 / 1.10³ + 146,000 / 1.10⁴

= $ 9,411.92 or $ 9,412  

So we have find the NPV's of both projects, but in case of mutually exclusive projects, we need to select only one project out of various projects.

In this case the Project B should be accepted by Consolidated, since the NPV of Project B is greater than the NPV of Project A

So the correct answer would be option e. i.e. Accept Project B with an NPV of $9,412.

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