Question

Problem 7-14 Problems with Profitability Index The Bosa Corporation is trying to choose between the following two mutually exclusive design projects: Year Cash Flow (1) -$ 66,000 29,000 29,000 29,000 Cash Flow (II) -$17,800 9,600 9,600 9,600 a-1 If the required return for both projects is 10 percent, what is the profitability Index for both projects? (Do not round Intermediate calculations and round your answers to 3 decimal places, e.g., 32.161.) Profitability Index Project I Project II a-2 If the company applies the profitability Index decision rule, which project should the firm accept? Project Project II b-1 What is the NPV for both projects? (Do not round Intermediate calculations. A negative answer should be indicated by a minus sign. Round your answers to 2 decimal places, e.g., 32.16.) NPV Project I Project II b-2 If the company applies the NPV decision rule, which project should it choose? Project 1 Project II

Answer 1

a.1. The profitability index is computed as shown below:

Profitability index of project I is computed as follows:

= Present value of future cash flows / Initial investment

Present value of future cash flows is computed as follows:

= $ 29,000 / 1.10 + $ 29,000 / 1.10² + $ 29,000 / 1.10³

= $ 72,118.70774

Initial investment is equal to $ 66,000

So the profitability index will be:

= $ 72,118.70774 / $ 66,000

= 1.093 Approximately

Profitability index of project II is computed as follows:

= Present value of future cash flows / Initial investment

Present value of future cash flows is computed as follows:

= $ 9,600 / 1.10 + $ 9,600 / 1.10² + $ 9,600 / 1.10³

= $ 23,873.77911

Initial investment is equal to $ 17,800

So the profitability index will be:

= $ 23,873.77911 / $ 17,800

= 1.341 Approximately

a.2. Since the profitability index of project II is higher, the same shall be accepted

b.1. The NPV of project I is computed as shown below:

= - $ 66,000 + $ 29,000 / 1.10 + $ 29,000 / 1.10² + $ 29,000 / 1.10³

= $ 6,118.71 Approximately

The NPV of project II is computed as shown below:

= - $ 17,800 + $ 9,600 / 1.10 + $ 9,600 / 1.10² + $ 9,600 / 1.10³

= $ 6,073.78 Approximately

b.2. Since the NPV of project I is greater than the NPV of project II, the project I shall be accepted

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