Year       Cash Flow (I)   Cash Flow (II)   0            $51,000            $14,400   1              24,800              7,800   2              24,800              7,800   3              24,800              7,800 The Sloan Corporation is trying to choose between the following two mutually exclusive design projects: a. If the required return is 10 percent and the company applies the profitability index decision rule, which project should the firm accept? b. If the company applies the NPV decision rule, which project should it take? c. Explain why your answers in (a) and (b) are different.

Question
Asked Apr 3, 2019
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Year       Cash Flow (I)   Cash Flow (II)

   0            $51,000            $14,400

   1              24,800              7,800

   2              24,800              7,800

   3              24,800              7,800

 

The Sloan Corporation is trying to choose between the following two mutually exclusive design projects: a. If the required return is 10 percent and the company applies the profitability index decision rule, which project should the firm accept? b. If the company applies the NPV decision rule, which project should it take? c. Explain why your answers in (a) and (b) are different.

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Expert Answer

Step 1

Part (a)

Profitability Index, PI  = PV of future cash flows / Initial investment

PV of a cash flow, Ci occuring at the end of period "i" = Ci / (1 + r)i where r = required return = 10%

For Project I:

PV of future cash flows = 24,800 / (1 + 10%) + 24,800 / (1 + 10%)2 + 24,800 / (1 + 10%)3 = $61,673.93 

Initial investment = $51,000

Hence, PII = 61,673.93 / 51,000 = 1.21

Step 2

For Project II:

PV of future cash flows = 7,800 / (1 + 10%) + 7,800 / (1 + 10%)2 + 7,800 / (1 + 10%)3 = $19,397.45

Initial investment = $14,400

Hence, PIII = 19,397.45 / 14,400 = 1.35

Step 3

Decision criteria using PI: Accept a project if it's PI > 1.0

Since, PI of both the projects are > 1.0, hence the firm should...

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