Consider projects A and B with the following cash flows:

Consider projects A and B with the following cash flows:

		C0					C1					C2					C3
A		−	$	34			+	$	18			+	$	18			−	$	18
B		−		59					34					34					34

a-1. What is the NPV of each project if the discount rate is 10%?


Explanation
Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

a.
NPVA = −$34 + [$18 × Annuity factor (10%, 3 periods)]
= −$34 +  $18  ×  [1.10 − 1.10 ×  (1.10)3] =  $10.76
NPVB = −$59 + [$34 × Annuity factor (10%, 3 periods)]
= −$59 +  $34  ×  [1.10 − 1.10 ×  (1.10)3] =  $25.55
Thus Project B has the higher NPV if the discount rate is 10%.
b.
PIA = NPVA / Initial investment = $10.76 / $34 = .32
PIB = NPVB / Initial investment = $26 / $59 = .43
Project B has the higher profitability index.

c-1.
For a firm with unlimited funds, the preferred project is the project with the highest NPV.

c-2.
For a firm with limited funds, the preferred project is the project with the highest PI that the firm can afford. In this case, we are assuming the firm can afford either project.
Thank you!