Question

The following project is under consideration by Smith's Food Markets, Inc. Smith's requires a 14% rate of return on projects of this nature.

Cost Year 0 = -$200,000

Cash Flows Years 1-3: +$90,000

What is the Profitability Index of the project?

a. 1.50

b. 1.67

c. 1.08

d. 1.35

e. 1.04

Answer 1

Profitability index is given by the formula (1+Npv/initial investment)

Net present value, NPV is the sum of future cash flows discounted to present value net of investment.

Npv = -initial investment + CF1/(1+r) + CF2/(1+r)^2 + CF3/(1+r)^3

Where CF1,2,3 are cash flows in year 1,2,3 respectively and r is the required rate of return

= -200,000 + 90000/(1.14) + 90000/(1.14^2) + 90000/(1.14^3)

= 8946.88

Thus, profitability index = (1+8946.88/200000) = 1.044

Thus, the correct option is e. 1.04