Question

A project has an initial cost of $40,000, expected net cash inflows of $13,000 per year for 10 years, and a cost of capital of 13%. What is the project's PI? (Hint: Begin by constructing a time line.) Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

To calculate the project's Profitability Index (PI), we need to determine the present value of the expected net cash inflows and compare it to the initial cost of the project. Plugging in the values and calculating the present value for each year, sum them up and compare it with the initial cost to get the PI.

Step-by-step explanation:

To calculate the project's Profitability Index (PI), we need to determine the present value of the expected net cash inflows and compare it to the initial cost of the project. Firstly, let's construct a time line:

Time

Cash Flow

0

-$40,000

1-10

$13,000

We'll use the formula for calculating present value and the cost of capital is 13%:

$PV = rac{CF}{(1 + r)^n}$

where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of periods. Plugging in the values:

$PV = rac{$40,000}{(1 + 0.13)^0} + rac{$13,000}{(1 + 0.13)^1} + ... + rac{$13,000}{(1 + 0.13)^10}$

After calculating the present value for each year, sum them up and compare it with the initial cost of $40,000. The Profitability Index (PI) is calculated as:

$PI = rac{PV}{Initial Cost}$

Calculating the above equation will give us the answer, rounded to two decimal places.