Question

1)A 25- year project has a cost of $1,500,000 and has annual cash flows of $400,000 in years 1-15, and $200,000 in years 16-25. The company's required rate is 14%. Given this information, calculate the profitability index of the project.
Answer is 1.74

Can someone explain this with the steps?

Answer 1

First look at the tabular method then I will show you the formula method.

Excel formulas for this table, I will post at the end of this solution.

We know Profitability Index = Total Discounted Cash outflow / Total of Discounted Cash Inflow

From below table, we can see these values,

Therefore, Profitability Index =  $2,603,019 /  $1,500,000 = 1.74

Discount factor = 1/(1+i)^n

Formula Method:

Formula to find discount factor of first 15 years

Where,

i = required rate

n = number of years.

......................(you can see that in the table, sum of first 15 years discount factor comes to 6.1422)

To find the discount factor from 16 years to 25 years, first we need to find discount factor for 25 years period then subtract discount factor of 15 years from that.

Therefore, Discount factor for 16 to 25 years = 6.8729 - 6.1422

=0.7307

Therefore, present value of cash inflows = 400,000 (6.1422) + 200,000(0.7307)

=2,456,880 + 146,140

= 2,603,020

Now, Profitability Index = 2,603,020 / 1,500,000

= 1.74