Question

5.7 Calculating Profitability Index Bill plans to open a self serve grooming center in a storefront. The grooming equipment will cost $325,000, to be paid immediately. Bill expects after tax cash inflows of $67,000 annually for 7 years, after which he plans to scrap the equipment and retire to the beaches of Nevis. The first cash inflow occurs at the end of the first year. Assume the required return is 13 percent. What is the project’s PI? Should it be accepted?

Answer 1

The formula for calculating the profitability index is:

Profitability index = Present value of cash inflows / Initial investment

First we will calculate the present value of cash inflows as per below:

Here, the cash inflow will be same every year, so it is an annuity. For calculating the present value of annuity, we will use the following formula:

PVA = P * (1 - (1 + r)^-n / r)

where, PVA = Present value of annuity, P is the periodical amount = $67000, r is the rate of interest = 13% and n is the time period = 7

Now, putting these values in the above formula, we get,

PVA = $67000 * (1 - (1 + 13%)^-7 / 13%)

PVA = $67000 * (1 - ( 1+ 0.13)^-7 / 0.13)

PVA = $67000 * (1 - ( 1.13)^-7 / 0.13)

PVA = $67000 * (1 - 0.42506064374) / 0.13)

PVA = $67000 * (0.57493935626 / 0.13)

PVA = $67000 * 4.422610432

PVA = $296314.90

So, Present value of cash inflows = $296314.90

Initial investment = $325000

Now, we will calculate the profitability index as below:

Profitability index = Present value of cash inflows / Initial investment

Profitability index = $296314.90 / $325000 = 0.9117

Since the value of profitability index is less than 1, so project should not be accepted.