Question

Project Q has an initial cost of $211,415 and projected cash flows of $121,300 in Year 1 and $176,300 in Year 2. Project R has an initial cost of $415,000 and projected cash flows of $187,500 in Year 1 and $236,600 in Year 2. The discount rate is 8.5 percent and the projects are independent. Which project(s), if either, should be accepted based on its profitability index value?

Answer 1

Answer:

Project Q should be accepted.

Explanation:

In this question, we have to use the profitability index formula which is shown below:

Profitability index = Present value of all years cash flows ÷ Initial investment

where,

Present value of cash inflows is calculated by applying the discount rate which is presented below:

For this, we have to first compute the present value factor which is computed by a formula

= 1 ÷ (1 +rate) ∧ number of year

number of year = 0

number of year = 1

Number of year = 2

So,

For year 1 = 0.9216 (1 ÷ 1.085) ∧ 1

For year 2 = 0.8495 (1 ÷ 1.085) ∧ 2

Now, multiply this present value factor with yearly cash inflows

So

For Project Q,

The present value of year 1 = $121,300 × 0.9216 = $111,797.235

The present value of year 2 = $176,300 × 0.8495 = $149,758.967

and the sum of all year cash inflow is 261,556.202

So, the Profitability index would be equal to

= $261,556.202 ÷ $211,415

= 1.23

For Project R,

The present value of year 1 =  $187,500 × 0.9216 = $172,811.059

The present value of year 2 = $236,600 × 0.8495 = $200,981.121

and the sum of all year cash inflow is $373,792.180

So, the Profitability index would be equal to

= $373,792.180 ÷ $415,000

= 0.90

Since, the Project Q has high profitability index than Project R, so Project Q should be accepted.