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.
