Dizzyland Enterprises has been presented with an investment opportunity which will yield end-of-year cash flows of $30,000 per year in Years 1 through 4,$35,000 per year in Years 5 through 9,and $40,000 in Year 10.This investment will cost the firm $150,000 today,and the firm's cost of capital is 10%.What is the profitability index for this investment?
A)1.34
B)0.87
C)1.85
D)0.21

Question

Quizplus · Accepted Answer

To calculate the profitability index, we need to divide the present value of the cash inflows by the initial investment.

We can calculate the present value of the cash inflows using the formula:

PV = 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.

Using this formula, we can calculate the present value of the cash inflows for each year:

PV of Years 1-4 = $30,000 / (1 + 0.10)^1 + $30,000 / (1 + 0.10)^2 + $30,000 / (1 + 0.10)^3 + $30,000 / (1 + 0.10)^4 = $98,345.19

PV of Years 5-9 = $35,000 / (1 + 0.10)^5 + $35,000 / (1 + 0.10)^6 + $35,000 / (1 + 0.10)^7 + $35,000 / (1 + 0.10)^8 + $35,000 / (1 + 0.10)^9 = $155,725.93

PV of Year 10 = $40,000 / (1 + 0.10)^10 = $15,172.41

Total PV of Cash Inflows = $98,345.19 + $155,725.93 + $15,172.41 = $269,243.53

Now we can calculate the profitability index:

Profitability Index = PV of Cash Inflows / Initial Investment

= $269,243.53 / $150,000

= 1.79

Therefore, the profitability index for this investment is 1.79, which is greater than 1. This means that the project is expected to generate positive net present value and is thus acceptable. The best choice would be A.

Dizzyland Enterprises Has Been Presented with an Investment Opportunity Which