Step 1 :The profitability index (PI) is calculated by dividing the present value of future cash flows by the initial investment cost. In this case, the future cash flow is the sale price in three years, and the initial investment cost is the cost today. The annual discount rate is 12%.
Step 2 :For Parkside Acres, the future cash flow is $800,000 and the initial investment cost is $400,000.
Step 3 :The formula for the present value of future cash flows is: \(PV = \frac{FV}{(1 + r)^n}\) where: \(PV\) is the present value, \(FV\) is the future value, \(r\) is the discount rate, and \(n\) is the number of periods.
Step 4 :So, the present value of the future cash flow for Parkside Acres is: \(PV = \frac{$800,000}{(1 + 0.12)^3} = $567,431.69\)
Step 5 :Then, the profitability index (PI) is calculated as: \(PI = \frac{PV}{\text{Initial Investment Cost}}\)
Step 6 :So, the profitability index for Parkside Acres is: \(PI = \frac{$567,431.69}{$400,000} = 1.42\) (rounded to two decimal places)
Step 7 :\(\boxed{\text{So, the profitability index for Parkside Acres is 1.42.}}\)