Determine the profitability index for Parkside Acres.:
Kartman Corporation is evaluating four different real estate investments. Management plans to buy the properties today and sell them three years from today. The annual discount rate for these investments is $12 \%$. The following table summarizes the initial cost and the sale price in three years for each property:
\begin{tabular}{lrc}
& Cost Today & Sale Price in Three Years \\
\hline Parkside Acres & $\$ 400,000$ & $\$ 800,000$ \\
Real Property Estates & 850,000 & $1,410,000$ \\
Lost Lake Properties & 670,000 & $1,070,000$ \\
Overlook & 170,000 & 370,000 \\
\hline
\end{tabular}

Kartman has a total capital budget of $\$ 850,000$ to invest in properties. Which properties should it choose?

The profitability index for Parkside Acres is $\square$. (Round to two decimal places.)

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 ：\(\boxed{\text{So, the profitability index for Parkside Acres is 1.42.}}\)