Practice Problem – Profitability Index

Practice Question

Intro to Finance
Capital Budgeting
Profitability Index
Short Answer

Company XYZ is considering Project A. Project A requires an initial investment of $75,000. It generates $35,000 each year for the coming 3 years. What is the project PI for this project if the proper discount rate is 18%?

Answer +
1.015
Explanation +

Sure, let's tackle the problem step-by-step.

Step 1: Define Key Variables
  • Initial Investment (C₀): $75,000
  • Annual Cash Inflows: $35,000 for 3 years
  • Discount Rate (r): 18% or 0.18
Step 2: Calculate Present Value of Cash Inflows

The present value (PV) of future cash flows is calculated using the formula:

\[ PV = \frac{C_1}{(1 + r)^1} + \frac{C_2}{(1 + r)^2} + \frac{C_3}{(1 + r)^3} \]

Substituting in the values:

\[ PV = \frac{35{,}000}{1.18} + \frac{35{,}000}{1.3924} + \frac{35{,}000}{1.6432} \] \[ PV = 29{,}661.02 + 25{,}133.67 + 21{,}298.45 = 76{,}093.14 \]
Step 3: Calculate the Profitability Index (PI)

The formula for the profitability index is:

\[ PI = \frac{PV \text{ of future cash inflows}}{\text{Initial Investment}} \] \[ PI = \frac{76{,}093.14}{75{,}000} \approx 1.015 \]
Final Answer

Profitability Index (PI): 1.015

Interpretation

The profitability index of 1.015 suggests that for every dollar invested in Project A, the present value of future returns is $1.015. Since this value is greater than 1, it indicates that the project adds value and is financially viable under the given assumptions.