Asked by Josie Pagnucco on Jun 22, 2024
Verified
A 25- year project has a cost of $1,500,000 and has annual cash flows of $400,000 in years 1-15, and $200,000 in years 16-25. The company's required rate is 14%. Given this information, calculate the profitability index of the project.
A) 1.74
B) 1.50
C) 1.25
D) 1.00
E) 0.75
Required Rate
The minimum return an investor expects to achieve by investing in a particular asset, often used in capital budgeting.
Profitability Index
A ratio that compares the present value of future cash flows generated by an investment to the investment's initial cost, indicating its relative profitability.
- Gain insight into the theory and numerical evaluation of the Profitability Index (PI).
- Implement discounted cash flow approaches in the evaluation of long-term ventures.
Verified Answer
JF
Jennifer FuentesJun 27, 2024
Final Answer :
A
Explanation :
The profitability index (PI) is calculated by dividing the present value (PV) of future cash flows by the initial investment. First, calculate the PV of cash flows for years 1-15 and 16-25 separately using the formula PV = Cash Flow / (1 + r)^n, where r is the discount rate (14% or 0.14) and n is the year. Then, sum these PVs and divide by the initial investment of $1,500,000. The calculation shows a PI greater than 1, indicating the project generates a return exceeding the cost, with the correct answer being closest to 1.74 when calculated accurately.
Learning Objectives
- Gain insight into the theory and numerical evaluation of the Profitability Index (PI).
- Implement discounted cash flow approaches in the evaluation of long-term ventures.
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