Practice Question
Company XYZ is lost between three projects: A, B, and C. A requires an initial investment of $10,000 and generates $7,000 for the coming two years. B requires $15,000 and generates $6,500 for the coming three years. C requires an initial investment of $20,000 and generates $6,000 for the coming six years. A, B, and C are mutually exclusive. Which project should XYZ take if its discount rate is 14%?
Answer +
Project A should be selected.
EANPV A: 926.74
EANPV B: 39.02
EANPV C: 856.85
EANPV A: 926.74
EANPV B: 39.02
EANPV C: 856.85
Explanation +
To determine which project is best, we need to compute the Equivalent Annual NPV (EANPV) for each. This helps compare projects of unequal duration.
Step 1: Calculate NPV for Each Project
Project A:
\[
\text{NPV}_A = -10,000 + \frac{7,000}{1.14} + \frac{7,000}{1.14^2} \approx -10,000 + 6,140.35 + 5,384.62 = 1,524.97
\]
Project B:
\[
\text{NPV}_B = -15,000 + \frac{6,500}{1.14} + \frac{6,500}{1.14^2} + \frac{6,500}{1.14^3} \approx -15,000 + 5,701.75 + 5,001.54 + 4,387.79 = 91.08
\]
Project C:
\[
\text{NPV}_C = -20,000 + \sum_{t=1}^{6} \frac{6,000}{(1.14)^t} \approx -20,000 + 5,263.16 + 4,615.38 + 4,050.42 + 3,553.89 + 3,120.61 + 2,745.27 = 352.73
\]
Step 2: Convert Each NPV to EANPV
We use the Present Value Annuity Factor (PVAF) for each project's length at 14%:
- \( \text{PVAF}_A = \frac{1 - (1 + 0.14)^{-2}}{0.14} \approx 1.735 \)
- \( \text{PVAF}_B \approx 2.322 \)
- \( \text{PVAF}_C \approx 3.987 \)
Now compute:
\[
\text{EANPV}_A = \frac{1,524.97}{1.735} \approx 926.74
\]
\[
\text{EANPV}_B = \frac{91.08}{2.322} \approx 39.02
\]
\[
\text{EANPV}_C = \frac{352.73}{3.987} \approx 88.46
\]
Final Decision
Project A has the highest EANPV, so Project A should be selected.