Practice Question
NIKE is considering two mutually exclusive projects: A and B. The projects have the following characteristics: project A requires an initial investment of \$75,000 and will generate cash flows of \$15,000 per year for eight (8) years. Note that at the end of the 8 years, the machinery will have a value of zero. On the other hand, project B requires an initial investment of \$166,000 and will earn cash flows of \$25,000 per year for the next seventeen (17) years. At the end of year 17, the machinery will have a value of zero. All projects can be replicated indefinitely. Also, the company pays no taxes. Please note that the beta of project A is 0.80 and the beta of project B is 1.3. The risk-free rate is 3%, and the expected return on the market is 10%. These rates will remain forever. What project should Nike undertake?
Step 1: Calculate the discount rates using CAPM
CAPM Formula: \( R = R_f + \beta (R_m - R_f) \)
For Project A:
\( R_A = 3\% + 0.80 \times (10\% - 3\%) = 8.6\% \)
For Project B:
\( R_B = 3\% + 1.3 \times (10\% - 3\%) = 12.1\% \)
Step 2: Calculate the NPV for Project A
\( NPV_A = \sum_{t=1}^{8} \frac{15,000}{(1 + 0.086)^t} - 75,000 \)
Approximated breakdown:
\( \frac{15,000}{1.086} = 13,812.50 \)
\( \frac{15,000}{1.179396} = 12,715.38 \)
\( \frac{15,000}{1.279109} = 11,726.09 \)
\( \frac{15,000}{1.384084} = 10,835.51 \)
\( \frac{15,000}{1.494247} = 10,034.29 \)
\( \frac{15,000}{1.609524} = 9,313.43 \)
\( \frac{15,000}{1.729847} = 8,664.71 \)
\( \frac{15,000}{1.855151} = 8,080.57 \)
Total PV of inflows = \$85,182.48
\( NPV_A = 85,182.48 - 75,000 = 10,182.48 \)
Step 3: Calculate the NPV for Project B
\( NPV_B = \sum_{t=1}^{17} \frac{25,000}{(1 + 0.121)^t} - 166,000 \)
First few terms:
\( \frac{25,000}{1.121} = 22,297.06 \)
\( \frac{25,000}{1.256641} = 19,898.08 \)
\( \frac{25,000}{1.407383} = 17,767.97 \)
\( \frac{25,000}{1.574326} = 15,874.16 \)
\( \frac{25,000}{1.758589} = 14,187.87 \)
... (continued for 17 years)
Total PV of inflows ≈ \$255,000
\( NPV_B = 255,000 - 166,000 = 89,000 \)
Step 4: Convert to Equivalent Annual NPV (EANPV)
Use the annuity factor:
\( EANPV_A = \frac{10,182.48 \times 0.1621} = 1,650.21 \)
\( EANPV_B = \frac{89,000 \times 0.01742} = 1,550.07 \)
Step 5: Final Recommendation
Even though Project B has a higher raw NPV, Project A is better when comparing equivalent annual NPVs, due to differences in time horizon and repeatability.
Conclusion: Nike should undertake Project A.