Your division is considering two projects with the following net cash flows0 1 2 3Project A -$25 $5 $10 $17Project B -$20 $10 $9 $6a.What are the projects’ NPVs assuming the WACC is 5%? 10%? 15?b.What are the projects’ IRR at each of these WACCs?c.If the WACC was 5% and A and B were mutually exclusive, which project would you choose? What if the WACC was 10% and 15%? (Hint: The crossover rate is 7.81%)
Question
Your division is considering two projects with the following net cash flows0 1 2 3Project A -5 17Project B -10 6a.What are the projects’ NPVs assuming the WACC is 5%? 10%? 15?b.What are the projects’ IRR at each of these WACCs?c.If the WACC was 5% and A and B were mutually exclusive, which project would you choose? What if the WACC was 10% and 15%? (Hint: The crossover rate is 7.81%)
Solution
Sure, let's break this down:
a. The Net Present Value (NPV) is calculated by subtracting the initial cost of a project from the present value of its future cash flows. The formula for NPV is:
NPV = ∑ [Rt / (1+i)^t] - C0
Where: Rt = net cash inflow during the period t i = discount rate or WACC t = number of time periods C0 = initial investment
Let's calculate the NPV for both projects at different WACCs:
For Project A:
- At WACC 5%, NPV = -5/(1+0.05) + 17/(1+0.05)^3 = $4.57
- At WACC 10%, NPV = -5/(1+0.10) + 17/(1+0.10)^3 = $1.36
- At WACC 15%, NPV = -5/(1+0.15) + 17/(1+0.15)^3 = -$1.43
For Project B:
- At WACC 5%, NPV = -10/(1+0.05) + 6/(1+0.05)^3 = $3.36
- At WACC 10%, NPV = -10/(1+0.10) + 6/(1+0.10)^3 = $1.62
- At WACC 15%, NPV = -10/(1+0.15) + 6/(1+0.15)^3 = $0.11
b. The Internal Rate of Return (IRR) is the discount rate that makes the NPV of all cash flows (both positive and negative) from a project or investment equal to zero. IRR can be calculated using financial calculators or software like Excel. However, it's not typically calculated at different WACCs. Instead, it's compared to the WACC to determine if a project is a good investment. If the IRR is greater than the WACC, the project is considered a good investment.
c. If the WACC was 5% and projects A and B were mutually exclusive, you would choose Project A because it has a higher NPV (3.36). If the WACC was 10%, you would still choose Project A because it has a higher NPV (1.62). However, if the WACC was 15%, you would choose Project B because it has a higher NPV ($0
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