For two investment projects with a 10% WACC, Project A and Project B have similar payback periods between 2 and 3 years. Project A has a higher NPV of $40.82, compared to Project B's NPV of $39.81, indicating Project A could be the preferred option.
To determine whether to proceed with Project A or Project B, we need to calculate the payback period and the net present value (NPV) for each project. The firm's weighted average cost of capital (WACC) is given as 10%.
Payback Period
The payback period for Project A would be calculated by adding the yearly cash flows until the initial investment is recouped. By adding up the cash flows, we see that Project A’s investment is recovered sometime in the third year.
Project A:
- Year 1: $19
- Year 2: $19 + $38 = $57
- Year 3: $57 + $69 = $126
Project A's payback period is between 2 and 3 years.
For Project B, similarly:
- Year 1: $55
- Year 2: $55 + $44 = $99
- Year 3: $99 + $35 = $134
Project B's payback period is between 2 and 3 years.
Net Present Value (NPV)
To calculate NPV, we need to discount the future cash flows back to their present value using the WACC and then subtract the initial investment.
Project A:
- NPV = (-$60) + $19 / (1 + 0.10)^1 + $38 / (1 + 0.10)^2 + $69 / (1 + 0.10)^3
- NPV = (-$60) + $17.27 + $31.40 + $52.15
- NPV = $40.82
Project B:
- NPV = (-$73) + $55 / (1 + 0.10)^1 + $44 / (1 + 0.10)^2 + $35 / (1 + 0.10)^3
- NPV = (-$73) + $50 + $36.36 + $26.45
- NPV = $39.81
Both projects have a similar payback period, but Project A has a slightly higher NPV, suggesting it may be the better investment choice.
The complete question is :
A firm has a WACC of 10% and is deciding between two mutually exclusive projects. Project A has an initial investment of $60. The additional cash flows for project A are: year 1 = $19, year 2 = $38, year 3 = $69. Project B has an initial investment of $73.The cash flows for project B are: year 1 = $55, year 2 = $44, year 3 = $35. Calculate the payback and NPV for each project.