The present value of a flow of payments from a business, project, or investment is determined using net present value (NPV). It is the distinction between the current value of cash inflows and outflows over a given time period.
a. The NPV for the given question is calculated and attached in the form
of an image. The following computations are as under
IRR: IRR is the rate at which present value of cash inflows is equal present value of cash outflows.
Project A : 9000 = 3000/ (1+r)^1 + 3000/ (1+r)^2 + 3000/ (1+r)^3 + 3000/ (1+r)^4 + 3000/ (1+r)^5
Solving for r we get, IRR = 19.86%
Project B : 27000 = 8400/ (1+r)^1 + 8400/ (1+r)^2 + 8400/ (1+r)^3 + 8400/ (1+r)^4 + 8400/ (1+r)^5
Solving for r we get, IRR = 16.80%
MIRR = [Square root of (Present value of cash flows/ Initial Investment)] - 1
The present value of cash flows are calculated above in the table
MIRR Project A = [Square root of 10299.24/9000] - 1 = 1.0697 - 1 = 6.97%
MIRR Project B = [Square root of 28837.88/27000] - 1 = 1.0335 - 1 = 3.35%
Payback period is the number of years in which the initial investment is recovered.
Payback period A = 9000 /3000 = 3 years
Payback period B = 27000 / 8400 = 3.21 years
Discounted Payback period:
As per the NPV table above,
For project A, amount recovered upto 4 years = $8741.14, Balance to be recovered = $9000 - $8741.14 = $258.86
Discounted payback period = 4 + 258.86 / 3000 = 4.09 years
For project B, amount recovered upto 4 years = $24475.18, balance to be recovered = $27000 - $24475.18 = $2524.82
Discounted payback period = 4 + 2524.82 / 8400 = 4.30 years
b. Both projects would be accepted since both of their NPV's are positive
c. If the projects are mutually exclusive, the project with the highest
positive NPV is chosen. Accept Project B.
d. Since the cash flow timing is the same , The conflict between NPV and
IRR occurs due to the difference in the size of the projects.
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Complete question:
A firm with a 14% WACC is evaluating two projects for this year's capital budget. After-tax cash flows, including depreciation, are as follows Project A $9,000 $3,000 $3,000 $3,000 $3,000 $3,000 Project B $27,000 $8,400 $8,400 $8,400 $8,400 $8,400
a. Calculate NPV for each project. Calculate IRR for each project. Calculate MIRR for each project. Calculate payback for each project. Calculate discounted payback for each project. Round your answers to two decimal places.
b. Assuming the projects are independent, which one(s) would you recommend?
c. If the projects are mutually exclusive, which would you recommend?
d. Notice that the projects have the same cash flow timing pattern. why is there a conflict between npv and irr?
