Konyvkiado Inc. is considering two mutually exclusive projects. Both require an initial investment of $15,000 at t = 0. Project S has an expected life of 2 years with after-tax cash inflows of $7,000 and $12,000 at the end of Years 1 and 2, respectively. In addition, Project S can be repeated at the end of Year 2 with no changes in its cash flows. Project L has an expected life of 4 years and a cash-flow of $5200/year. Each project has a WACC of 9%. What is the equivalent annual annuity of the most profitable project?
NPV is calculated by discounting the cashflows
PV = C/(1+r)^n
C - Cashflow
r - Discount rate
n - years to the cashflow
Using replacement method for project S;
| Rate | 9.00% | ||||
| Year | Cashflow (S) | Discount rate = 1/(1+r)^(n) | Present value of cashflow = A*discount rate | Cashflow (L) | Present Value = B*discount rate |
| 0 | -15000.00 | 1.0000 | -15000.00 | -15000.00 | -15000.00 |
| 1 | 7000.00 | 0.9174 | 6422.02 | 5200.00 | 4770.64 |
| 2 | -3000.00 | 0.8417 | -2525.04 | 5200.00 | 4376.74 |
| 3 | 7000.00 | 0.7722 | 5405.28 | 5200.00 | 4015.35 |
| 4 | 12000.00 | 0.7084 | 8501.10 | 5200.00 | 3683.81 |
| NPV | 2803.37 | NPV | 1846.54 |
Project S is more profitable.
Formula for calculation of equivalent annual annuity is:
C = r*NPV/(1-(1+r)^-n)
C = 0.09*2803.37/(1-(1+0.09)^-4) = $865.31
Equivalent annual annuity = $865.31
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