Question

Consider the following projects, X and Y where the firm can only choose one. Project X costs $1500 and has cash flows of $678, $652, $347, $111, $54, $16 in each of the next 6 years. Project Y also costs $1500, and generates cash flows of $738, $693, $405 for the next 3 years, respectively. WACC=9.5%.

1. A) Draw the timelines for both projects: X and Y.

2. B) Calculate the projects’ NPVs, IRRs, payback periods.

3. C) If the two projects are independent, which project(s) should be chosen?

4. D) If the two projects are mutually exclusive, which projects should be chosen?

5. E) Plot NPV profiles for the two projects. Identify the projects’ IRRs on the graph.

6. F) If the WACC were 5.5 percent, would this change your recommendation if the projects were

   mutually exclusive? If the WACC were 16.5 percent, would this change your recommendation? Explain your answers.

7. G) There is a “crossover rate” of X’s and Y’s NPV curves, and mark it on the graph with Point O. Explain in words what this rate is and how it affects the choice between mutually exclusive projects.

8. H) If it possible for conflicts to exist between the NPV and the IRR when independent projects are being evaluated? Explain your answer.

Answer 1

Part A

Project X timeline:

Project Y timeline:

Part B:

NPV, IRR and Payback of project X:

NPV is the surplus earned by a project in absolute terms after discounting the cash flows by an appropriate rate(in this case WACC) to its present value. This can be calculated using NPV function on Excel.

Internal rate of Return(IRR) is the discount rate that makes the NPV of all cash flows equal to Zero. It can be calculate using IRR function on Excel.

Calculation on Excel is as follows:

The formulas used are as follows:

Payback period signifies the amount of time a project will take to recover the initial costs. It can be used by calculating cumulative cash flows. Firstly, we need to count the number of years before the initial investment is fully recovered. Then, we need to divide the remaining initial cost to be recovered by the cash flows of the next year. This will give us the fraction of the year.

So, from the calculate cumulative cash flows above, we can derive that the project is recovering the initial costs between year 2 and year 3. To calculate the fraction of the year, we need to divide the remaining cost to be recovered, i.e. $170, by cash flow in the year 3, i.e. $347. So, $170/$347= 0.48. Now, we need add this figure to the full years it took to recover the costs, i.e. 2 years

So, the payback period will be 2.48 years.

NPV, IRR and Payback of project Y:

The formulas used are as follows:

Payback period of project Y

In project Y, initial cost is being recovered between Year 2 and Year 3. For calculation of fraction of the year, we need to divide the costs remaining to be recovered in year 2. i.e. $69 by cash flow in Year 3, i.e. $405 which is equal to 0.17.

So, the payback period is 2.17 years.

Part C:

If the projects X and Y are independent, both of them could be chosen as both the projects have positive NPV. This means that both the projects will be profitable for the firm.

Part D:

If the projects X and Y are mutually exclusive, Project Y should be chosen as it has a higher NPV which signifies that Project Y will be more profitable for the firm.