NPV and IRR Analysis for Mutually Exclusive Projects & Ethical Considerations
NPV Profiles: Scale Differences
A company is considering two mutually exclusive expansion plans:
Plan A
Requires a $40 million expenditure on a large-scale integrated plant that would provide expected cash flows of $6.4 million per year for 20 years.
Plan B
Requires a $12 million expenditure to build a somewhat less efficient, more labor-intensive plant with expected cash flows of $2.72 million per year for 20 years. The firm’s WACC is 10%.
a) Calculate each project’s NPV and IRR
Using a financial calculator, we get:
- NPVA = $14,486,808
- NPVB = $11,156,893
- IRRA = 15.03%
- IRRB = 22.26%
b) Graph the NPV profiles for Plan A and Plan B and approximate the crossover rate
Using a financial calculator, calculate each plan’s NPVs at different discount rates (as shown in the table below) and graph the NPV profiles.
| Discount Rate | NPV Plan A | NPV Plan B |
|---|---|---|
| 0% | $88,000,000 | $42,400,000 |
| 5% | $39,758,146 | $21,897,212 |
| 10% | $14,486,808 | $11,156,893 |
| 15.03% | $0 | $4,997,152 |
| 20% | -$8,834,690 | $1,245,257 |
| 22.26% | -$11,765,254 | $0 |
The crossover rate is somewhere between 11% and 12%.
c) Calculate the crossover rate where the two projects’ NPVs are equal
To calculate the crossover rate, create Project Δ which represents the cash flow differences between the two projects. Once those cash flows are calculated, find the IRR of Project Δ, and this is the crossover rate. Enter the data (in millions) for Project Δ as follows:
CF0 = -28; CF1-20 = 3.68; and solve for IRR = 11.71%.
d) Why is NPV better than IRR for making capital budgeting decisions that add to shareholder value?
The NPV method implicitly assumes that the opportunity exists to reinvest the cash flows generated by a project at the WACC, while the use of the IRR method implies the opportunity to reinvest at the IRR. The firm will invest in all independent projects with an NPV > $0. As cash flows come in from these projects, the firm will either pay them out to investors or use them as a substitute for outside capital which, in this case, costs 10%. Because these cash flows are expected to save the firm 10%, this is their opportunity cost reinvestment rate.
The IRR method assumes reinvestment at the internal rate of return itself, which is an incorrect assumption, given a constant expected future cost of capital and ready access to capital markets.
Capital Budgeting Criteria: Ethical Considerations
A mining company is considering a new project. Because the mine has received a permit, the project would be legal; but it would cause significant harm to a nearby river. The firm could spend an additional $10 million at Year 0 to mitigate the environmental problem, but it would not be required to do so. Developing the mine (without mitigation) would cost $60 million, and the expected cash inflows would be $20 million per year for 5 years. If the firm does invest in mitigation, the annual inflows would be $21 million. The risk-adjusted WACC is 12%.
a) Calculate NPV and IRR with and without mitigation
No Mitigation Analysis (in millions of dollars):
| 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| -60 | 20 | 20 | 20 | 20 | 20 |
Using a financial calculator, enter the data as follows: CF0 = -60; CF1-5 = 20; I/YR = 12. Solve for NPV = $12.10 million and IRR = 19.86%.
With Mitigation Analysis (in millions of dollars):
| 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| -70 | 21 | 21 | 21 | 21 | 21 |
Using a financial calculator, enter the data as follows: CF0 = -70; CF1-5 = 21; I/YR = 12. Solve for NPV = $5.70 million and IRR = 15.24%.
b) How should the environmental effects be dealt with when this project is evaluated?
The environmental effects, if not mitigated, could result in additional loss of cash flows and/or fines and penalties due to ill will among customers, community, etc. Therefore, even though the mine is legal without mitigation, the company needs to make sure that they have anticipated all costs from not doing the environmental mitigation in the original analysis.
c) Should this project be undertaken? If so, should the firm do mitigation?
Even when mitigation is considered, the project has a positive NPV, so it should be undertaken. The question becomes whether to mitigate or not mitigate for environmental problems. Under the assumption that all costs have been considered, the company would not mitigate for the environmental impact of the project because its NPV is $12.10 million vs. $5.70 million when mitigation costs are included in the analysis.