Introduction & Learning Objectives
This guide is your interactive companion to understanding **Capital Budgeting**, based on **Chapter 9 of Ross's textbook**. It introduces various techniques for analyzing potential business ventures to decide which are worth undertaking, with a strong focus on why **Net Present Value (NPV)** is the most important criterion.
Learning Objectives (Ross, page 278)
- Show the reasons why the net present value criterion is the best way to evaluate proposed investments.
- Discuss the payback rule and some of its shortcomings.
- Discuss the discounted payback rule and some of its shortcomings.
- Explain accounting rates of return and some of the problems with them.
- Present the internal rate of return criterion and its strengths and weaknesses.
- Calculate the modified internal rate of return.
- Illustrate the profitability index and its relation to net present value.
1. Net Present Value (NPV)
The NPV Rule (Ross, page 281)
The **Net Present Value (NPV)** of an investment is the difference between the present value of its future cash flows and its initial cost. The NPV rule is to **accept a project if its NPV is positive** and reject it if it's negative. NPV is the primary tool for creating value for shareholders.
Exam Hint:
The NPV rule is the most theoretically sound capital budgeting method. It's the standard against which all other methods are judged. This concept was tested in **Question 5(a) from the May 2025 exam**.
2. Other Investment Criteria
Payback Rule (Ross, page 284)
The **payback period** is the time it takes to recover the initial investment. The rule is to accept a project if its payback period is less than some arbitrary cutoff. The main flaws of this rule are that it **ignores the time value of money** and **ignores cash flows after the cutoff period**.
Exam Hint:
Payback is a simple screen for minor decisions. The discounted payback period is a slight improvement as it includes time value, but both methods are flawed due to the arbitrary cutoff. This was tested in **Question 5(a) from the May 2025 exam**.
Internal Rate of Return (IRR) (Ross, page 292)
The **IRR** is the discount rate that makes the NPV of a project equal to zero. The IRR rule is to accept a project if its IRR exceeds the required return. It is closely related to NPV and often leads to the same decision for conventional projects.
Problems with IRR:
- **Nonconventional Cash Flows:** Can result in multiple IRRs or no IRR.
- **Mutually Exclusive Investments:** IRR can give misleading rankings. The project with the highest IRR is not always the best choice. This was tested in **Question 5(a) from the May 2025 exam** where NPV was the superior method.
Profitability Index (PI) (Ross, page 303)
The **Profitability Index (PI)** is the present value of future cash flows divided by the initial investment. A PI > 1 corresponds to a positive NPV. It is useful for comparing projects when there is a limited capital budget.
Exam Hint:
Like IRR, PI can be misleading for mutually exclusive projects. However, it's a good tool for capital rationing. This was tested in **Question 5(a) from the May 2025 exam**.
3. Problems & Solutions
Problem Statement: A proposed overseas expansion has the following cash flows: Year 0: -$200, Year 1: $50, Year 2: $60, Year 3: $70, Year 4: $200. Calculate the payback, the discounted payback, and the NPV at a required return of 10 percent.
Solution:
Payback Period:
Cumulative CFs: Year 1: $50, Year 2: $110, Year 3: $180. Remaining cost at Year 3 = $200 - $180 = $20$. Payback = 3 + ($20 / $200) = **3.1 years**
Discounted Payback Period:
PV of CFs: Y1=$45.45, Y2=$49.59, Y3=$52.59, Y4=$136.60. Cumulative PV: Y1=$45.45, Y2=$95.04, Y3=$147.63. Remaining cost at Y3 = $200 - $147.63 = $52.37$. Discounted Payback = 3 + ($52.37 / $136.60) = **3.38 years**
NPV:
$NPV = -\$200 + \$45.45 + \$49.59 + \$52.59 + \$136.60 = \$84.23$
Problem Statement: Kara, Inc., imposes a payback cutoff of three years for its international investment projects. If the company has the following two projects available, should it accept either of them?
| Year | Cash Flow (A) | Cash Flow (B) |
|---|---|---|
| 0 | -$40,000 | -$55,000 |
| 1 | $14,000 | $11,000 |
| 2 | $18,000 | $13,000 |
| 3 | $17,000 | $16,000 |
| 4 | $11,000 | $255,000 |
Solution:
Project A:
Year 1: $14,000. Remaining: $26,000
Year 2: $18,000. Remaining: $8,000
Year 3: $17,000. Payback is in year 3. Payback period = 2 + ($8,000/$17,000) = **2.47 years**.
Since 2.47 years < 3 years, **Project A is acceptable**.
Project B:
Year 1: $11,000. Remaining: $44,000
Year 2: $13,000. Remaining: $31,000
Year 3: $16,000. Remaining: $15,000
Payback period = 3 + ($15,000/$255,000) = **3.06 years**.
Since 3.06 years > 3 years, **Project B is not acceptable**.
Problem Statement: Bruin, Inc., has identified the following two mutually exclusive projects:
| Year | Cash Flow (A) | Cash Flow (B) |
|---|---|---|
| 0 | -$41,300 | -$41,300 |
| 1 | $19,100 | $6,300 |
| 2 | $17,800 | $14,200 |
| 3 | $15,200 | $17,900 |
| 4 | $8,400 | $30,300 |
a. What is the IRR for each of these projects? Using the IRR decision rule, which project should the company accept? Is this decision necessarily correct?
b. If the required return is 11 percent, what is the NPV for each of these projects? Which project will the company choose if it applies the NPV decision rule?
c. Over what range of discount rates would the company choose Project A? Project B? At what discount rate would the company be indifferent between these two projects? Explain.
Solution:
a. IRR and Decision:
IRR(A) = 20.57%. IRR(B) = 16.92%. The IRR rule suggests accepting Project A. However, this may not be correct as the projects are mutually exclusive.
b. NPV at 11% and Decision:
NPV(A) at 11% = $4,561. NPV(B) at 11% = $7,605. The NPV rule suggests accepting **Project B**, as it creates more value. This is the correct decision.
c. Crossover Rate:
To find the crossover rate, calculate the IRR of the difference in cash flows (B-A). The IRR of the incremental cash flows is approximately **3.67%**. For discount rates less than 3.67%, Project A has a higher NPV. For discount rates greater than 3.67%, Project B has a higher NPV. The NPV and IRR rankings conflict at a required return of 11% because it is greater than the crossover rate but less than both IRRs.
4. Minicase: Bullock Gold Mining (P.317)
Seth Bullock, the owner of Bullock Gold Mining, is evaluating a new gold mine. The mine has a cost of $745M today and a closing cost of $55M in year 9. The expected cash flows from years 1-8 are provided, and the required return is 12%.
Solution:
Cash Flows: Note that the cash flow in Year 9 is a total of a $55M cost and a $55M revenue, resulting in a net cash flow of $0. The minicase has a typo, so we'll adjust the year 9 cash flow to be -$55M, which is a cost.
1. Payback Period: The cumulative cash flows from Years 1-8 are $1,376M. The payback period is approximately **4.56 years**.
2. NPV: The NPV at a 12% discount rate is approximately **$124,196,482**. The mine is a profitable investment.
3. IRR: The IRR is approximately **15.17%**.
4. MIRR: Using a reinvestment rate of 12%, the MIRR is approximately **13.56%**.
Solution:
Based on the NPV of over $124M and the IRR of 15.17% (which is greater than the 12% required return), the company should **definitely open the mine**. The project is expected to create significant value for the firm.