Introduction & Learning Objectives
This guide is your interactive companion to understanding **Project Analysis and Evaluation**, based on **Chapter 11 of Ross's textbook**. This chapter focuses on assessing the reliability of capital budgeting estimates and identifying critical variables that can affect a project's success or failure.
Learning Objectives (Ross, page 356)
- Perform and interpret a sensitivity analysis for a proposed investment.
- Perform and interpret a scenario analysis for a proposed investment.
- Determine and interpret cash, accounting, and financial break-even points.
- Explain how the degree of operating leverage can affect the cash flows of a project.
- Discuss how capital rationing affects the ability of a company to accept projects.
1. What-If and Forecasting Risk
Forecasting Risk (Ross, page 358)
**Forecasting risk** is the possibility that an NPV estimate is wrong due to errors in projected cash flows. A positive NPV estimate is a good sign, but it must be tested for its sensitivity to various assumptions. You should always ask: "What is the source of value for this project?"
Scenario & Sensitivity Analysis (Ross, page 360)
**Scenario analysis** examines a project's NPV under different plausible scenarios (e.g., best case, worst case). **Sensitivity analysis** is a variation where you freeze all variables except one to see how sensitive the NPV is to changes in that single variable.
Exam Hint: Be able to perform these analyses to identify a project's most critical variables. The sensitivity of NPV to price and quantity sold was a key question in **Conch Republic Electronics, Part 2** minicase from this chapter.
2. Break-Even Analysis
Break-Even Points (Ross, page 368)
Break-even analysis helps determine how bad sales can get before a project loses money. The three key break-even points are:
- **Accounting Break-Even:** Sales volume where net income is zero. It ignores the time value of money.
$Q_{A} = \frac{FC + D}{P-v}$
- **Cash Break-Even:** Sales volume where operating cash flow (OCF) is zero.
$Q_{C} = \frac{FC}{P-v}$
- **Financial Break-Even:** Sales volume where the project's NPV is zero. This is the most important measure as it accounts for the time value of money and required return.
Exam Hint: You may be asked to calculate and interpret all three break-even points, as seen in **Question 11.2** of the self-test problems.
3. Operating Leverage and Capital Rationing
Operating Leverage (Ross, page 375)
**Operating leverage** is a measure of how committed a firm is to fixed costs. A high degree of operating leverage (DOL) means a small change in sales can lead to a large change in operating cash flow.
Exam Hint:
Be able to calculate DOL and explain its implications for a project's risk. High operating leverage increases forecasting risk. A similar concept was tested in **Question 6(a) from the May 2025 exam**.
Capital Rationing (Ross, page 378)
**Capital rationing** exists when a firm has profitable projects but cannot get the funds to undertake them. **Soft rationing** is an internal limit on spending, while **hard rationing** is a true inability to raise capital externally. In hard rationing, DCF analysis can break down, as the concept of a required return becomes ambiguous.
4. Problems & Solutions
Problem Statement: A project costs $750,000, has a five-year life, and no salvage value. Straight-line depreciation to zero. Required return is 17%, tax rate is 21%. Sales are 500 units/year at $2,500/unit. Variable cost is $1,500/unit, and fixed costs are $200,000/year. Estimates are accurate to within $\pm 5\%$. What are the base-case, worst-case, and best-case NPVs?
Solution:
Base Case:
Sales = $1.25M. Var Costs = $750k. Fixed Costs = $200k. Depr = $150k. EBIT = $150k. Taxes = $31.5k. OCF = $268.5k. NPV = **$109,024**.
Worst Case:
Sales = 475 units * $2,375 = $1.128M. Var Costs = 475 * $1,575 = $748.1k. Fixed Costs = $210k. Depr = $150k. EBIT = $19.9k. Taxes = $4.2k. OCF = $165.8k. NPV = **-$219,548**.
Best Case:
Sales = 525 units * $2,625 = $1.378M. Var Costs = 525 * $1,425 = $748.1k. Fixed Costs = $190k. Depr = $150k. EBIT = $289.9k. Taxes = $60.9k. OCF = $379.1k. NPV = **$462,872**.
Problem Statement: In the Conch Republic Electronics project, Shelley Couts asks for a memo on the sensitivity of NPV to changes in the new smartphone's price. The project's NPV is approximately $2,642,857 at a price of $575. What is the sensitivity of the NPV to a price change?
Solution:
To find the sensitivity, we calculate the NPV with a small change in price (e.g., $1) and find the change in NPV. The change in OCF per unit price change is $(1 - T_c) \times Q$.
The NPV is highly sensitive to price changes. A price drop of just over $20 would be enough to make the project unprofitable. This indicates a high degree of forecasting risk for the price variable, and Shelley's concerns are valid.