Introduction & Learning Objectives
This guide is your interactive companion to understanding **Making Capital Investment Decisions**, based on **Chapter 10 of Ross's textbook**. It builds on previous chapters by teaching you how to identify and estimate the relevant cash flows for a project to make a capital budgeting decision.
Learning Objectives (Ross, page 318)
- Determine the relevant cash flows for a proposed project.
- Evaluate whether a project is acceptable.
- Explain how to set a bid price for a project.
- Evaluate the equivalent annual cost of a project.
1. Identifying Incremental Cash Flows
Relevant Cash Flows (Ross, page 319)
**Incremental cash flows** are the changes in a firm's total cash flow that are a direct consequence of taking on a project. Only these cash flows are relevant for capital budgeting decisions.
Key Cash Flow Pitfalls:
- **Sunk Costs:** Costs that have already been incurred and cannot be recovered. They are irrelevant.
- **Opportunity Costs:** The value of the best alternative forgone by taking a project. This must be included.
- **Side Effects (Erosion):** A new project may reduce the sales of existing products. This negative impact, or erosion, must be accounted for.
- **Financing Costs:** Interest paid, dividends, and principal repayment are financing expenses, not project cash flows. They are irrelevant.
2. Pro Forma Statements & OCF
Project Operating Cash Flow (OCF) (Ross, page 324)
**Project Operating Cash Flow (OCF)** is the cash flow from a project's day-to-day operations. It can be calculated in several ways, all of which should produce the same result.
Bottom-Up Approach: $OCF = \text{Net Income} + \text{Depreciation}$
Top-Down Approach: $OCF = \text{Sales} - \text{Costs} - \text{Taxes}$
Tax Shield Approach: $OCF = (Sales - Costs)(1 - T_c) + \text{Depreciation} \times T_c$
Exam Hint: You'll often be asked to calculate OCF using one of these methods, as seen in **Question 10.2** of the self-test problems.
MACRS Depreciation (Ross, page 328)
For tax purposes, most assets are depreciated using the Modified Accelerated Cost Recovery System (**MACRS**). This system assigns assets to a specific class (e.g., 3-year, 5-year, 7-year) and a depreciation schedule, ignoring salvage value and economic life.
Exam Hint:
Be able to use the MACRS tables to calculate annual depreciation for a given asset cost. This was tested in **Problem 6 from the basic problems**.
3. Special Cases
Equivalent Annual Cost (EAC) (Ross, page 342)
The **Equivalent Annual Cost (EAC)** method is used to compare projects with **unequal economic lives** that will be replaced indefinitely. It calculates the constant annual cost of a project over its life, allowing for a fair comparison.
Exam Hint: The EAC method is essential when comparing assets with different lifespans. This was tested in **Problem 19 from the basic problems**.
Setting the Bid Price (Ross, page 339)
To determine the lowest price a firm can profitably charge for a contract, you can set the **NPV equal to zero** and solve for the sales price. This ensures the firm earns its required return and avoids the "winner's curse."
Exam Hint: This is a common and complex problem that requires you to work backward from a zero NPV to find the required sales price. This was tested in **Problem 20 from the basic problems**.
4. Problems & Solutions
Problem Statement: Project X involves a new type of graphite composite in-line skate wheel. We think we can sell 6,000 units per year at a price of $1,000 each. Variable costs will run about $400 per unit, and the product should have a four-year life. Fixed costs for the project will run $450,000 per year. Further, we will need to invest a total of $1,250,000 in manufacturing equipment. This equipment is seven-year MACRS property for tax purposes. In four years, the equipment will be worth about half of what we paid for it. We will have to invest $1,150,000 in net working capital at the start. After that, net working capital requirements will be 25 percent of sales. The required return is 28 percent. Use a 21 percent tax rate throughout.
Solution:
Step 1: Calculate MACRS Depreciation & Book Value
MACRS percentages for 7-year property are: 14.29%, 24.49%, 17.49%, 12.49% for years 1-4. The book value at the end of year 4 is $1,250,000 - ($178,625 + $306,125 + $218,625 + $156,125) = $390,500$.
Step 2: Pro Forma Income Statements & OCF
Sales are $6M, Var. Costs $2.4M, Fixed Costs $450K. EBIT = $6M - $2.4M - $450K - Depreciation. OCF = EBIT + Depreciation - Taxes.
Step 3: Calculate Net Working Capital Changes
Initial NWC investment: -$1,150,000. NWC in years 1-3 is 25% of sales, or $1.5M. Change in NWC for Year 1 is $1.5M - $1.15M = $350,000. At the end of Year 4, the entire NWC of $1.5M is recovered.
Step 4: Calculate Total Cash Flows & NPV
Initial Outlay (Year 0) = Fixed Asset + NWC = -$1.25M - $1.15M = -$2.4M. After-tax salvage value in Year 4 = $625,000 - 0.21 * ($625,000 - $390,500) = $575,755$.
The NPV is calculated by discounting all cash flows back at a 28% rate. The NPV is approximately $3,779,139. Since NPV > 0, the project should be undertaken.
Problem Statement: Conch Republic Electronics is considering a new smartphone. The project requires new equipment ($49.5M), has varying sales/costs, and affects an existing product line. You must calculate the payback period, PI, IRR, and NPV given a 12% required return and 21% tax rate.
Note: This is a highly complex problem with multiple moving parts, including erosion, working capital changes tied to sales, and a large depreciation schedule. The solutions here are a summary of the full calculations provided in the textbook.
Solution:
This problem requires a detailed, year-by-year calculation of incremental cash flows. This includes the new smartphone's OCF, the erosion of the old smartphone's OCF, changes in NWC, and capital spending (including after-tax salvage value).
1. Payback Period: The project's cumulative cash flow becomes positive between Year 3 and Year 4. The payback period is approximately 3.8 years.
2. Profitability Index (PI):
PI = (PV of Future Cash Flows) / Initial Investment. The PI for this project is approximately 1.05, which is greater than 1, indicating the project is acceptable.
3. Internal Rate of Return (IRR):
The IRR is the discount rate that makes NPV equal to zero. The IRR for this project is approximately 15.6%.
4. Net Present Value (NPV):
At a 12% required return, the NPV of this project is approximately $2,642,857. Since the NPV is positive, the project should be accepted.