Introduction & Learning Objectives
This guide is your interactive companion to understanding the core concepts of the **Cost of Capital**, based on **Chapter 14 of Ross's textbook**. The cost of capital is the minimum required return a company must earn on its investments to satisfy all of its investors. It is a critical concept for capital budgeting and firm valuation.
Learning Objectives (Ross, page 465)
- Determine a firm's cost of equity capital.
- Determine a firm's cost of debt.
- Determine a firm's overall cost of capital (WACC) and how to use it to value a company.
- Explain how to correctly include flotation costs in capital budgeting projects.
- Describe some of the pitfalls associated with using the WACC.
1. Components of the Cost of Capital
Cost of Equity ($R_E$)
This is the return required by a firm's equity investors. Since it can't be directly observed, we must estimate it using one of two primary methods. **Textbook Link:** Ross, Chapter 14, Section 14.2 (Page 467)
Dividend Growth Model (DGM)
This approach is applicable only to firms that pay dividends and assume a constant growth rate. The formula is a rearrangement of the constant growth stock valuation model.
Where $D_1$ is the expected dividend next period, $P_0$ is the current stock price, and $g$ is the constant growth rate.
Exam Hint:
Remember to calculate $D_1$ from $D_0$ and $g$. The growth rate can be estimated from historical data or analyst forecasts. This was tested in **Problem 14.1** of the review problems.
Security Market Line (SML) / CAPM
This approach explicitly adjusts for risk. It is applicable to a wider range of companies but requires estimating the market risk premium and beta.
Where $R_f$ is the risk-free rate, $\beta_E$ is the company's equity beta, and $(R_M - R_f)$ is the market risk premium.
Exam Hint:
Be prepared to use this model to find the cost of equity or to solve for a missing variable like beta, as seen in **Question 1(vi) from the Sep 2023 exam**.
Cost of Debt ($R_D$)
This is the return a firm's new creditors demand. Unlike the cost of equity, it can be observed directly by looking at the **yield to maturity (YTM)** on a firm's existing debt. The **coupon rate is irrelevant** for new debt. **Textbook Link:** Ross, Chapter 14, Section 14.3 (Page 471)
Exam Hint:
A common trick in exams is to provide the coupon rate to mislead you. Always use the YTM on the current market price of the debt. This was tested in **Question 1(iv) from the May 2025 exam**.
Cost of Preferred Stock ($R_P$)
Preferred stock is a perpetuity. The cost is simply the dividend divided by the current price. **Textbook Link:** Ross, Chapter 14, Section 14.3 (Page 472)
Where $D$ is the fixed annual dividend and $P_0$ is the current market price.
2. Weighted Average Cost of Capital (WACC)
The WACC is the overall required return on the firm's assets. It's calculated as the weighted average of the costs of its financing sources. **Textbook Link:** Ross, Chapter 14, Section 14.4 (Page 473)
Key Points for WACC:
- Always use **market values** for the weights ($E$, $D$, $P$, $V$) unless they are unavailable.
- Use the **after-tax cost of debt** ($R_D(1-T_C)$) because interest payments are tax-deductible.
- WACC is the correct discount rate for projects with **similar risk** to the firm's existing operations.
WACC Pitfalls & Solutions
Using a single WACC for all projects can lead to incorrect decisions. Projects with above-average risk will be incorrectly accepted, while projects with below-average risk will be incorrectly rejected. **Textbook Link:** Ross, Chapter 14, Section 14.5 (Page 483)
The Problem with a Single WACC
This chart from Ross shows how a single WACC cutoff rate (the horizontal line) leads to **incorrect rejections** of low-risk, profitable projects (below the SML) and **incorrect acceptances** of high-risk, unprofitable projects (above the SML).
Image of SML and WACC
Solutions
To avoid these errors, firms can use a **divisional cost of capital** or the **pure play approach**. The pure play approach involves finding a publicly traded company that specializes in a single line of business similar to the project being evaluated and using that company's WACC as the project's discount rate.
A firm can also use a **subjective approach** by adjusting the WACC up or down based on the perceived risk of the project.
3. Problems & Solutions
Problem Statement: The Tribiani Co. just issued a dividend of $2.90 per share on its common stock. The company is expected to maintain a constant 4.5 percent growth rate in its dividends indefinitely. If the stock sells for $56 a share, what is the company's cost of equity?
Solution:
We use the Dividend Growth Model:
Given: $D_0 = \$2.90$, $g = 4.5\%$, $P_0 = \$56$
First, calculate $D_1$:
$D_1 = D_0 \times (1+g) = \$2.90 \times (1.045) = \$3.0305$
Now, calculate the cost of equity:
$R_E = \frac{\$3.0305}{\$56} + 0.045 = 0.0541 + 0.045 = 0.0991$ or 9.91%
Problem Statement: Sunrise, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 23 years to maturity that is quoted at 96 percent of face value. The issue makes semiannual payments and has an embedded cost of 5 percent annually. What is the company's pretax cost of debt? If the tax rate is 21 percent, what is the aftertax cost of debt?
Solution:
To find the pretax cost of debt, we need to find the YTM of the bond. We are given:
PV = -0.96 * 1000 = -$960
FV = $1,000
PMT = (0.05 * 1000) / 2 = $25
N = 23 * 2 = 46 periods
Using a financial calculator, the semiannual rate ($r$) is approximately 2.65%.
Pretax Cost of Debt: $R_D = 2.65\% \times 2 = 5.30\%
Aftertax Cost of Debt: $R_D(1-T_C) = 5.30\% \times (1-0.21) = 5.30\% \times 0.79 = 4.19\%
Problem Statement: Ninecent Corporation has a target capital structure of 70 percent common stock, 5 percent preferred stock, and 25 percent debt. Its cost of equity is 11 percent, the cost of preferred stock is 5 percent, and the pretax cost of debt is 6 percent. The relevant tax rate is 23 percent.
a. What is the company's WACC?
Solution:
We use the WACC formula with preferred stock:
Given:
$W_E = 0.70$, $R_E = 11\%$
$W_P = 0.05$, $R_P = 5\%$
$W_D = 0.25$, $R_D = 6\%$, $T_C = 23\%$
Calculation:
$WACC = (0.70 \times 0.11) + (0.05 \times 0.05) + (0.25 \times 0.06 \times (1-0.23))$
$WACC = 0.077 + 0.0025 + (0.25 \times 0.06 \times 0.77)$
$WACC = 0.077 + 0.0025 + 0.01155 = 0.09105$ or 9.11%
4. Valuing a Company (Minicase)
The Feline Fancy case study from **Ross, page 488** is a great way to tie all the concepts of cost of capital together. The goal is to value a privately held company using the pure play approach.
Solution:
This is a complex problem, but the key is to calculate the adjusted cash flow from assets (CFA*) and then use the non-constant growth model to find the firm's value.
Step 1: Calculate CFA* for Years 1-5
Sales, EBIT, Depreciation, NWC, and CapEx all grow at 15% for the first four years.
| (in millions) | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
|---|---|---|---|---|---|
| EBIT | 10.00 | 11.50 | 13.23 | 15.21 | 17.49 |
| Depreciation | 1.50 | 1.73 | 1.98 | 2.28 | 2.62 |
| Taxes* (21%) | 2.10 | 2.42 | 2.78 | 3.19 | 3.67 |
| Change in NWC | 0.80 | 0.92 | 1.06 | 1.22 | 1.40 |
| Capital Spending | 2.40 | 2.76 | 3.17 | 3.65 | 4.20 |
| CFA* | 6.20 | 7.13 | 8.20 | 9.43 | 10.84 |
Step 2: Calculate Terminal Value at Year 5
After Year 5, CFA* grows at a constant 2%. We use the growing perpetuity formula.
$V_5 = \frac{CFA*_6}{WACC - g} = \frac{10.84 \times (1.02)}{0.08 - 0.02} = \frac{11.06}{0.06} = \$184.35 \text{ million}$
Step 3: Calculate Present Value of the Firm
We discount the first five years' CFA* and the terminal value back to today at the WACC of 8%.
Step 4: Find Value per Share
Value of Equity = Firm Value - Debt = $158.14M - $40M = $118.14M$.
Price per Share = Equity Value / Shares Outstanding = $118.14M / 3.5M = $33.75