Cost of Capital Lecture Notes

Cost of Capital Overview

• Cost of capital: Refers to the rate of return that a firm must earn on its investments to maintain its value and satisfy its investors.

• It is used as a benchmark for evaluating the viability of projects.

Learning Objectives

• Understand that the discount rate should reflect the expected return on a financial asset of comparable risk.

• Estimate cost of equity capital (RE), cost of preferred stock (RP), and cost of debt (RD).

• Calculate the firm's Weighted Average Cost of Capital (WACC).

• Explain issues with using WACC for evaluating projects with varying risks.

Required Return and Cost of Capital

• Required return, discount rate, and cost of capital are synonymous.

• A project yields a positive NPV if its return exceeds the cost of capital.

• The cost of capital is driven by investment risk, not by the means of capital acquisition.

Financial Policy and Cost of Capital

• A firm’s capital structure defines the mix of debt and equity used.

• The cost of capital is influenced by the firm's leverage, reflecting the required return on both debt and equity.

Calculating WACC

• Cost of Equity (RE): Determined by:

  • Dividend Growth Model

  • Capital Asset Pricing Model (CAPM)

• Cost of Preferred Stock (RP):

  • Constant Dividend Model

• Cost of Debt (RD): Typically observed from the yield to maturity (YTM) of current liabilities.

Cost of Equity: Dividend Growth Model

• Formula: RE = \frac{D1}{P0} + g where:

  • D_1 : Dividend expected next period

  • P_0 : Current share price

  • g : Constant growth rate of dividends

• Example Calculation:

  • If a firm pays a $4 dividend, shares at $60, and dividends grow at 6%:

  • RE = \frac{4 \times 1.06}{60} + 0.06 = 0.1307 = 13.07\%

Cost of Equity: CAPM Approach

• The required return relies on:

  1. Risk-free rate (Rf)

  2. Market risk premium (E(RM) - Rf)

  3. Systematic risk (beta, β)

• Formula:
  RE = Rf + β \times (E(RM) - Rf)

• Example:

  • Rf = 4.8%, E(RM) = 12%, β (Costco) = 0.79

  • R_{Costco} = 4.8\% + 0.79 \times 7.2\% \approx 10.5\,\%

Cost of Debt

• The return required by lenders on new debt (RD) is determined through:

  • The current YTM on existing bonds.

• Always use the market-required rate on new borrowings, not historical coupon rates.

Cost of Preferred Stock

• Preferred stock has fixed dividends; its cost is calculated: RP = \frac{D}{P_0} where:

  • D : Annual dividend

  • P_0 : Current market price

WACC Calculation

• WACC Formula: WACC = \left( \frac{E}{V} \right) \times RE + \left( \frac{D}{V} \right) \times RD \times (1 - T_C) where:

  • V = E + D

• Calculations involve market value estimates of equity (E) and debt (D).

Tax Considerations in WACC

• Interest expenses are tax-deductible, while dividends are not.

• After-tax cost of debt is calculated:
  RD{after-tax} = RD \times (1 - TC)

WACC Example Calculation

• Given values for market equity, debt, risk-free rate, and beta, calculate WACC using:

  • Market value of equity: 1.4 million shares at $20 each.

  • Market value of debt: Derived from quoted prices.

SML and Project Evaluation

• Caution is required when using WACC to evaluate diverse projects, as it might lead to:

  • Accepting risky unprofitable projects.

  • Rejecting less risky profitable projects.

• Two alternative approaches:

  1. Pure Play Approach: Use firms with similar risk profiles to establish project-specific discount rates.

  2. Subjective Approach: Adjust WACC based on project risk classifications.

Practical Applications and Examples

• Warehouse renovation example provides practical applications of calculated WACC against comparable market projects using the principles above to illustrate decision-making processes based on cash flows and investment risks.

1. Understand that the discount rate for evaluating a project should be the expected return on a financial asset of comparable risk.

   • When a firm has extra cash, it can either distribute it to investors or reinvest in projects. The firm should opt for the path that yields the highest return for investors.

   • The cost of capital, the required rate of return on a capital project, and the appropriate discount rate are essentially the same as they all represent what investors expect to earn on the investment.

   • The cost of capital is dependent on the risk of the investment; thus, it relates primarily to the purpose of the funds rather than their source.

2. Estimate the firm’s cost of equity capital, RE.

   • The Dividend Discount Model (DDM) can be utilized to estimate the cost of equity, which reflects the stockholders’ expected rate of return on the stock.

   • To find the stock price, P0, and the dividend, D0, reliable sources online should be consulted.

   • The growth rate, g, can be derived from online sources or historical data. The advantages of the DDM include its simplicity and focusing on cash flows, while disadvantages may include sensitivity to growth rate assumptions and dividends not fully reflecting company value.

3. Use the SML (Security Market Line) approach to estimate the cost of equity.

   • The risk-free rate (Rf), the market risk premium (E(RM) - Rf), and the stock's beta (β) need to be obtained from online resources.

   • The SML approach benefits from incorporating market risk into the calculation, but it also requires accurate market data and may not apply well in unstable markets.

4. Determine the firm’s cost of preferred stock, RP, and debt, RD.

   • The cost of preferred stock can be calculated using the DDM.

   • The Yield to Maturity (YTM) is calculated for existing debt, serving as the appropriate rate for estimating the pre-tax cost of existing debt. Understanding the cost of debt includes knowing that it is the return creditors demand for new borrowing and that the YTM reflects current market conditions.

   • The coupon rate on an outstanding bond does not represent the firm’s current cost of debt because it is based on past borrowing conditions, not the market's current expectation.

5. Calculate and employ the firm’s Weighted Average Cost of Capital (WACC).

   • The market value of the firm, V, is defined as the total of market value of debt, D, plus market value of equity, E.

   • The after-tax cost of debt is lower than the pre-tax cost because interest expenses are tax-deductible.

   • Costs of common and preferred stock are not adjusted for taxes as they do not incur tax liabilities.

   • The firm’s WACC is appropriate to use as the discount rate for capital projects that carry the same risk as the firm’s existing operations.

   • Caution is warranted when using WACC for projects of differing risks, as it could lead to poor investment decisions. The pure play approach involves identifying similar firms to establish a required return, while the subjective approach adjusts WACC based on risk classifications of projects.