Ch13: The Cost of Capital

TOC

Capital Structure and Cost of Capital 1. Capital Structure 2. WACC Definition Costs of Debt and Equity Capital 1. Cost of Debt Capital 2. Cost of Preferred Stock Capital 3. Cost of Common Stock Capital WACC Calculation 1. WACC Equation 2. Methods in Practice Using WACC to Value a Project 1. Levered Value & WACC method 2. Key Assumptions ⚠️3. Project-Based Costs of Capital

Capital Structure and Cost of Capital

1. Capital Structure

A firm’s sources of financing which usually consist of debt and equity, represent its capital. The typical firm raises funds to invest by selling shares to stockholders (its) equity and borrowing from lenders (its) debt. The relative. proportions of debt, equity, and other securities that a firm has outstanding constitute its capital structure.

2. WACC Definition

Since a portfolio return is the weighted average of the returns of the securities in the portfolio. The weighted average cost of capital (WACC) is the average of a firm’s equity and debt costs of capital, weighted by the fractions of the firm’s value that correspond to equity and debt, respectively.

When determine the proportions, we must use the market values other than book values listed on the balance sheet. Book values reflect historical costs while market values are forward-looking, based on what the assets are expected to produce in the future. It’s useful to think about the market-value balance sheet, which based on the equation: Market Value of Equity + Market Value of Debt = Market Value of Assets

Costs of Debt and Equity Capital

1. Cost of Debt Capital

YTM

We can use the yield to maturity to estimate the firm’s current cost of debt. Actually, the market price of the firm’s existing debt implies a yield to maturity, which is the return that current purchases of the debt would earn if they held the debt to maturity and received all of the payments as promised.

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A common mistake in estimating a company’s overall cost of capital is to use the coupon rate on its existing debt as its debt cost of capital. YTM are the actual expected (or promised) return of the debt.

Taxes

When a firm uses debt financing, the cost of the interest it must pay is offset to some extent by the tax savings from the tax deduction. Taking tax savings into consideration, we can compute the effective cost of the debt

where, is the pretax debt cost of capital and is the tax rate.

2. Cost of Preferred Stock Capital

Firms may raise capital by issuing preferred stock. Typically, holders of the preferred stock are promised a fixe dividend, which must be paid “in preference to” (before) any dividends can be paid to common stockholders.

If the preferred dividend is known and fixed, we can estimate the preferred stock’s cost of capital using

where growth rate , thus

3. Cost of Common Stock Capital

A company cannot directly observe its cost of common stock (equity), but must instead estimate it. There are two major methods for doing so, CAPM and CDGM.

Capital Asset Pricing Model

General Steps:

Estimate the firm’s beta of equity, typically by regressing 60 months of the company’s returns against 60 months of returns for a market proxy such as the S&P 500.

Determine the risk-free rate, typically by using the yield on Treasury bills or bonds.

Estimate the market risk premium, typically by comparing historical returns on a market proxy to historical risk-free rates.

Apply the CAPM:

Constant Dividend Growth Model

General Steps:

Acquire the current price of the stock, the expected dividend in one year. The former is easy to obtain on line and the latter is easy to estimate reasonably.

Estimate the future dividend growth rate. It’s kind of difficult to be estimated. One common approach is to use estimates produced by stock analysts.🧐

Apply the CDGM:

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We should not be surprised that the two estimates of cost of equity do not match, because each was based on different assumptions.

ㅤ	CAPM	CDGM
Inputs	1. Equity beta	1. Current stock price
ㅤ	2. Risk-free rate	2. Expected dividend next year
ㅤ	3. Market risk premium	3. Future dividend growth rate
Major Assumptions	1. Estimated beta is correct	1. Dividend estimate is correct
ㅤ	2. Market risk premium is accurate	2. Growth rate matches market expectations
ㅤ	3. CAPM is the correct model🙃	3. Future dividend growth is correct

☝🏻

CAPM & CDGM Comparison: Because of the difficulties with the CDGM, the CAPM is the most popular approach for estimating the cost of equity.

WACC Calculation

1. WACC Equation

Unlevered & Levered

If a firm do not issue debt, then it is unlevered. Otherwise, it is levered and the leverage is the relative amount of debt on a firm’s balance sheet.

WACC of Unlevered Firms

All of the free cash flows generated by the firm’s assets are ultimately paid out ot its equity holders. Therefore, the cost of capital is equal to the return on its assets.

WACC of Levered Firms

The cost of capital is the weighted average of the firm’s equity and debt cost of capital

WACC considering tax

2. Methods in Practice

Some issues when estimating the WACC in practice

Net Debt

When calculating the weights for WACC (), many analysts use net debt

Net Debt = Debt - Cash and Risk-Free Securities

Significant excess cash on a firm’s balance sheet can complicate the assessment of the risk (and hence the cost of capital). Actually, cash and Risk-free securities can be viewed as negative debt. (Assume that a firm holds $1 in cash and has $1 of risk-free debt, then the interest earned on the cash will equal the interest paid on the debt. The cash flows from each source cancel each other, just as if the firm held no cash and no debt.)

When we use net debt,

Enterprise Value = Market Value of Equity + Net Debt

and the weights in WACC would then be

The Risk-Free Interest Rate

The risk-free interest rate is generally determined using the yields of U.S. Treasury securities, which are free from default risk. As for the horizon, the vast majority of large firms and financial analysts report using the yields o flong-term (10- to 30- year) bonds to determine the risk-free rate.

The Market Risk Premium

One way to estimate the market risk premium is to look at historical data. Because we are interested in the future market risk premium, we face a tradeoff in terms of the amount of data we use — the more the histroical data we use, the lower the volatility (as supposed) while the lower relevance to future market risk premium.

Using WACC to Value a Project

A project’s cost of capital depends on its risk. When the market risk of the project is similar to the average market risk of the firm’s investments, then its cost of capital is equivalent to the cost of capital for a portfolio of all the firm’s securities.

1. Levered Value & WACC method

Levered value: The value of an investment, including the benefit of the interest tax deduction, given the firm’s leverage policy.

WACC method: Discounting future incremental free cash flows using the firm’s WACC, which produces the levered value of a project.

2. Key Assumptions ⚠️

When using WACC as the discount rate in capital budgeting, we should be aware of the underlying assumptions:

Average Risk:

We assume initailly that the market risk of the project is equivalent to the average market risk of the firm’s investments. In that case, we assess the project’s cost of capital based on the risk of the firm.

The assumption is likely to fit typical projects of firms with investments concentrated in a single industry. In that case, the market risk of both the project and the firm will primarily depend on the sensitivity of the industry to the overall economy.

Constant Debt-Equity Ratio:

We assume that the firm adjusts its leverage continuously to maintain a constant ratio of the market value of debt to the market value of equity—a relationship referred to as the debt-equity ratio. This policy determines the amount of debt the firm will take on when it accepts a new project. It also implies that the risk of the firm’s equity and debt, and therefore its WACC, will not fluctuate owing to leverage changes.

The assumption, while unlikely to hold exactly, reflects the fact that firms tend to increase their levels of debt as they grow larger; some may even have an explicit target for their debt-equity ratio.

Limited Leverage Effects:

We assume initially that the main effect of leverage on valuation follows from the interest tax deduction. We assume that any other factors (such as possible financial distress) are not significant at the level of debt chosen.

For firms without very high levels of debt, the interest tax deduction is likely to be the most important factor affecting the capital budgeting decision. Hence, the assumption is a reasonable starting point to begin our analysis.

3. Project-Based Costs of Capital

Appropriate WACC

In many firms, the corporate treasurer performs the second step, calculating the firm’s WACC. This rate can then be used throughout the firm as the companywide cost of capital for new investments that are of comparable risk to the rest of the firm and that will not alter the firm’s debt-equity ratio. Employing the WACC method in this way is very simple and straightforward.

However, there are some investments which cannot be analysed using the firm’s WACC. For instance, if DuPont want to acquire Nike🤫, then it should use the WACC of Nike instead of WACC of its to estimate the investment.

Cost of Raising External Capital

In reality, issuing new equity or bonds carries a number of costs. These costs include the costs of filing and registering with the Securities and Exchange Commission and the fees charged by investment bankers to place the securities.

We can simply subtract these cost (cash flows) when analysing.