CHAPTER 14

COST OF CAPITAL

## SLIDES

## CHAPTER ORGANIZATION

**S14.1: Key Concepts and Skills**

**S14.2: Chapter Outline**

**14.1THE COST OF CAPITAL: SOME PRELIMINARIES**

Required Return versus Cost of Capital

Financial Policy and Cost of Capital

**14.2THE COST OF EQUITY**

The Dividend Growth Model Approach

The SML Approach

**14.3THE COSTS OF DEBT AND PREFERRED STOCK**

The Cost of Debt

The Cost of Preferred Stock

**14.4THE WEIGHTED AVERAGE COST OF CAPITAL**

The Capital Structure Weights

Taxes and the Weighted Average Cost of Capital

Solving the Warehouse Problem and Similar Capital Budgeting Problems

Performance Evaluation: Another Use of the WACC

**14.5DIVISIONAL AND PROJECT COSTS OF CAPITAL**

The SML and the WACC

Divisional Cost of Capital

The Pure Play Approach

The Subjective Approach

**14.6FLOTATION COSTS AND THE WACC**

The Basic Approach

Flotation Costs and NPV

**14.7CALCULATING WACC FOR BOMBARDIER**

**14.8SUMMARY AND CONCLUSIONS**

**14AADJUSTED PRESENT VALUE**

**14BECONOMIC VALUE ADDED AND THE MEASUREMENT OF FINANCIAL PERFORMANCE**

## ANNOTATED CHAPTER OUTLINE

14.1THE COST OF CAPITAL: SOME PRELIMINARIES

**S14.3: Why Cost of CapitalIs Important**

Perspectives:

*Students often find it easier to grasp the intricacies of cost of capital estimation when they understand why it is important. You should point out that an accurate estimate of the cost of capital is required for:*

*-good capital budgeting decisions - neither the NPV rule nor the IRR rule can be implemented without knowledge of the appropriate discount rate.*

*-financing decisions – the optimal/target capital structure is that which minimizes the cost of capital.*

*-operating decisions – cost of capital is used by regulatory agencies in order to determine the "fair return" in some regulated industries (e.g., electric utilities)*

**A.Required Return versus Cost of Capital**

*Cost of capital, required return, appropriate discount rate—*denote the same opportunity cost of using capital in one way as opposed to an alternative investment in the financial market having the same systematic risk.

-required return is from an investor's point of view

-cost of capital is the same return from the firm’s point of view

-appropriate discount rate is the same return as used in a PV calculation

**S14.4: Required Return **

**B.Financial Policy and Cost of Capital**

Capital structure—the firm's combination of debt and equity. Taken as given for now, the capital structure decision is discussed later in the text. A firm's cost of capital will reflect the average riskiness of all its securities, which individually may be less risky (bonds) or more risky (common stock).

14.2THE COST OF EQUITY

**A.The Dividend Growth Model Approach**

S14.5: Cost of Equity

S14.6: The Dividend Growth Model Approach and Examples (5 pages)

According to the constant growth model,

P0 = D1/(RE - g).

Rearranging terms and solving for the cost of equity gives:

RE = D1/P0 + g

which equals the dividend yield plus the growth rate (capital gains yield).

1.Implementing the Approach

Price and latest dividend are directly observed—g must be estimated.

Estimating g—Typically use historical growth rates or analysts' forecasts.

*The text mentions that there are other ways to compute g. Rather than use the arithmetic mean as in the example, the geometric mean (which implies a compound growth rate) can be used. OLS regression with the log of the dividends as the dependent variable and time as the independent variable is also an option. *

Example:

Year / Dividend / Dollar change / Percentage change1992 / $4.00 / – / –

1993 / 4.40 / $.40 / 10.00

1994 / 4.75 / .35 / 7.95

1995 / 5.25 / .50 / 10.53

1996 / 5.65 / .40 / 7.62

Average growth rate = (10 + 7.95 + 10.53 + 7.62)/4 = 9.025%

2.Advantages and Disadvantages of the Approach

-Approach only works for dividend paying firms.

-RE is very sensitive to the estimate of g.

-Historical dividend growth rates may not reliably predict future growth rates.

-Risk is only indirectly accounted for by the use of price.

*Some students may question how one would value a non-dividend paying firm since, as the text states in the following paragraph, "the dividend growth model is obviously only applicable to companies that pay dividends." In anticipation of this question, point out that, in the case of growth-oriented, non-dividend-paying firms, analysts often look at the trend in earnings or use similar firms to project the future date of the first expected dividend and its future growth rate. However, such processes are subject to greater estimation error and when companies fail to meet (or even exceed) estimates, the stock price can experience a high degree of variability. It should also be pointed out that no firm pays zero dividends forever - at some point, every going concern will begin to pay dividends. Note: Some estimates of the proportion of firms that do not pay dividends are as high as 30%*

B.The SML Approach

RE depends upon:

1.The risk-free rate, Rf

S14.11: The SML Approach (3 pages)

2.The expected market risk premium, E(RM) – Rf

3.The amount of systematic risk as measured by

By the CAPM: RE = Rf + E × [E(RM) – Rf]

1.Implementing the Approach

Betas are widely available from various sources. T-bill rates are often used for Rf. The sticky point is the market risk premium, i.e., the market price of a unit of systematic risk. Many use the historical average value or an average of analysts' forecasts.

2.Advantages and Disadvantages of the Approach

-Consistent with capital market history, the approach adjusts for risk.

-Applicable to virtually all publicly traded stocks

-The past doesn’t predict the future for the MRP and beta.

Perspectives:

*Students are frequently surprised when they find that the two approaches typically result in different estimates. Suggest that it would be more surprising if the results were identical. Why? The underlying assumptions of the two models are very different. The constant growth model (which came to prominence in the mid-1950s) is a variant of the growing perpetuity model and requires little more in terms of assumptions than that (a) dividends are expected to grow at a constant rate forever, (b) the required return exceeds the discount rate.*

*The CAPM (and, therefore, the SML) approach, on the other hand, is built on the work of Markowitz and Sharpe, and therefore requires assumptions of normality of returns and/or quadratic utility functions, as well as the absence of taxes, transactions costs, and other market imperfections.*

S14.14: Example – Cost of Equity

14.3THE COSTS OF DEBT AND PREFERRED STOCK

A.The Cost of Debt

S14.15: Cost of Debt and Example (2 pages)

Cost of debt (RD)—the interest rate on new debt can easily be estimated using the yield-to-maturity on outstanding debt or by knowing the debt's bond rating and looking up the rate on new issues of that rating.

Example:

If Pohl Corp. issued a 10-year bond 5 years ago with a coupon rate of 13% that currently sells for $1,075, what is Pohl's cost of debt?

Assuming annual interest, the yield-to-maturity that makes an annuity of $130 per period for 5 periods plus $1,000 face value in 5 periods have a PV of $1,075 is 10.97%.

*It is beneficial to re-emphasize the distinction between coupon rate, the current yield, and the yield-to-maturity (cost of debt) to the class. The first represents the firm's promise to pay, the second represents the income portion of total return, and the third is the relevant figure for the current discussion. Otherwise, some will have a tendency to simply select the coupon rate as the cost of debt. *

B.The Cost of Preferred Stock

To determine the cost of preferred stock, use the formula

RP = DP/P0

S14.17: Cost of Preferred Stock and Example (2 pages)

14.4THE WEIGHTED AVERAGE COST OF CAPITAL

A.The Capital Structure Weights

S14.19: The Weighted Average Cost of Capital and Capital Structure Weights (3 pages)

E—market value of the firm's equity (#shares common × price per share)

D—market value of the firm's debt (#bonds × price per bond)

V—combined market value of the firm's equity and debt, V = E + D

*Capital structure weights—E/V and D/V*

Perspectives:

*It may be helpful to mention and differentiate between the three types of weightings in the capital structure equation: book, market, and target. End-of-chapter problem 12 provides the opportunity to practice the calculation of book and market value weights. It may also be helpful to mention that the total market value of equity (the number of common shares outstanding times the current market price of a company's common share) measures the value of the three equity accounts (common stock, capital in excess of par value, and retained earnings) from the balance sheet.*

B.Taxes and the WACC

Aftertax cash flows require an aftertax discount rate. Letting TC stand for the firm's marginal tax rate:

WACC = (E/V) × RE + (D/V) × RD× (1 – TC)

S14.22: Taxes and the WACC

WACC—overall return the firm must earn on its assets to maintain the value of its stock.

*If the firm utilizes preferred stock in addition to common equity, equation 14.6 from the text should be modified as follows:*

WACC = (E/V) × RE + (D/V) × RD× (1 – TC) + (P/V) × RP

*where P/V represents the market value weight of preferred stock in the firm's capital structure (and, therefore, V = E + D + P), and RP is the cost of preferred stock as defined above.*

S14.23: Example 1 – WACC (3 pages)

C.Solving the Warehouse Problem and Similar Capital Budgeting Problems

*The warehouse problem employs the WACC as the discount rate in a NPV calculation. At least two assumptions are required for this to be precisely correct. First, it must be assumed that the warehouse has approximately the same risk characteristics of the firm as a whole. More importantly, it is assumed that the project will be financed (i.e., new funds will be raised) in the target proportions. In reality, firms rarely engage in simultaneous debt and equity financing. On the other hand, financial data suggest that, while financing is "lumpy", observed capital structures tend to fluctuate around a "norm" value, which is often assumed to be the target capital structure.*

S14.26: Cost of Equity, Debt and WACC Summarized (3 pages)

D.Performance Evaluation: Another Use of the WACC

14.5DIVISIONAL AND PROJECT COSTS OF CAPITAL

S14.29: Divisional and Project Costs of Capital

S14.30: Using WACC for All Projects – Example

A.The SML and the WACC

The WACC is the appropriate discount rate only if the proposed investment is similar to the overall business and only if financed with the same capital structure weights.

*Ask the class to consider a situation in which a company maintains a large portfolio of marketable securities. Now ask them to consider the impact this large security balance would have on a company's current and acid-test ratios and how this might impact the company's ability to meet short-term obligations. The students should easily remember that a larger liquidity ratio implies less risk (and less potential profit). Although the revenue realized from the marketable securities would be less than the interest expense on the company's comparable debt issues, these holdings would result in a lowering of the firm's beta and WACC. This example allows the student to recognize that the expected return and beta of an investment in marketable securities would be below the company's WACC, and justification for such investments must be considered relative to a benchmark other than the company's overall WACC. *

B.Divisional Cost of Capital

When a firm has different operating divisions with different risks, its WACC is an average of the divisional required returns. In such cases the cost of capital for different risks within the same firm needs to be established.

Perspectives:

*It may help students to distinguish between the average cost of capital to the firm and the required return on a given investment if the idea is turned around from the firm's point of view to one of an investor's. That is, consider an investor holding a portfolio of T-bills, corporate bonds and common stocks. Suppose there is an equal amount invested in each and further suppose that the securities have on average returned 5%, 10%, and 15% respectively. The average portfolio return will have been 10%. Now ask students if the investor should use the portfolio's average return of 10% to evaluate new security acquisitions, say T-bills offering 7% and common stocks expected to return 13%.*

C.The Pure Play Approach

Pure play—a company that has a single line of business. The idea is to find the required return on a near substitute investment.

*Point out that, although company betas can be easily found from such publications as Value Line or Merrill Lynch's "beta book," such publications do not provide betas of individual company divisions. A quick method to identify divisional betas might be to identify publicly-traded companies which are in similar lines of business or pure plays as the text discusses. The analyst could then average these betas and apply the average value to the division or new project to determine a risk-adjusted cost of capital. However, as the text discusses, firms often rely on "The Subjective Approach" because of the difficulty in objectively establishing discount rates for individual projects. *

S14.31: The Pure Play Approach

D.The Subjective Approach

S14.32: Subjective Approach and Example (2 pages)

Assigns investments to "risk" categories that have higher and higher risk premiums.

*The difficulty in arriving at an appropriate estimate of the cost of capital for project analysis is magnified for firms engaged in multinational investing. In Financial Management for the Multinational Firm, Abdullah suggests that adjustments to foreign project hurdle rates should reflect the effects of the following:*

1. foreign exchange risk

2. political risk

3. capital market segmentation

4. international diversification effects

*Making these adjustments requires a great deal of judgment and expertise, as well as an understanding of underlying financial theory. Most multinational firms find it expeditious to adjust hurdle rates subjectively, rather than attempting to quantify precisely the effects of these factors for each foreign project.*

14.6FLOTATION COSTS AND THE WACC

A.The Basic Approach

*Weighted average flotation cost (fA) —*sum of all flotation costs as a percent of the amount of security issued, multiplied by the target structure weights.

The multiplier 1/(1 – fA) is used to determine the gross amount of capital to be raised so after-flotation cost amount is sufficient to fund the investment.

B.Flotation Costs and NPV

If a project nominally requires an investment of $I before flotation costs, the procedure is to compute the gross capital requirement as I × 1/(1 –fA), and to use this figure as the investment cost in calculating the NPV.

Example:

Suppose Penultimate Paraprofessionals, Inc. is considering opening another office. The expansion will cost $50,000 and is expected to generate aftertax cash flows of $10,000 per year in perpetuity. The firm has a target debt/equity ratio of .50. New equity has a flotation cost of 10% and a required return of 15%, while new debt costs 5% to issue and has a required return of 10%.

Cost of capital:WACC = (E/V) × RE + (D/V) × RD × (1 – TC)

WACC = 2/3 × 15% + 1/3 × 10% × (1 – .34) = 12.2%.

Flotation costs: / fA = E/V × fE + D/V × fDfA = 2/3 × 10% + 1/3 × 5%

fA = 8.33%

NPV: / Investment = $50,000/(1 – .083) / = $54,526

PV of cash flow = $10,000/.122 / = $81,967

NPV = – $54,526 + $81,967 / = $27,441

*Some students will recognize that while new debt and equity issues would be subject to flotation costs, the retained earnings component of equity would not. The retention of these earnings does have a cost, but it would be lower than the cost of issuing new equity. The key point to make is that whenever external financing is used, there is an additional cost associated with that financing, and that cost is a relevant cash flow for capital budgeting purposes.*

S14.34: Flotation Costs, NPV and Example (3 pages)

14.7CALCULATING WACC FOR BOMBARDIER

See this section for a real-world WACC application.

14.8SUMMARY AND CONCLUSIONS

S14.37: Quick Quiz

S14.38: Summary

14AADJUSTED PRESENT VALUE

14BECONOMIC VALUE ADDED AND THE MEASUREMENT OF FINANCIAL PERFORMANCE

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