business Ethics & Financial Management homework assessments

BBA 3301, Financial Management 1

UNIT VIII STUDY GUIDE

Cost of Capital

Learning Objectives Upon completion of this unit, students should be able to:

1. Calculate the cost of debt capital. 2. Apply the CAPM to assessing the cost of equity capital. 3. Calculate the cost of equity capital using the Gordon Growth Model. 4. Develop the cost of capital for preferred equity. 5. Create a weighting schedule based on market value of securities. 6. Develop a model to measure the weighted average cost of capital.

Written Lecture The last unit in this course is dedicated to developing a measure of the cost of capital. The cost of capital is the average rate paid for the use of the firm’s capital funds. Capital refers to money acquired for use over a long period. The cost of capital provides a benchmark against which to evaluate investment returns. Projects should not be undertaken unless they return more than the cost of the funds invested in them. The cost of capital is used as the discount rate in net present value (NPV) analysis and also as a comparison point for the internal rate of return (IRR). From Unit VII recall the following rules supporting a capital investment decision:

 Project IRR exceeds the cost of capital

 Project NPV > 0 when calculated at the cost of capital A firm’s capital components include debt, common equity (stock) and preferred stock. Equity is the riskiest investment, earns the highest return, and has the highest cost. Debt is the safest investment, earns the lowest return, costs the firm less and is tax advantaged. Preferred stock offers investors intermediate risk and return levels and has a cost between that of equity and debt. Capital structure is the mix of the three capital components - generally expressed in percentages as seen below:

The above figure can be found in your textbook on page 559. Target capital structure is a mix of components that management considers optimal and strives to maintain. Additionally, management seeks to raise money

Reading Assignment Chapter 13: Cost of Capital

Key Terms 1. Cost of capital 2. Cost of debt 3. Cost of equity 4. Cost of preferred

stock 5. Flotation cost 6. Gordon model

(dividend discount model)

7. Investment opportunity schedule (IOS)

8. IRR 9. Marginal cost of

capital 10. NPV 11. Retained earnings 12. Risk premium 13. Weighted average

cost of capital (WACC)

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in the proportion of the capital structure. Thus, in cost of capital calculations, we assume money is raised in a constant proportion of debt, preferred and common equity. Investors provide capital by purchasing securities. Returns paid to investors adjusted for taxes and administrative expenses are the firm’s costs. A firm’s cost of capital is a weighted average of the costs of the three capital components where the weights reflect the $ amounts of each component in use. This is usually referred to in two ways:

 k, the cost of capital

 WACC, for weighted average cost of capital Example: Calculate the Weighted Average Cost of Capital (WACC) for the Following

Capital Component Value Cost

Debt $60,000 9%

Preferred Stock $50,000 11%

Common Stock $90,000 14%

$200,000 Below: First, calculate the component weights by dividing their individual dollar values by the total. For instance the weighting of Debt is $60,000/$200,000. Then, multiply the weight by cost to arrive at the last column. For example, .25 x 11% = 2.75% for preferred stock.

Capital Component

Value Weight Cost

Debt $60,000 30% 9% 2.70%

Preferred Stock $50,000 25% 11% 2.75%

Common Stock $90,000 45% 14% 6.30%

$200,000 WACC 11.75% WACC is expressed in terms of either book or market values of capital components. WACC is used to evaluate next year’s capital projects as the discount rate in NPV and PI. Also, it can be used as a hurdle mark for IRR. Market values are the appropriate basis for WACC. The formal steps in calculating WACC are as follows:

Step 1: Develop a market-value-based capital structure Step 2: Adjust market returns on the underlying securities to reflect the

costs of the underlying capital components Step 3: Combine in calculating the WACC

Example: Developing Market Value Capital Structure The ABC Corporation has the following capital situation. Debt: Two thousand bonds were issued five years ago at a coupon rate of 12%. They had 30-year terms and $1,000 face values. They are now selling to yield 10%. Preferred stock: Four thousand shares of preferred are outstanding, each of which pays an annual dividend of $7.50. They originally sold to yield 15% of their $50 face value. They're now selling to yield 13%. Equity: ABC has 200,000 shares of common stock outstanding, currently selling at $15 per share.

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Solution The price of ABC’s bonds in the market must be determined. We know the bonds have 25 years remaining until maturity, pay interest of $120 annually ($60 semi-annually) and are yielding 10% annually (5% semi-annually). Thus, each bond is selling for $1,182.55 in the market (per Bond Calculations earlier in Course). Since there are 2,000 bonds outstanding, the market value of debt is: $1,182.55 x 2,000 = $2,365,100. The firm's preferred stock represents a perpetuity that pays $7.50 annually and is yielding 13%. Thus, the value of each share of preferred stock is $7.50 / .13 = $57.69. The total market value of ABC’s preferred stock is: $57.69 x 4,000 = $230,760 Each share of ABC's common stock is trading at $15, thus the total market value of the firm's equity is: $15 x 200,000 shares = $3,000,000 Next summarize and calculate the component weights:

Debt $2,365,100 42.3%

Preferred Stock $230,760 4.1%

Equity (Common Stock)

$3,000,000 53.6%

$5,595,860 100.0% Calculating the Component Costs of Capital Begin with the market return received by new investors in each capital

component kd, kp, and ke . Cost of Debt Tax adjustment applies only to debt (Tax rate is T), Cost of debt = kd (1 – T). Debt, the cheapest source, is made even cheaper by tax adjustment. Flotation costs are a percentage of a security’s price (f). This is applied to preferred and new sales of common equity which increases effective cost. With flotation the costs are found with the following equation:

kp / (1 – f)

ke / (1 – f) Example: Cost of Debt Blackstone Inc. has 12% coupon rate bonds outstanding that yield 8% to investors buying them now. Blackstone’s marginal tax rate including federal and state taxes is 37%. What is Blackstone’s cost of debt? First notice that kd is the current market yield of 8%, not the coupon rate. To calculate the cost of debt we simply write equation 13.1 and substitute from the information given cost of debt = kd(1 - T) = .08(1 - .37) = 5.04%

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Cost of Equity The cost of common stock is not precise due to the uncertainty of future equity cash flows. The market return on common equity is estimated through three models:

 CAPM

 Gordon model

 Risk premium The CAPM Approach The sources of new common equity include retained earnings and newly sold stock. Retained earnings (RE) are not free because they belong to stockholders. No adjustments to the return on RE are necessary to calculate component cost of equity from RE. Payments to stockholders are not tax deductible to the firm. Thus, investor return on RE = Component cost of RE. The market return on a stock can be approximated by estimating the required or expected return using the CAPM’s SML (security market line):

kx = kRF + (kM - kRF) bX where: kX is the required return on stock X kRF is the risk-free rate (return on three-month T bills) kM is the return on the market or on an “average” stock (usually estimated through a market index like the S&P 500) bX is stock X’s beta, the measure of its market risk Example: Cost of RE using the CAPM The return on the Strand Corporation’s stock is relatively volatile as reflected by the company’s beta of 1.8. The return on the S&P 500 is currently 12% and is expected to remain at that level. Treasury bills are yielding 6.5%. Estimate Strand’s cost of retained earnings. Write equation 13.5 and substitute directly, using the return on the S&P 500 as kM and the treasury bill yield as kRF. cost of RE = kX kRF (kM kRF)bX = 6.5% (12% 6.5%)1.8 = 16.4% The Dividend Growth Approach (the Gordon Model) The Gordon model is used to calculate the intrinsic value of a stock. However, we can use the Gordon model to solve for the expected return by plugging in the current price of the stock.

The above figure can be found in your textbook on page 570. The Risk Premium Approach The relationship between the risks of debt and equity is fairly constant among firms. The incremental risk premium between debt and equity returns is similar for high-risk and low-risk firms. The return on a firm's equity can be estimated by

BBA 3301, Financial Management 5

adding 3 to 5 percentage points to the market return on its debt, if rpe is the

additional risk premium on equity: ke = kd + rpe The Cost of New Common Stock Firms often need to raise more equity than that generated by retained earnings. Equity from new stock is just like equity from RE, except it involves flotation costs. Market return estimates for RE must be adjusted for flotation costs to determine the cost of issuing new common stock. Use the Gordon model and insert (1- f) to recognize flotation cost (see below).

The above figure can be found in your textbook on page 572. Marginal Cost of Capital A firm's WACC is not independent of the amount of capital raised. The WACC typically rises as the firm raises more capital. The Marginal Cost of Capital (MCC) is a graph of the WACC, showing abrupt increases as larger amounts of capital are raised in a planning period. Breaks (jumps) in the MCC occur when cheap sources of financing are used up. The first increase in MCC usually occurs when the firm runs out of RE and starts raising external equity by selling stock. As debt increases the firm becomes riskier so lenders require higher interest rates. This causes further upward breaks in the MCC. See the following example for better explanation: Example: Marginal Cost of Capital

These figures can be found in your textbook on pages 573-574.

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Assume the business plan projects RE of $3,000,000 and note that capital structure is 60% equity. Since capital is raised in the proportions of the capital structure we ask $3M is 60% of what number? $3M / .6 = $5M

The above figure can be found in your textbook on page 575.

The investment opportunity schedule (IOS) is a plot of the IRRs of available projects arranged in descending order. The MCC and IOS plotted together show which projects should be undertaken. The firm's WACC for the planning period is at the intersection of the MCC and the IOS (see below).

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The above figure can be found in your textbook on page 576.