# Valuing New Bonds

## Valuing New Bonds

 Adjusting Bond Valuation for New Issue Fees You learned how to value a basic bond in Chapter 8 The difference here is that the company is considering a issue of new bonds. There are costs involved in issuing bonds You will need to adjust the price of the new issue by subtracting the issuing fees. Example A firm can sell a 20-year, \$1000 par value, 9% bond for \$980. A flotation cost of 2% of the face value would be required in addition to the discount of \$20. Compute the rate of this bond. Note: The \$20 discount has already been added. The discount is what brought the price down from \$1000 to \$980. Debt NPER 20 <

## Valuing Stock

 Stocks Valuing Common Stocks – Examples and Practice Preferred Stocks The Constant (Gordon) Growth Model: Cost of Stock (RATE) = (D1 / P ) + g You should know that most companies do not issue preferred stock. Note: This method ONLY works for stock with dividends that are expected to grow at a constant rate However, you still need to learn how to value it. The firm’s common stock is currently selling for \$40 per share. The dividend The good part is that it is very easy to calculate. expected to be paid at the end of the coming year is \$5.07. Its dividend payments have been Because preferred stock receives a fixed periodic dividend – it is calculated like a perpetuity growing at a constant rate for the last five years. Five years ago, the dividend was \$3.45. It is expected that to sell, a new common stock issue must be underpriced at \$1 per share and the firm <<<<<<< Note: Just like the new issue of bonds, when a problem Cost/RATE = Dividend / Price must pay \$1 per share in flotation costs. gives you costs for a new issue of stock, you will need Price = Dividend / RATE Calculate the cost (RATE) of the new issue of preferred stock to subtract the cost from the price of the stock. Common Stock Common Stock Computing Growth Rate The value of a share of stock is equal to the PV of all future cash flows (dividends) Price \$40 NPER 5 Computing the Gordon Growth Model Equation for Yield/Cost/Rate of Stock Shareholders can earn capital gains if they sell their stock for more than the purchase price but, D1 \$5.07 RATE ? Cost of Stock = (D1 / P ) + g what the stockholder really pays for is the right to all future dividends g 8% PV -3.45 (5.07 / 38) + 8% = 21.34% Stock valuation equations measure stock value at a point in time based on expected risk and return. Cost/share \$2 PMT 0 Note: You were given the expected dividend (D1) in this problem. The textbook mentions several methods for valuing stock – you need to be aware of all of the various methods Adj. Price \$38 FV 5.07 The expected or future dividend is used in the formula. However, in the assignments and exams, we will concentrate on the most widely used approach, The Constant-Growth Model CPT ? 8.00% Always read the problem carefully to determine if it gives you the and the Capital Asset Pricing Model (CAPM) expected or the current dividend. If you are given the current You can use excel to calculate both models, however there are no excel formulas that do it automatically, so you have to enter the exact equations. dividend, it will need to be adjusted. (See note below) The constant-growth model is also called the Gordon Growth Model Calculating the Price of the Stock Calculating the RATE of the stock The Gordon Growth Model: Current Price of Stock = D1 / (r – g) P0 = D1 / (rs – g) rs = (D1 / P0) + g The Bradshaw Company’s most recent dividend was \$6.75. The historical dividend payment Expected dividend divided by (rate – growth rate) Expected dividend divided by price plus the growth rate by the company shows a constant growth rate of 5% per year. If the required rate of return is 8%, what is the price of the stock. In most of the constant-growth model problems, you are not given the growth rate of the dividends – you must calculate that yourself So, before you can work the Gordon Growth Model – you need to calculate the growth rate with the excel RATE formula Common Stock Computing the Gordon Growth Model Equation for Value/Price of Stock Once you get the growth rate calculated, you can then work the equation Price ? Price of Stock = D1 / (r – g) One other thing to be aware of is the dividend you are given in the problem D1 6.75 * (1 + g) = 6.75 * (1 + 5%) / ( 8% – 5%) The gordon growth model uses the Expected Dividend (D1), so if the problem gives you the expected or future dividend then you are good to go Cost of Stock 8.00% = 7.0875 / (3%) However, if the problem gives you the current dividend (D0), then you will need to multiply that by (1 + g) to get the expected dividend (D1) growth rate 5.00% 236.25 Note: You were given the current dividend (D0) in this problem, since you need the expected dividend in the formula, The Capital Asset Pricing Model for valuing stock quantifies the relationship between risk and return you will needed to multiply the 6.75 by (1 + g) to convert the D0 to D1. When a question gives you the beta of a share of common stock, this is a signal that you will need to use the CAPM equation Rs = RF + (b * (rm – RF)) Note: The extra parenthesis in this equation are for Excel The Capital Asset Pricing Model (CAPM) Rs = RF + (b * (rm – RF)) or kp = krf + (km – krf) x b They tell Excel to calculate the Market Risk Premium (rm-RF) first, then multiply by beta, then add the RF Note: This method is used to calculate the required rate of return of an investment given its degree of risk. Note the part of the formula in the parenthesis: (rm – RF), this is called the Market Risk Premium Note: The two formulas are the same, just stated a little different. When entering the formula in excel, you will need to add the extra parenthesis so excel knows which The Market Risk Premium (rm – RF) is different from the Market Return (rm) order to compute the components. The reason I am pointing this out is because sometimes a problem will give you the Market Risk Premium Assume the risk-free rate is 5%, the expected rate of return on the market is 15%, and the beta of your firm is 1.2. instead of the Return on Market (rm). Given these conditions, what is the required rate of return on your company’s stock? When this happens, you need to know that there is no need to subtract the risk free rate from the market return because this part of the equation has already been calculated for you. Computing the CAPM Required Rate of Return: Rs = RF + (b * (rm – RF)) = 5% + (1.2 * ( 15% – 5%)) <<

## Part 1 – WACC

 PART 1 A – COMPUTING A WEIGHTED AVERAGE COST OF CAPITAL (WACC) A firm has determined its optimal capital structure, which is composed of the following sources and target market value proportions: Source of Capital Target Market Proportions Long-term debt 60% Preferred stock 5% Common stock equity 35% Debt: The firm can sell a 15 year bond, compounded monthly, with a \$1000 par value and 6.8% coupon rate for \$1254. A flotation cost of 1.15% of the face value would also be required. Preferred Stock: The firm has determined that it can issue preferred stock at \$125 per share par value. The preferred stock wil pay a \$6.75 per share annual dividend. The cost of issuing and selling the preferred will be \$3.28 per share. Common Stock: The firm’s common stock is currently selling for \$23.75per share. The firm will be paying a dividend of \$5.25 at the end of the year. Its dividend payments have been growing at a constant rate for the last five years. Five years ago, the dividend was \$3.25. For a new issue of common stock to sell, it has been determined that the new issue would need to be underpriced at \$1.50 per share and that the firm must pay \$1.20per share in flotation costs. The firm’s marginal tax rate is 21%, plus 4% for state and local taxes. (ISTR = 25%) To determine the firm’s WACC, please complete the following steps, entering your formulas in the blue cells: 1A-A A. Calculate the rate for the bond, notice is has monthly compounding. 1A-B B. Calculate the after-tax cost of the bond. 1A-C C. Calculate the cost of the new issue of preferred stock. 1A-D D. Calculate the growth rate of the common stock dividends. 1A-E E. Calculate the cost of the new common stock issue. 1A-F F. Finally, calculate the firm’s weighted average cost of capital assuming the firm has exhausted all retained earnings. Standard formats for your calculations: Common Stock Preferred Stock Inputs Debt Growth Rate Price NPER NPER New Issue Costs Coupon Price PV Adjusted Price Coupon Rate FV Dividend PMT RATE = Mkt Price Formula Inputs WACC Market Rate Price Proportions Costs Amount FV New Issue Costs Compounding periods Adjusted Price RATE= D1 g TOTAL >> PART 1 B- CAPITAL BUDGETING The same firm as in Part 1 is considering the investment of two independent projects, X and Y, which are described below. Please do not assume anything. Use the firm’s WACC which you just calculated to evaluate the projects. Cost of Capital>> Year PROJECT X PROJECT Y A. Calculate Payback Period for both projects For the Payback Period Calculation Cash Inflows B. Calculate NPV for both projects Cash End of Year Balances Initial Investment (\$11,050,000) (\$11,250,000) 0 C. Calculate PI for both projects PROJECT X PROJECT Y Year 1 \$3,500,000 \$5,500,000 1 D. Calculate IRR for both projects 1 2 \$3,500,000 \$5,800,000 2 E. Which project should the firm accept?  Why? 2 3 \$5,800,000 \$2,900,000 3 3 4 \$5,800,000 \$1,950,000 4 4 Please enter your formulas in the blue cells: 1B-A A. Payback 1B-B B. NPV 1B-C C. IRR 1B-D D. MIRR 1B-E E. Accept projects>>> Yes or No Yes or No Why?: End of Part 1

## Part 2 – CAPM

 PART 2 – COMPUTING WACC WITH CAPM This problem has NO relation to the problem in Part 1 The current risk-free rate is 5.51% and the market is expected to return 7.55% per year.  The company’s beta is 1.57. The company expects to pay 4.9% for its debt. the target capital structure for the company is 35% equity and 65% debt. The marginal tax rate is 21% plus 4% for state and local taxes (ISTR = 25%). CAPM Inputs A. What is the after-tax cost of debt? rF B. What is the cost of equity? rM C. Calculate the WACC. Beta Cost/Debt ISTR 2-A Answer A Capital Structure 2-B Answer B Debt 2-C Answer C Equity WACC Total>> End of Part 2
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