Bonds and Common Stock

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1 Bonds and Common Stock

2 Bonds 2/22

3 Yield-To-Maturity Yield-To-Maturity (YTM) is the discount rate at which the sum of all future cash flows from the bond (coupons and principal) equal the price of the bond. Alternatively, the YTM is the Internal Rate of Return (IRR) earned by an investor who buys the bond today at the market price when assuming that the bond will be held until maturity and that all coupon and principal payments will be made on schedule. Remember if: Coupon rate < YTM bond is selling at discount Coupon rate > YTM bond is selling at premium Coupon rate = YTM bond is selling at par 3/22

4 Present Value of Bonds P V = c 1 (1 + r) 1 + c 2 (1 + r) c T + principal (1 + r) T (1) 4/22

5 Example 1 If today is October 1, 2016, what is the value of the following bond? An IBM Bond pays $115 every September 30 th for 5 years. In September 2021 it pays an additional $1,000 and retires the bond. The bond is rated AAA with a YTM of 7.5%. P V = 115 (1.075) (1.075) (1.075) , (1.075) 4 (1.075) 5 = $1, /22

6 Example 2 In December 2015, Christian purchased e100 of bonds in France which pay a 8.5% coupon every year. If the bond matures in 2019 and the YTM is 3.0%, what is the value of the bond? P V = 8.50 (1.03) (1.03) (1.03) 3 (1.03) 4 =e /22

7 Example 3 In February 2015, John purchased a 2-year US Government bond. The bond has an annual coupon rate of 4.875% that is paid semi-annually. If investors demand a 2% semiannual return, what is the value of the bond? P V = (1.02) (1.02) , (1.02) 3 (1.02) 4 =$1, /22

8 Example 4 In February 2015, Anne purchased a 2-year US Government bond. The bond has an annual coupon rate of 4.875% that is paid semi-annually. If investors demand a 4% semiannual return, what is the value of the bond? P V = (1.04) (1.04) , (1.04) 3 (1.04) 4 =$ /22

9 Duration Duration = 1 P V (c 1) V + 2 P V (c 2) V + + T P V (c T ) V (2) 9/22

10 Example Year Ct PV(Ct) at 5.0% Proportion of Total Value [PV(Ct)/V] Proportion of Total Value Time V = Duration= years 10/22

11 Bond Ratings 11/22

12 Common Stock 12/22

13 Common Stock Companies, governments or public sector institutions can obtain funds through the sale of either bond issues or new stock. This is typically done through an investment bank. Common stock: ownership shares in a publicly held corporation. Primary market: market for the sale of new securities by corporations. Secondary market: market in which previously issued securities are traded among investors (for example, New York Stock Exchange, London Stock Exchange, Nasdaq). Exchange-Traded Funds (ETFs): portfolios of stocks that can be bought or sold in a single trade. There exist index ETFs, stock ETFs, bond ETFs etc. 13/22

14 Valuation of Common Stock Book value: total assets - intangible assets (patents, goodwill) - total liabilities. Dividends: periodic cash distribution from the firm to the shareholders. P/E Ratio: share price divided by earnings per share. Market value: # of shares outstanding share price. 14/22

15 Discounted Cash Flow The Discounted Cash Flow formula computes today s share price as the present value of all expected future cash flows. P 0 = div 1 (1 + r) 1 + div 2 (1 + r) div T + sp T (1 + r) T (3) 15/22

16 Example 1 Fledgling Electronics is forecasted to pay a $5.00 dividend at the end of Yr 1 and a $5.50 dividend at the end of Yr 2. At the end of Yr 2, the stock will be sold for $121. If the discount rate is 15%, what is the price of the stock? P V = (1.15) 1 (1.15) 2 = $ /22

17 Example 2 Current forecasts are for Apple to pay dividends of $3.00, $3.24 and $3.50 over the next three years, respectively. At the end of three years, John anticipates selling his stock at a market price of $ What is the price of the stock given a 12% expected return? P V = 3.00 (1.12) (1.12) 2 (1.12) 3 = $ /22

18 Return on Equity Return on Equity = ROE = Earnings Per Share Book Value of Equity Per Share (4) 18/22

19 Dividend Growth Rate g = ROE plowback ratio (5) where g is the dividend growth rate that is derived from applying the ROE to the percentage of earnings plowed back into operations. Payout ratio: fraction of earnings paid out as dividends. Plowback ratio: fraction of earnings retained by the firm. Therefore, if a firm elects to pay a lower dividend, and reinvest the funds, the share price may increase because future dividends may be higher. 19/22

20 Dividend Yield The dividend yield is the expected return on a stock plus the expected growth in dividends. That is, r = div 1 p 0 + g. (6) Alternatively, a handy formula is the following p 0 = div 1 r g. 20/22

21 Example Ford forecasts to pay a $8.33 dividend next year, which represents 100% of its earnings. This will provide investors with a 15% expected return. Instead, the chief financial officer of Ford decides to plowback 40% of the earnings at the firm s current return on equity of 25%. What is the value of the stock before and after the plowback decision? 21/22

22 Example (Cont.) Ford forecasts to pay a $8.33 dividend next year, which represents 100% of its earnings. This will provide investors with a 15% expected return. Instead, the chief financial officer of Ford decides to plowback 40% of the earnings at the firm s current return on equity of 25%. What is the value of the stock before and after the plowback decision? No Growth p 0 = div 1 r g = = $55.53 With Growth p 0 = g = = = $ /22

Review Class Handout Corporate Finance, Sections 001 and 002

. Problem Set, Q 3 Review Class Handout Corporate Finance, Sections 00 and 002 Suppose you are given a choice of the following two securities: (a) an annuity that pays $0,000 at the end of each of the