Review Bond Yields and Prices

Learning Objectives Calculate the price of a bond. Calculate major bond yield measures, including yield to maturity, current yield, coupon rate Account for changes in bond prices. Explain and apply the concept of duration. 2

Bond Valuation Principle Intrinsic value Is an estimated value Present value of the expected future cash flows Required to compute intrinsic value Expected future cash flows Timing of expected cash flows Discount rate, or required rate of return by investors 10

Bond Valuation Value of a coupon bond with semi-annual payments: Biggest problem is determining the discount rate or required yield Required yield is the current market rate earned on comparable bonds with same maturity and credit risk 11

Yield to Maturity Yield to maturity (YTM) Rate of return on bonds most often quoted for investors Promised compound rate of return received from a bond purchased at the current market price and held to maturity Equates the present value of the expected future cash flows to the initial investment Similar to internal rate of return 6

Yield to Maturity Solve for YTM (semi-annual coupons): Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM 7

Reinvestment Risk For: (1) longer-term bonds (2) bonds with higher coupon rates (i.e., have more money to reinvest) NO reinvestment risk for “Zeroes”

Bond Price Changes Over time, bond prices that differ from face value must change Bond prices move inversely to market yields The change in bond prices due to a yield change is directly related to time to maturity and inversely related to coupon rate 12

Measuring Bond Price Volatility: Duration Important considerations Different effects of yield changes on the prices and rates of return for different bonds Maturity inadequate measure of a bond’s economic lifetime A measure is needed that accounts for both size and timing of cash flows 14

Duration A measure of a bond’s lifetime, stated in years, that accounts for the entire pattern (both size and timing) of the cash flows over the life of the bond The weighted average maturity of a bond’s cash flows Weights determined by present value of cash flows 15

Calculating Duration Duration depends on three factors Need to time-weight present value of cash flows from bond Duration depends on three factors Maturity of the bond Coupon payments Yield to maturity 16

Duration Relationships Duration increases with time to maturity, but at a decreasing rate For coupon paying bonds, duration is always less than maturity For zero coupon-bonds, duration equals time to maturity Duration increases with lower coupons Duration increases with lower yield to maturity 17

Why is Duration Important? Allows comparison of effective lives of bonds that differ in maturity, coupon Used in bond management strategies, particularly immunization Measures bond price sensitivity to interest rate movements, which is very important in any bond analysis 18

Convexity Refers to the degree to which duration changes as the yield to maturity changes Price-yield relationship is convex Duration equation assumes a linear relationship between price and yield Convexity largest for low coupon, long-maturity bonds, and low yield to maturity 20

Duration Conclusions To obtain maximum price volatility, investors should choose bonds with the longest duration Duration is additive Portfolio duration is just a weighted average Duration measures volatility, which is not the only aspect of risk in bonds 21

Common Stock Valuation Review part 2 Common Stock Valuation Company Analysis

Learning Objectives The dividend discount model to estimate stock prices Explain the P/E ratio approach. Fundamental Analysis : estimate share’s intrinsic value

Present Value Approach DDM Intrinsic value of a security is Estimated intrinsic value compared to the current market price What if market price is different than estimated intrinsic value? 3

Required Inputs Expected cash flows Dividends paid out of earnings Earnings important in valuing stocks Retained earnings enhance future earnings and ultimately dividends Retained earnings imply growth and future dividends Produces similar results as current dividends in valuation of common shares 5

Dividend Discount Model Current value of a share of stock is the discounted value of all future dividends 6

Dividend Discount Model Problems: Need infinite stream of dividends Dividend stream is uncertain Must estimate future dividends Dividends may be expected to grow over time Must model expected growth rate of dividends and need not be constant 7

Dividend Discount Model Assume constant growth rate in dividends Dividends expected to grow at a constant rate, g, over time D1 is the expected dividend at end of the first period D1 = D0 x (1+g) 9

Dividend Discount Model Multiple growth rates: two or more expected growth rates in dividends Ultimately, growth rate must equal that of the economy as a whole Assume growth at a rapid rate for n periods, followed by steady growth 11

P/E Ratio Approach P/E ratio can be derived from To estimate share value P/E ratio can be derived from Indicates the factors that affect the estimated P/E ratio 17

Other Valuation Techniques Market-to-book ratio (M/B) Ratio of share price to per share shareholder’s equity as measured on the balance sheet Price paid for each $1 of equity Price-to-sales ratio (P/S) Ratio of company’s market value (price times number of shares) divided by sales Market valuation of a firm’s revenues 23

Company Analysis

P0 = estimated EPS  justified P/E ratio Fundamental Analysis Earnings multiple could also be used P0 = estimated EPS  justified P/E ratio Stock is under- (over-) valued if intrinsic value is larger (smaller) than current market price Focus on earnings and P/E ratio Dividends paid from earnings Close correlation between earnings and stock price changes 3

Required Rate of Return A function of the riskless rate of return and a risk premium k = RF + RP Constant growth version of dividend discount model can be rearranged so that k = (D1/P0) + g Growth forecasts are readily available 20

Required Rate of Return Risk premium for a stock regarded as a composite of business, financial, and other risks If the risk premium rises (falls), then k will rise (fall) and P0 will fall (rise) If RF rises (falls), then k will rise (fall) and P0 will fall (rise) Discount rates and P/E ratios move inversely to each other 21

Appendix 17-A Financial Ratio Analysis Five types of ratios used to analyze a firm: Liquidity: ability to generate cash and meet short-term debt Asset Management: ability to effectively manage its assets to generate sales and profits Debt Management: ability to effectively handle its debt Profitability: ability to generate profits Value: market value versus accounting values

DuPont Analysis XYZ (2004) Industry averages (2004) ROE = (NI/Sales) (Sales/TA) ((TA/Equity) = (.0299)(1.042)(4.339) = 13.51% Industry averages (2004) = (.0568)(1.23)(1.74) = 12.16% This analysis suggests that XYZ displays an above average ROE due to its higher leverage factor, and despite the fact it has below average profitability and asset turnover