Introduction to Finance - Spring 06 - Evan Sekeris 1 Valuing Bonds and Stocks

Introduction to Finance - Spring 06 - Evan Sekeris 2 Bonds Terminology Bond - Security that obligates the issuer to make specified payments to the bondholder. Coupon - The interest payments made to the bondholder. Face Value (Par Value or Maturity Value) - Payment at the maturity of the bond. Coupon Rate - Annual interest payment, as a percentage of face value.

Introduction to Finance - Spring 06 - Evan Sekeris 3 Bonds WARNING The coupon rate IS NOT the discount rate used in the Present Value calculations.

Introduction to Finance - Spring 06 - Evan Sekeris 4 Bonds WARNING The coupon rate IS NOT the discount rate used in the Present Value calculations. The coupon rate merely tells us what cash flow the bond will produce. Since the coupon rate is listed as a %, this misconception is quite common.

Introduction to Finance - Spring 06 - Evan Sekeris 5 Bond Pricing The price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return.

Introduction to Finance - Spring 06 - Evan Sekeris 6 Bond Pricing Example What is the price of a 6.5 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 3.9%.

Introduction to Finance - Spring 06 - Evan Sekeris 7 Bond Pricing Example (continued) What is the price of the bond if the required rate of return is 6.5 %?

Introduction to Finance - Spring 06 - Evan Sekeris 8 Bond Pricing Example (continued) What is the price of the bond if the required rate of return is 15 %?

Introduction to Finance - Spring 06 - Evan Sekeris 9 Bond Pricing Example (continued) What is the price of the bond if the required rate of return is 3.9% AND the coupons are paid semi- annually?

Introduction to Finance - Spring 06 - Evan Sekeris 10 Bond Pricing Example (continued) Q: How did the calculation change, given semi-annual coupons versus annual coupon payments?

Introduction to Finance - Spring 06 - Evan Sekeris 11 Bond Pricing Example (continued) Q: How did the calculation change, given semi-annual coupons versus annual coupon payments? Time Periods Paying coupons twice a year, instead of once doubles the total number of cash flows to be discounted in the PV formula. Discount Rate Since the time periods are now half years, the discount rate is also changed from the annual rate to the half year rate.

Introduction to Finance - Spring 06 - Evan Sekeris 12 Bond Yields Current Yield - Annual coupon payments divided by bond price. BUT, current yield does not capture any capital gains or losses. If Bond Price > Face Value, bond sells at a premium. Overall return < current yield If Bond Price < Face Value, bond sells at a discount. Overall return > current yield.

Introduction to Finance - Spring 06 - Evan Sekeris 13 Price Path for Premium and Discount Bonds Price path for Premium Bond Price path for Discount Bond Today Maturity

Introduction to Finance - Spring 06 - Evan Sekeris 14 Bond Yields (contd.) Yield To Maturity - Interest rate for which the present value of the bond’s payments equal the price. Calculating Yield to Maturity (YTM=r) If you are given the price of a bond (PV) and the coupon rate, the yield to maturity can be found by solving for r.

Introduction to Finance - Spring 06 - Evan Sekeris 15 Bond Yields Example What is the YTM of a 10 % annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,

Introduction to Finance - Spring 06 - Evan Sekeris 16 Bond Yields WARNING Calculating YTM by hand can be very tedious. The calculation should be made either in Excel or by using the “IRR” or “YTM” or “i” functions on a financial calculator. You will not be required to calculate yields in this course.

Introduction to Finance - Spring 06 - Evan Sekeris 17 Risks of Holding Bonds There are two types of risks associated with holding bonds: Interest Rate risk: due to fluctuations in bond prices as interest rates vary. Default risk: due to risk of bankruptcy.

Introduction to Finance - Spring 06 - Evan Sekeris 18 Interest Rate Risk 30 yr bond 3 yr bond When the interest rate equals the 6.5% coupon rate, both bonds sell at face value

Introduction to Finance - Spring 06 - Evan Sekeris 19 Default Risk Credit risk Default premium Investment grade Junk bonds

Introduction to Finance - Spring 06 - Evan Sekeris 20 Default Risk

Introduction to Finance - Spring 06 - Evan Sekeris 21 Credit (or Yield) Spread on Bonds

Introduction to Finance - Spring 06 - Evan Sekeris 22 The Yield Curve Term Structure of Interest Rates - A listing of bond maturity dates and the interest rates that correspond with each date. Yield Curve - Graph of the term structure. The previous slide showed yield curves of three types of bonds. Reading: “The Living Yield Curve”.

Introduction to Finance - Spring 06 - Evan Sekeris 23 Stock Valuation A first attempt

Introduction to Finance - Spring 06 - Evan Sekeris 24 What is a Stock Price based on? Book value: value of net assets of a company. Liquidation value: what the company could net by selling its assets and repaying its debts. Market value: amount that investors are willing to pay per share.

Introduction to Finance - Spring 06 - Evan Sekeris 25 Valuing Common Stocks Expected Return - The percentage yield that an investor forecasts from a specific investment over a set period of time. Sometimes called the holding period return (HPR).

Introduction to Finance - Spring 06 - Evan Sekeris 26 Valuing Common Stocks The formula can be broken into two parts. Dividend Yield + Capital Appreciation

Introduction to Finance - Spring 06 - Evan Sekeris 27 Valuing Common Stocks Dividend Discount Model - Computation of today’s stock price which states that share value equals the present value of all expected future dividends. H - Time horizon for your investment.

Introduction to Finance - Spring 06 - Evan Sekeris 28 Blue Skies Value

Introduction to Finance - Spring 06 - Evan Sekeris 29 Valuing Common Stocks Example Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $ What is the price of the stock given a 12% expected return?

Introduction to Finance - Spring 06 - Evan Sekeris 30 Valuing Common Stocks Example Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $ What is the price of the stock given a 12% expected return?

Introduction to Finance - Spring 06 - Evan Sekeris 31 Valuing Common Stocks If we forecast no growth, and plan to hold out stock indefinitely, we will then value the stock as a PERPETUITY. Assumes all earnings are paid to shareholders.

Introduction to Finance - Spring 06 - Evan Sekeris 32 Valuing Common Stocks Constant Growth DDM - A version of the dividend growth model in which dividends grow at a constant rate (Gordon Growth Model). Given any combination of variables in the equation, you can solve for the unknown variable.

Introduction to Finance - Spring 06 - Evan Sekeris 33 Valuing Common Stocks Example What is the value of a stock that expects to pay a $3.00 dividend next year, and then increase the dividend at a rate of 8% per year, indefinitely? Assume a 12% expected return.

Introduction to Finance - Spring 06 - Evan Sekeris 34 Valuing Common Stocks Example- continued If the same stock is selling for $100 in the stock market, what might the market be assuming about the growth in dividends? Answer The market is assuming the dividend will grow at 9% per year, indefinitely.

Introduction to Finance - Spring 06 - Evan Sekeris 35 Valuing Common Stocks If a firm elects to pay a lower dividend, and reinvest the funds, the stock price may increase because future dividends may be higher. Payout Ratio - Fraction of earnings paid out as dividends Plowback Ratio - Fraction of earnings retained by the firm.

Introduction to Finance - Spring 06 - Evan Sekeris 36 Valuing Common Stocks Growth can be derived from applying the return on equity to the percentage of earnings plowed back into operations. g = return on equity X plowback ratio

Introduction to Finance - Spring 06 - Evan Sekeris 37 Valuing Common Stocks Example Our company forecasts to pay a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plow back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision?

Introduction to Finance - Spring 06 - Evan Sekeris 38 Valuing Common Stocks Example Our company forecasts to pay a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to blow back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision? No GrowthWith Growth

Introduction to Finance - Spring 06 - Evan Sekeris 39 Valuing Common Stocks Example - continued If the company did not plowback some earnings, the stock price would remain at $ With the plowback, the price rose to $ The difference between these two numbers ( =33.33) is called the Present Value of Growth Opportunities (PVGO).

Introduction to Finance - Spring 06 - Evan Sekeris 40 Valuing Common Stocks Present Value of Growth Opportunities (PVGO) - Net present value of a firm’s future investments. Sustainable Growth Rate - Steady rate at which a firm can grow: plowback ratio X return on equity.

Introduction to Finance - Spring 06 - Evan Sekeris 41 Can You Beat the Market? Be a Technical Analyst wiggle watchers Forecast stock prices based on the watching the fluctuations in historical prices (thus “wiggle watchers”)

Introduction to Finance - Spring 06 - Evan Sekeris 42 Can You Beat the Market?

Introduction to Finance - Spring 06 - Evan Sekeris 43 Random Walk Theory The movement of stock prices from day to day DO NOT reflect any pattern. Statistically speaking, the movement of stock prices is random (skewed positive over the long term).

Introduction to Finance - Spring 06 - Evan Sekeris 44 Random Walk Theory $ $ $ $ $97.50 $ $95.06 Coin Toss Game Heads Tails

Introduction to Finance - Spring 06 - Evan Sekeris 45 Random Walk Theory

Introduction to Finance - Spring 06 - Evan Sekeris 46 Random Walk Theory

Introduction to Finance - Spring 06 - Evan Sekeris 47 Random Walk Theory Last Month This Month Next Month 1,300 1,200 1,100 Market Index Cycles disappear once identified

Introduction to Finance - Spring 06 - Evan Sekeris 48 Perhaps now you can beat the market. Be a Fundamental Analyst Research the value of stocks using NPV and other measurements of cash flow

Introduction to Finance - Spring 06 - Evan Sekeris 49 Web Links for Bonds rate/index.html

Introduction to Finance - Spring 06 - Evan Sekeris 50 Web Links for Stocks