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## CORPORATE FINANCE

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**CORPORATE FINANCE**Slide Set 3: Basic Approaches to Stock and Bond Valuation**The Discounted Cash Flow Approach to Valuation**• Estimate The Size And Timing Of Future Cash Flows • Determine The Required Rate Of Return or Discount Rate For Each Cash Flow. • Based on current interest rates, and the riskiness of the cash flow; • Different Discount Rates May Be Appropriate For Different Cash Flows • Discount Each Cash Flow To Present • Sum The Present Values Of The Cash Flows.**First, Bond Valuation. The terminology:**• Par or Face Value (F); The Bond promises to pay its face value at the Maturity Date. • Coupon Interest. The bond makes interest payments at a rate of C per year, with actual payments of C/2 every six months. C/F is defined as the coupon interest rate. Note that the coupon rate is constant over the life of the bond. • Call Provision; Call Protection; Call Premium • Default Risk • Discount Rate, r. • This changes day to day. • Yield to maturity. The discount rate that equates the bond’s promised payments to its observed price, V. • Current yield: C/V.**Bond and Stock Valuation**• Last Time: • Time value examples • Introduction to bond pricing • This Time: • Bond valuation • Common Stock valuation**Valuing a semiannual coupon bond**• Valuation of a semiannual coupon bond with annual coupon payment C, maturity value of F, N years to maturity, and annual discount rate r. • Two components. • The coupon payments comprise an annuity. • Lump sum payment of face value at maturity**N-1**1 2 N 0 C/2 C/2 C/2 C/2 C/2 C/2 C/2 C/2 F Value of a semiannual coupon bond • Two Pieces: • Annuity of C/2 for 2N periods. • Lump sum of F received at the end of 2N periods. Technical note: Here r is the stated annual discount rate, but we are implicitly using semiannual compounding.**Bond Pricing Example**• Dupont issued 30-year bonds with a coupon rate of 7.95%. These bonds currently have 28 years remaining to maturity and are rated AA. Newly issued AA bonds with similar maturities are currently yielding 7.73%. The bonds have a face value of $1000. What is the value of a Dupont bond today?**Bond Example (continued)**• Annual coupon payment=0.0795*$1000=$79.50 • Semiannual coupon payment=$39.75 • Semiannual discount rate=0.0773/2=0.03865 • Number of semiannual periods=28*2=56**Bond Example (calculator)**• Annual coupon payment=0.0795*$1000=$79.50 • Semiannual coupon payment=$39.75 • Semiannual discount rate=0.0773/2=0.03865 • Number of semiannual periods=28*2=56 • Face value=1000 • So, enter N=56, I/YR=3.865 (the semiannual rate because you’re tricking the calculator), FV=1000, PMT=39.75 and hit PV to get –1025.06, which is what we got before.**Bond Prices And Interest (Discount) Rates**• When The Discount Rate Is Equal To The Coupon Rate The Bond Will Sell At Par • When The Discount Rate Is Above The Coupon Rate The Bond Will Sell At A Discount To Par • When The Discount Rate Is Below The Coupon Rate The Bond Will Sell At A Premium To Par • At The Instant Before Maturity The Bond Will Sell At Par • The price does not include accrued interest (see 3020 for details) • What Feature Of A Bond Is The Primary Determinant Of Its Price Sensitivity To Interest Rates?**Bond Prices and Time to Maturity**Discount Rates What is the coupon rate?**Bond Prices and Interest (Discount) Rates**Years to maturity What is the coupon rate? Why is the long maturity bond more volatile?**Volatility of long vs. short bonds**• Take two 10% bonds with semiannual coupons, one with a 10 year life and the other with a 5 year life. • Find the prices of each at 8, 10, and 12% interest. • At r=8% (simple): P10=1135.90, P5=1081.11 • At r=12%: P10=885.30, P5=926.40 • The reason that payments far in the future are affected a lot by interest rate changes due to the compounding effect. • This is related to a measure called Duration which measures the sensitivity of bond prices to changes in interest rates. It is (recall economics) an elasticity. • More on duration in FNCE4030**Yield To Maturity/Call**• The Yield To Maturity Is The Discount Rate That Equates The Bond’s Current Price With Its Stream of Promised Future Cash Flows. • The Yield To Call Is The Discount Rate That Equates the Bond’s Current Price With Its Stream of Promised Cash Flows until the expected Call Date. • Given two bonds equivalent in all respects except that one is callable, the non-callable bond will have a higher price.**Yield to Maturity Example**• On 9/1/95, PG&E bonds with a maturity date of 3/01/25 and a coupon rate of 7.25% were selling for 92.847% of par, or $928.47 each. What is the YTM on these bonds? • Semiannual coupon payment = 0.0725 * $1000/2 = $36.25 • number of semiannual periods =30*2-1=59**Yield to Maturity Example (cont.)**• r/2 can only be found by trial and error or calculator. • Here, on the calculator, N=59, PV=928.57, PMT=36.25, FV=1000, • I, is the YTM, which in this case is • r/2 which equals 3.939%, so that r is 7.877%. • This simple interest rate is with half-year compounding interval yields an EAR of: (1.03939)2 - 1 = 8.03%.**YTM (calculator)**• To find YTM, you essentially do the same calculation we did for the bond price, but here, we know the price, and it is the YTM that we are solving for,**Preferred Stock Valuation**• Preferred Stock • fixed dividend payment • preferred dividends can be omitted without placing the firm in bankruptcy • no maturity date • Does preferred stock have the same risk as the firm’s debt? • Preferred stock looks like a perpetuity**Preferred Stock Valuation**• Preferred stock is typically valued as a perpetuity. Given the promised dividend payment, Divp, and the discount rate, rp, the value of a share of preferred stock is:**Preferred Stock Example**• Example • On 8/24/95 Sears preferred stock had a dividend of $2.22 per share and was selling at $26.25 per share. What rate of return were investors requiring on Sears preferred stock?**Common Stock Valuation**• DCF techniques can be implemented either by • discounting the forecasted dividend stream, or • by discounting future flows to equity. • The important issues for valuation are • inherent ability to generate cash flows • riskiness of the cash flows. • This will have implications for the dividends.**Common Stock Valuation Terminology**• Dt =dividend per share of stock at time t • P0=market price of the stock at time 0. • Pt=market price of the stock at time t. (Prior to date t, this would be the expected price). • g=expected growth rate in dividend payments • rs=required rate of return • D1/P0=dividend yield during period 1. • [P1 - P0]/P0= capital gain rate during period 1.**The Dividend Discount Model**• The return on a share of stock is given by: • That is, it is the percentage dividend plus the price appreciation. • Let rs denote the expected return required by investors, i.e., the appropriate discount rate. Then,**Stock Valuation: substituting out P**• We need to get rid of the expected future price in our formula. What determines P1? • An investor purchasing the stock at time 1 and holding it until time 2 would be willing to pay: • Substituting into the equation for P0, the price at time zero is:**Common Stock Valuation (continued)**• Repeat this process H times and we have: • If we continue to apply the same logic (let H go to infinity), we get: • The current market value of a share of stock is the present value of all its expected future dividends!**Usefulness of the Formula**• So far, we have a fairly useless representation. We’ve just said that an asset’s price should be the discounted sum of its cash flows. • Now, we’ll start with strong unrealistic assumptions to use the formula and then relax the assumptions to get a more practical formula (one you might actually be able to use).**Stock Valuation if Dividends display constant growth**(forever) • If the dividend payments on a stock are expected to grow at a constant rate, g, and the discount rate is rs, the value of the stock at time 0 is: • g must be less than rs to use this formula • If g=0 then the formula reduces to the perpetuity formula**Example**• Geneva steel just paid a dividend of $2.10. Geneva’s dividend payments are expected to grow at a constant rate of 6%. The appropriate discount rate is 12%. What is the price of Geneva Stock? • D0 = $2.10 D1 = $2.10(1.06) = $2.226**Estimating the Required Return from the Price.**• We are focusing on valuation - determination of the price. • Suppose you observe a price that you consider reliable, and instead wish to infer the required return, rs. Rearrange the constant growth valuation formula to obtain: rs = D1/ P0 + g. Example: US East stock currently sells for $22. Its most recent dividend was $1.50, and dividend growth of 6% is expected. D1 = 1.50*1.06 = 1.59 rs = 1.59/22 + .06 = .0723 + .06 = 13.23%**Back to Valuation. Estimating the growth rate.**• A starting point for estimating the growth rate is to assume: • (1) The firm’s ROE is constant over time and across projects. ROE = net income/stockholder’s equity. • (2) The proportion of the firm’s income paid as dividends is also constant. • (3) The firm will have no future financing. • Remark: ROE is not the same as the required rate of return on the stock. • It’s related to the return on a firm’s projects • The required rate of return on the stock can be higher or lower. • For example, if a firm has good projects, its current price gets bid up and the stock return can be lower than the ROE**2/5/01 Lecture**• Last Time: • Application of time value techniques to bond pricing • Use of the annuity formula • Application of time value techniques to preferred stock pricing. • Introduction to common stock pricing • This Time: • Continuation of stock pricing • Comparison of NPV and alternative project valuation techniques such as • IRR • Payback • Etc.**Back to Valuation. Estimating the growth rate.**If assumptions (1) - (3) are met, then • Then, income and dividends will both grow at the same rate as owner’s equity, and owners equity will grow only due to retained earnings. • The growth rate will be ROE(1 - d), where d is the dividend payout ratio (proportion of earnings paid out). • This growth doesn’t necessarily mean that the firm is doing well. The growth rate is higher when dividends are smaller. • Be cautious about using this technique in cases where the assumptions may be way off base!**Common Stock Valuation Example: Sears**• As of (very) early 1996, • ROE = 13%, d = 45%, • implying g = .13(1-.45) = .0715. • 1995 dividend was $1.64, • so D1 = 1.64(1.0715) = 1.757. • Assuming rs = .11, we have P0 = D1/(rs - g) P0 = 1.757/(.11 - .0715) = $45.64. (The actual share price was $45)**Stock Valuation Based on Dividends, with Nonconstant Growth**• Firms often go through life cycles • Fast growth • Growth that matches the economy • Slower growth or decline. • A supernormal growth stock is one experiencing rapid growth. But, supernormal growth is generally only temporary.**Valuation of Nonconstant Growth Stocks**• Find the present value of the dividends during the period of rapid growth. • Project the stock price at the end of the rapid growth period. This will be the discounted value of the subsequent dividends. Discount this price back to the present. • Add these two present values to find the intrinsic value (price) of the stock.**Example**• Batesco Inc. just paid a dividend of $1. The dividends of Batesco are expected to grow by 50% next year (year1) and 25% the year after that (year 2). Subsequently, Batesco’s dividends are expected to grow at 6% per year in perpetuity. • The proper discount rate for Batesco is 13%. • What is a fair price for a share of Batesco stock?**0**1 2 3 4 g=50% g=25% g=6% g=6% ...... 1.50 1.875 1.9875 2.107 Example (continued) • First, determine the dividends. • D0=$1 g1=50% • D1=$1(1.50)=$1.50 g2=25% • D2=$1.50(1.25)=$1.875 g3=6% • D3=$1.875(1.06)=$1.9875**Example (continued)**• Supernormal growth period: • Constant growth period. Value at time 2: • discount to time 0 and add to Ps:**What About Stocks That Pay No Dividends?**• If investors value dividends, how much is a stock that pays no dividends worth? • A stock that will literally never pay dividends in any form, has a value of zero. • In actuality, a company that has not paid dividends to date can be worth a lot, if the company has good investment projects or it has assets that can be liquidated. • McDonald’s started in the 1950's but paid its first dividend in 1975. The market value of McDonald’s stock was in excess of $1 billion prior to 1975.**What About Stocks That Pay No Dividends - Continued**Consider Internet Stocks. • In early February 2000, Yahoo.com had a price of 185 1/8 (split adjusted). • Yet its were only 10 cents a share. • It pays no dividends • What’s going on? • Is this just the next McDonalds? • Ans: maybe not. Yahoo closed on 1/30/01 at 39 11/16. It had earnings of $0.43 per share and a P/E of 83.**What do firms actually do?**• Even firms that have been paying dividends for a long time don’t actually pay out a constant fraction of their earnings to shareholders. • They appear to adopt policies such that dividends mostly remain unchanged, but changes are usually increases. • An implication is that dividend cuts are really bad news. • Pettit finds that dividend decreases (1-99%) produce losses of 8% on average, while dividend increases produce gains of about 2% on average. Large increases (10-25%) produce gains averaging 4% • Asquith and Mullins find initial dividend announcements are accompanied by price increases of about 4%.**2/7/01**• Last Time: • Estimating the discount rate using past data on ROE, retention ratio, and prices. • Dividend discounting with nonconstant growth • This Time: • Valuing operations instead of dividends • P/E ratios • NPV vs. Alternative project selection rules**Valuing Operations Instead of Dividends**• Stocks can be(and often are) valued based on earnings and/or operating cash flows instead of dividends. • Both are used in practice, although surveys of corporate executives suggest that valuation of earnings is more pervasive (about a 3:1 split) • What we will show next is • How to value stocks using cash flow data. • The equivalence of the dividend discount model and the “earnings multiple” model.**Notation**• OCF: operating cash flow after taxes. • F: the net cash flow to the firm from financings (new debt and equity issues less any debt repaid or equity repurchased). • I: net new capital investment taken by the firm (count any increases in the cash balance as capital investment). • Then, because the cash flow identity says that dividends are Dt = OCF t + F t - I t, • We can value the firm by discounting future operating cash flows, financing flows, and requisite capital investments instead of dividends.**Valuing Operations Instead of Dividends (Cont.)**• Let NPVGO be the NPV of the firm’s future investments. • This is the present value of the operating cash flows those investments will create less the present value of the capital outflows that will be required. • Let NPVF be the NPV of the firm’s future financing transactions. This is the present value of the proceeds from financings less the present value of the resulting obligations --- interest and principal for debt, dividend dilution for equity (a good starting point is NPVF=0). • Let PVA denote the present value of the future cash flows from the firms existing assets. • Let PVL denote the present value of the future cash flows associated with the firm’s existing liabilities. • These should each be stated on a per share basis if we want the price per share.**Valuing Operations Instead of Dividends (Cont.)**• The following valuation approach is equivalent to the discounted dividend approach: P0 = PVA - PVL + NPVGO + NPVF • Even though it does not directly involve dividend projections at all! • Both this formula and the dividend discount formula take the NPV of the firm’s cash flows, so both formulas must generate the same price!**Connection to RWJ chapter 5**• Our formula: P0 = PVA - PVL + NPVGO + NPVF • How does this relate to RWJ? • They assume no future financings. (More generally, NPVF = 0 is probably a good first approximation). • They assume no existing debt, so PVL = 0. • They assume that existing assets pay a perpetuity in the amount of EPS per period. So, PVA = EPS/rs. So, with their special restrictions, we have: P0 = EPS/rs + NPVGO.**0**1 2 3 4 ...... 1 million 1 million 1 million 1 million XCORP EXAMPLE • Suppose that Xcorp’s current assets produce net cash flows of $1 million per year in perpetuity. The discount rate for Xcorp is 15%. • What is the market value of Xcorp?**0**1 2 3 4 ...... 0 million 0 million 0 million 1.75 million XCORP EXAMPLE (continued) • Now suppose that Xcorp has an R&D project that will require cash infusions of $1 million in each of the next three years. Subsequently, the project will generate additional cash flow of $0.75 million per year in perpetuity. Xcorp=s net cash flow with the project is shown below. • What is the market value of Xcorp with the project?**0**1 2 3 4 ...... 1 million 1 million 1 million 1 million 0 1 2 3 4 ...... -1 million -1 million -1 million 0.75 million XCORP EXAMPLE (continued) • Xcorp’s cash flow can be divided up into two pieces: • The cash flow from current assets • Plus the cash flows from the new project