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