BOND VALUATION. YTM Of An n-year Zero-Coupon Bond

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1 BOND VALUATION BOND VALUATIONS BOND: A security sold by governments and corporations to raise money from investors today in exchange for promised future payments 1. ZERO COUPON BONDS ZERO COUPON BONDS: A bond that does not make coupon payments Although the bond pays no interest directly, as an investor you are compensated for the time value of your money by purchasing the bond at a discount to its face value EG: TREASURY BONDS: US government bonds with a maturity of up to one year Zero-coupon bonds Price Of Zero-Coupon Bond FV P 0 = (1 + r n ) n YTM Of An n-year Zero-Coupon Bond YTM n = ' FV P + 1 n 1 RISK-FREE INTEREST RATES ZERO COUPON BONDS PROVIDE A RISK-FREE RETURN: Because a default-free zero-coupon bond that matures on date n provides a risk-free return over the same period, the LAW OF ONE PRICE guarantees that the risk-free interest rate equals the YTM on such a bond AKA: Spot Interest rates Risk-Free Interest Rate With Maturity n r n = YTM n We often refer to the YTM of the appropriate maturity, zero-coupon risk-free bond as the risk-free interest rate 2. COUPON BONDS COUPON BONDS: Pay investors their face value at maturity, and in addition, these bonds make regular coupon interest payments TREASURY NOTES: Original maturities from 1-10 years TREASURY BONDS: Original maturities of more than 10 years Yield To Maturity Of A Coupon Bond P = CPN x 1 y '1 1 (1 + y) n+ + FV (1 + y) n COUPON PAYMENT COUPON RATE x FACE VALUE = NO. OF COUPON PAYMENTS PER YEAR

2 YIELDS Internal Rate Of Return IRR: The discount rate at which the NPV of the cash flows of the investment opportunity is equal to ZERO The IRR of a zero-coupon bond is the rate of return that investors will earn on their money if they buy the bond at its current price and hold it to maturity The IRR of an investment in a bond is the YTM Yield To Maturity YTM: The yield to maturity of a bond is the discount rate that sets the present value of the promised bond payments equal the current market price of the bond The YTM is the per-period rate of return for holding the bond from today until maturity on date n DYNAMIC BEHAVIOUR OF BOND PRICES 1. TIME AND BOND PRICES AS TIME PASSES, THE BOND PRICE GETS CLOSER TO ITS FACE VALUE ZERO-COUPON BONDS If a bond s YTM has not changed, then the IRR of an investment in the bond equals the YTM even if you sell the bond early COUPON BONDS Between coupon payments, the prices of all bonds rise at a rate equal to the YTM as the remaining cash flows of the bond become closer As each coupon is paid, the price of the bond drops by the amount of the coupon IF THE BOND IS TRADING AT DISCOUNT PREMIUM EFFECT The price INCREASE between coupons will EXCEED the drop when a coupon is paid The bond s price will RISE Discount will DECLINE as time passes The price DROP when a coupon is paid ill be LARGER than the price INCREASE between coupons The bond s price will DROP Premium will DECLINE as time passes 2. BOND PRICES AND INTEREST RATE CHANGES AT ANY POINT IN TIME, CHANGES IN MARKET INTEREST RATES AFFECT THE BOND S YTM AND ITS PRICE A higher YTM implies a higher discount rate for a bond s remaining cash flows, reducing their present value and hence the bond s price INVERSE RELATIONSHIP: As interest rates and bond yields rise, bond prices will fall THE SENSITIVITY OF A BOND S PRICE TO CHANGES IN INTEREST RATES DEPENDS ON THE TIMING OF ITS CASH FLOWS Shorter-maturity zero-coupon bonds are less sensitive to changes in interest rates than are longerterm zero-coupon bonds The sensitivity of a bond s price to changes in interest rates is measured by the bond s duration Bonds with high durations are highly sensitive to interest rate changes SHORTER-MATURITY ZERO-COUPON BONDS Because it is discounted over a shorter period, the present value of a cash flow that will be received in the near future is less dramatically affected by interest rates than a cash flow in the distant future HIGHER COUPON RATE BONDS Because higher coupon rate bonds pay higher cash flows upfront, they are less sensitive to interest rate changes that otherwise identical bonds with lower coupon rates

3 THE YIELD CURVE AND BOND ARBITRAGE LAW OF ONE PRICE IMPLIES: Given the spot interest rates, which are the yields of the default-free zerocoupon bonds, we can determine the price and yield of any other default-free bond Replicating A Coupon Bond Match each coupon payment to a zero-coupon bond with a face value equal to the coupon payment and a term equal to the term remaining until the coupon date Because the coupon bond cash flows are identical to the cash flows of the portfolio of zero-coupon bonds the Law of One Price states that the price of the portfolio of zero-coupon bonds must be the same as the price of the coupon bonds IF PRICE OF COUPON BOND WERE HIGHER SELL COUPON BOND BUY ZERO-COUPON BOND IF PRICE OF COUPON BOND WERE LOWER BUY COUPON BOND SHORT SELL ZERO-COUPON BOND Coupon Bond Yields Because the coupon bond provides cash flows at different points in time, THE YTM OF A COUPON BOND IS A WEIGHTED AVERAGE OF THE YIELDS OF THE ZERO-COUPON BONDS OF EQUAL AND SHORTER MATURITIES The weights depend on the magnitude of the cash flows each period Most of the value in the present value calculation comes from the present value of the last cash flow, because it includes the principal, so the yield would be closest to the final year zero-coupon yield. COUPONS WITH THE SAME MATURITY CAN HAVE DIFFERENT YIELDS DEPENDING ON THEIR COUPON RATES As the coupon increases, earlier cash flows become relatively more important than later cash flows in the calculation of the present value YIELD CURVE UPWARD SLOPING DOWNWARD SLOPING FLAT EFFECT The YTM will DECREASE with the coupon rate The YTM will INCREASE with the coupon rate All zero-coupon and coupon-paying bonds will have the same yield, independent of their maturities and coupon rates CORPORATE BONDS CORPORATE BONDS: Bonds issued by corporations Issuer may default CREDIT RISK: The risk of default means that the bond s cash flows are not known with certainty Corporate Bond Yields INVESTORS PAY LESS FOR BONDS WITH CREDIT RISK THAN THEY WOULD FOR AN OTHERWISE IDENTICAL DEFAULT-FREE BOND Because the YTM for a bond is calculated using the promised cash flows, the yield of bonds with credit risk will be higher than that of otherwise identical default-free bonds The prospect of default lowers the cash flow investors expect to receive and hence the price they are willing to pay THE BOND S EXPECTED RETURN, WHICH IS EQUAL TO THE FIRM S DEBT COST OF CAPITAL, IS LESS THAN THE YTM IF THERE IS A RISK OF DEFAULT Moreover, a higher YTM does not necessarily imply that a bond s expected return is higher Note that the bond s price decreases, and its YTM increases, with the greater likelihood of default Bond Ratings The rating depends on the risk of bankruptcy as well as the bondholders ability to lay claim to the firm s assets in the event of such a bankruptcy Thus, debt issues with low-priority claim in bankruptcy will have a lower rating than issues from the same company that have a high-priority claim in bankruptcy or that are backed by a specific asset such as a building or a plant EG: Investment-grade bonds, speculative bonds, junk bonds, high-yield bonds

4 STOCK VALUATION THE LAW OF ONE PRICE IMPLIES: The price of a security should equal the present value of the expected cash flows an investor will receive and the appropriate cost of capital with which to discount those cash flows 1. DIVIDEND DISCOUNT MODEL A One-Year Investor Because the cash flows of a share are not risk-free, we cannot compute their PV using the risk-free interest rate Discount them based on the EQUITY COST OF CAPITAL re: The expected return of other investments available in the market with equivalent risk to the firm s shares) STOCK PRICE P 0 = DIV 1 + P r E In a competitive market, buying or selling a share of a stock must be a zero-npv investment opportunity Condition To BUY Stock P 0 DIV 1 + P r E Condition To SELL Stock P 0 DIV 1 + P r E A Multiyear Investor As a two-year investor, we care about the dividend and the stock-price in year 2 Does this imply that a two-year investor will value the stock differently than a one-year investor? No They care about the stock price in year 2 indirectly o These prices will affect the price for which she can sell the stock at the end of year 1 o o Suppose the investor sells the stock to another one-year investor with the same beliefs The investor will expect to receive the dividend and the stock price at the end of year 2, so he will be willing to pay the present value of those cash flows STOCK PRICE P 0 = DIV 1 + DIV 2 + P r E (1 + r E ) 2 The Dividend-Discount Model Equation Dividend-Discount Model P 0 = DIV 1 + DIV r E (1 + r E ) 2 + DIV 3 (1 + r E ) DIV n (1 + r E ) n The price of the stock is equal to the present value of the expected future dividends it will pay

5 Dividend Yields, Capital Gains & Total Returns Capital Gains Yield TOTAL Return r E = DIV 1 + P 1 P 0 1 = DIV 1 P 0 + P 1 P 0 P 0 Dividend Yield DIVIDEND YIELD: The percentage return the investors expects to earn from the dividend paid by the stock CAPITAL GAINS YIELD: The capital gain the investor will earn on the stock TOTAL RETURN TOTAL RETURN: The total return is the expected return that the investor will earn for one-year investment in the stock THE EXPECTED TOTAL RETURN OF THE STOCK SHOULD EQUAL THE EXPECTED RETURN OF OTHER INVESTMENTS AVAILABLE IN THE MARKET WITH EQUIVALENT RISK Firms must pay its shareholders a return commensurate with the return they can earn elsewhere while taking the same risk If the stock offered a higher return than other securities with the same risk, investors would sell those other investments and buy the stock instead o This activity would drive up the stock s current price, lowering its dividend yield and capital gain rate CONSTANT DIVIDEND GROWTH Constant Dividend Growth Model P 0 = DIV 1 r E g According to the constant dividend growth model, the value of the firm depends on the dividend level for the coming year, divided by the equity cost of capital adjusted by the expected growth rate of dividends Constant Dividend Growth Model r E = DIV 1 P 0 + g We see that g equals the expected capital gain rate. In other words, with constant expected dividend growth, the expected growth rate of the share price matches the growth rate of dividends

6 DIVIDEND VS. INVESTMENT AND GROWTH TO MAXIMISE ITS SHARE PRICE, A FIRM WOULD LIKE TO INCREASE BOTH DIVIDEND AND GROWTH RATE Often, however, the firm faces a trade-off: Increasing growth may require investment, and money spent on investment cannot be used to pay dividends DIVIDEND PAYOUT RATE: The fraction of its earnings that the firm pays as dividends each year Dividend Per Share At Time t DIV t = Earnings t Shares Outstanding t x Dividend Payout Rate IE: EPS x Dividend Payout Rate Thus, the firm can INCREASE ITS DIVIDEND in three ways: 1. Increase its earnings (Net Income) 2. Increase its dividend payout rate 3. Decrease its shares outstanding A FIRM CAN DO ONE OF TWO THINGS WITH ITS EARNINGS: 1. Pay out to investors 2. Retain and reinvest them By investing cash today, a firm can increase its future dividends. If all increases in future earnings result exclusively from new investment made with retained earnings, then: CHANGE IN EARNINGS = NEW INVESTMENT x RETURN ON NEW INVESTMENT NEW INVESTMENT = EARNINGS X RETENTION RATE CHANGE IN EARNINGS EARNINGS GROWTH RATE = EARNINGS EARNINGS GROWTH RATE = RETENTION RATE x RETURN ON NEW INVESTMENT If the firm chooses to keep its dividend payout rate constant, then the growth in dividends will equal growth of earnings PROFITABLE GROWTH A firm can INCREASE ITS GROWTH RATE BY RETAINING MORE OF ITS EARNINGS However, if the firm retains more earnings, it will be able to pay out less of those earnings, and will have to reduce dividends If a firm wants to increase its share price, should it cut its dividend and invest more, or should it cut investment and increase its dividend? o o The answer will depend on the profitability of the firm s investments The effect of cutting the firm s dividend to grow crucially depends on the RETURN ON NEW INVESTMENT CUTTING THE FIRM S DIVIDEND TO INCREASE INVESTMENT WILL RAISE THE STOCK PRICE IF, AND ONLY IF, THE NEW INVESTMENTS HAVE A POSITIVE NPV

7 CHANGING GROWTH RATES Dividend-Discount Model With Constant Long-Term Growth P 0 = DIV 1 + DIV r E (1 + r E ) DIV N (1 + r E ) N + 1 (1 + r E ) n 'DIV NU1 r E g + The price of the stock is equal to the present value of the expected future dividends it will pay 2. TOTAL PAYOUT MODEL Share Repurchases & The Total Payout Model SHARE REPURCHASE: The firm uses excess cash to buy back its own stock The more cash the firm uses to repurchase shares, the less it has available to pay dividends By repurchasing shares, the firm decreases its share count, which increases its earnings and dividends on a per-share basis TOTAL PAYOUT MODEL: Values ALL of the firm s equity, rather than a single share Discount the total payouts that the firm makes to shareholders, which is the total amount spent on both DIVIDENDS and SHARE REPURCHASES Then, we divided by the current number of shares outstanding to determine the share price TOTAL PAYOUT MODEL PV (Future Total Dividends & Repurchases) P 0 = Shares Outstanding 0 We can apply the same simplifications that we obtained by assuming constant growth in the dividend discount model The only change is that we discount total dividends and share repurchases and use the growth rate of total earnings (Rather than earnings per share) when forecasting the growth of the firm s total payouts

8 3. DISCOUNTED FREE CASH FLOW MODEL DISCOUNTED CASH FLOW MODEL: Begins by determining the total value of the firm to all investors both equity AND debt holders The advantage of the discounted free cash flow model is that it allows us to value a firm without explicitly forecasting its dividends share repurchases, or its use of debt Free Cash Flow FREE CASH FLOW: Measures the cash generated by the firm before any payments to debt or equity holders are considered NET INVESTMENT: Investment intended to support the firm s growth, above and beyond the level needed to maintain the firm s existing capital Free Cash Flow FCF = EBIT x (1 T c ) + Depreciation CapEx Increases In NWC Free Cash Flow FCF = EBIT x (1 T c ) Net Investment Increases In NWC Net Investment Net Investment = Capital Expenditures Depreciation ENTERPRISE VALUE: The value of the firm s underlying business, unencumbered by debt and separate from any cash or market The net cost of acquiring the firm s equity, taking its cash, paying off all debt and thus owning the unlevered business Enterprise Value ENTERPRISE VALUE = MARKET VALUE OF EQUITY + DEBT CASH WACC: The average cost of capital the firm must pay to all of its investors, both debt and equity holders DISCOUNTED FREE CASH FLOW MODEL V 0 = FCF 1 FCF r WACC (1 + r WACC ) FCF N + V N (1 + r WACC ) N Often, the terminal value is estimated by assuming a constant long-run growth rate gfcf for Free Cash flows beyond year N, so that: V N = FCF N = ' 1 + g FCF + x FCF r WACC g FCF r WACC g N FCF P 0 = V 0 + Cash 0 Debt 0 Shares Outstanding 0

9 A Comparison Of Discounted Cash Flow Models Of Stock Valuation PRESENT VALUE OF DETERMINES THE TO GET STOCK PRICE ESTIMATE.. Dividend Payments Stock Price No adjustment necessary Total Payouts (All Dividends & Repurchases) Equity Value Divide by shares outstanding Free Cash Flow (Cash Available To Enterprise Value Subtract what does not belong to Pay All Security Holders) equity holders (debt and preferred stock) Add back cash and marketable securities Divide by shares outstanding Valuations Value of Firm = Value Of Operations + Cash Value of Firm = Value Of Equity + Value Of Debt Value Of Equity + Value Of Debt = Value Of Operations + Cash Value Of Equity = Value Of Operations Value Of Debt + Cash

10 4. VALUATION BASED ON COMPARABLE FIRMS METHOD OF COMPARABLES: Rather than value of the firm s cash flows directly, we estimate the value of the firm based on the value of other, comparable firms or investments that we expect to generate very similar cash flows in the future VALUATION MULTIPLES VALUATION MULTIPLE: The ratio of the value to some measure of the firm s scale We can adjust for differences in scale between firms by expressing their value in terms of a valuation multiple PRICE-TO-EARNINGS MULTIPLE P/E RATIO: A firm s P/E ratio is equal to the share price divided by its earnings per share When you are buying a stock, you are buying the rights to a firm s future earnings Because differences in the scale of the firms earnings are likely to persist, you should be willing to pay proportionally more for a stock with higher current earnings P E RATIO = Share Price Earnings Per Share FORWARD P/E: The P/E multiple computed based on its forward earnings (Expected earnings over the next 12 months) For valuation purposes, the forward P/E is generally preferred, as we are most concerned about future earnings TRAILING P/E: A firm s trailing P/E is computed using its trailing earnings (earnings over the period 12 months) To interpret the P/E multiple, consider the stock price formula for the case of constant dividend growth: P0 = Div1/(rE g) If we divide both sides of this equation by EPS1, we have: Forward P E = Div 1 P 0 EPS1 = EPS 1 r E g = Dividend Payout Rate r E g This implies that if two stocks have the same payout and EPS growth rates, as well as equivalent risk (and therefore the same equity cost of capital), then they should have the same P/E It shows that firms and industries with high growth rates, and that generate cash well in excess of their investment needs so that they can maintain high payout rates, should have high P/E multiples ENTERPRISE VALUE MULTIPLES Because ENTERPRISE VALUE represents the total value of the firm s underlying business rather than just the value of equity, using the enterprise value is advantageous if we want to compare firms with different amounts of leverage Because the enterprise value represents the entire value of the firm before the firm pays its debt, to form an appropriate multiple, we divide it by a measure of earnings or cash flows BEFORE INTEREST PAYMENTS ARE MADE EV EBIT = EV EBITDA = EV FCF = Enterprise Value EBIT Enterprise Value EBITDA Enterprise Value FCF

11 ENTERPRISE VALUE TO EBITDA MULTIPLES: Because capital expenditures can vary substantially from period to period (EG: A firm may need to add capacity and build a new plant one year, but then not need to expand further for many years), most practitioners rely on EV/EBITDA multiples As with P/E multiples, this multiple is higher for firms with high growth rates and low capital requirements (so that FCF is high in proportion to EBITDA) V 0 EBITDA 1 = FCF 1/EBITDA 1 r WACC g FCF LIMITATIONS OF MULTIPLES 1. FIRMS ARE NOT IDENTICAL The usefulness of a valuation multiple will depend on the nature of the differences between the firms and the sensitivity of the multiples to these differences The differences in these multiples are most likely due to differences in their expected future growth rates, profitability and risk (And therefore cost of capital) 2. COMPARABLES ONLY PROVIDE INFORMATION REGARDING THE VALUE OF THE FIRM RELATIVE TO THE OTHER FIRMS IN THE COMPARISON SET Using multiples will not help us determine if an entire industry is overvalued COMPARISON WITH DISCOUNTED CASH FLOW METHODS ADVANTAGE OF MULTIPLES Rather than separately estimate the firm s cost of capital and future earnings or FCF, WE RELY ON THE MARKET S ASSESSMENT OF THE VALUE OF OTHER FIRMS WITH SIMILAR FUTURE PROSPECTS The multiples approach has the advantage of being based on actual prices of real firms, rather than what may be unrealistic forecasts of FCF ADVANTAGE OF DISCOUNTED FCF Discounted FCF allows us to INCORPORATE SPECIFIC INFORMATION ABOUT THE FIRM S PROFITABILITY, COST OF CAPITAL, OR FUTURE GROWTH POTENTIAL, as well as perform sensitivity analysis. Because the true driver of value for any firm is its ability to generate cash flows for its investors, the discounted cash flow methods have the potential to be more accurate and insightful than the use of a valuation multiple

12 FINANCIAL STATEMENT ANALYSIS Market Value Vs. Book Value Market Value Of Equity The market value of a share does not depend on the historical cost of the firm s assets Instead, it depends on what investors expect those assets to produce in the future Market Value Of Equity = Shares Outstanding x Market Price Per Share Market To Book Ratio The ratio of a firm s market capitalization to the book value of shareholders equity Market To Book Ratio = Market Value Of Equity Book Value Of Equity The market to book value for most successful firms substantially exceeds 1 This indicates the value of the firm s assets when put to use exceeds their historical cost o This is one way a company s share price provides feedback to its managers on the market s assessment of their decisions VALUE STOCKS: Low market-to book ratios GROWTH STOCKS: High market-to-book ratios Enterprise Value ENTERPRISE VALUE: The enterprise value of a firm assesses the value of the underlying business assets, unencumbered by debt and separate from any cash and marketable securities Enterprise Value = Market Value Of Equity + Debt Cash Retained Earnings RETAINED EARNINGS: The difference between a firm s net income and the amount it spends on dividends Also: The retention ratio x net income Retained Earnings = Net Income Dividends Profitability Ratios Gross Margin GROSS MARGIN: The ratio of gross profits to revenues (Sales) A firm s gross margin reflects its ability to sell a product for more than the cost of producing it (Only taking into account the COGS of the product)

Disclaimer: This resource package is for studying purposes only EDUCATION

Disclaimer: This resource package is for studying purposes only EDUCATION Chapter 6: Valuing stocks Bond Cash Flows, Prices, and Yields - Maturity date: Final payment date - Term: Time remaining until