The Valuation of Bond and CommonStock using DCF Text: Chapter 5

Valuation Fundamentals Future Cash Flows Risk Valuation

Valuation of Bonds and Stock First Principles: Value of financial securities = PV of expected future cash flows To value bonds and stocks we need to: Estimate future cash flows: Size (how much) and Timing (when) Discount future cash flows at an appropriate rate: The rate should be appropriate to the risk presented by the security.

Definition and Example of a Bond A bond is a legally binding agreement between a borrower and a lender: Specifies the principal amount of the loan. Specifies the size and timing of the cash flows: In dollar terms (fixed-rate borrowing) As a formula (adjustable-rate borrowing): ex: LIBOR+50 bps (basis points); T-Bond+30 bps

Definition and Example of a Bond Consider a government bond listed as 6 3/8 of December 2009. The Par Value of the bond is $1,000. Coupon payments are made semi-annually (June 30 and December 31 for this particular bond). Since the coupon rate is 6 3/8, the payment is $31.875. On January 1, 2002 the size and timing of cash flows are:

How to Value Bonds Identify the size and timing of cash flows. Discount at the correct discount rate. If you know the price of a bond and the size and timing of cash flows, the yield to maturity is the discount rate.

Pure Discount Bonds Information needed for valuing pure discount bonds: Time to maturity (T) = Maturity date - today’s date Face value (F) Discount rate (r) Present value of a pure discount bond at time 0:

Pure Discount Bonds: Example Find the value of a 30-year zero-coupon bond with a $1,000 par value and a YTM of 6%.

Level-Coupon Bonds Information needed to value level-coupon bonds: Coupon payment dates and time to maturity (T) Coupon payment (C) per period and Face value (F) Discount rate Value of a Level-coupon bond = PV of coupon payment annuity + PV of face value

Level-Coupon Bonds: Example Find the present value (as of January 1, 2002), of a 6-3/8 coupon T-bond with semi-annual payments, and a maturity date of December 2009 if the YTM is 5-percent. On January 1, 2002 the size and timing of cash flows are:

How to Calculate Yield (Rate of Return) of Bonds? Traditional way of thinking Two-period investment: C0 and C1, rate of return: r = C1/(-C0) -1 Three-period investment : C0, C1 and C2 ??? Alternative way of thinking Calculate the discount rate that produces a zero NPV NPV = C0 + C1/(1+r) = 0, r = C1/(-C0) -1

What is Yield to Maturity? YTM: the rate that produces zero NPV for bond NPV = -B + { F / (1 + r)T +  [Ci / (1+r)i] }= 0 , That is, B = F / (1 + r)T +  [Ci / (1+r)i] r is the only unkown (yield to maturity). The Yield Curve

An example $900 (1+r)2 = $20(1+r) + $1200 A 2-year bond with coupon rate 2% and face value 1000 is selling at $900. What is the annual rate of return (r)? Annual coupon payment? What is the balance at maturity in your account? Year 1 Year 2 Cash flow $20 $20 (1+?) + $20 + $1000 Assume ? = r, bal. at maturity is $20(1+r) + $1200 ………… eq(1) With annual rate of return, r, the balance at maturity should be $900 (1+r)2 ………..…….. eq(2) From eq(1) and eq(2) $900 (1+r)2 = $20(1+r) + $1200

An example … continued $900 (1+r)2 = $20(1+r) + 200…………eq.(3) We can rewrite eq. (3) : both sides divided by (1+r)2, and minus 900, we have r is yield to maturity

Bond Ratings

Bond Ratings, Spreads and Maturities

Term Structure Theories Expectations theory Liquidity preference theory Preferred habitat theory

Bond Concepts Bond prices and market interest rates move in opposite directions. 2. When coupon rate = YTM, price = par value. When coupon rate > YTM, price > par value (premium bond) When coupon rate < YTM, price < par value (discount bond)

YTM and Bond Value $1400 When the YTM < coupon, the bond trades at a premium. 1300 Bond Value When the YTM = coupon, the bond trades at par. 1200 1100 1000 6 3/8 800 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Discount Rate When the YTM > coupon, the bond trades at a discount.

Bond Price versus Maturity Which one is more risky, a bond with long or short maturity? A bond with longer maturity has higher relative (%) price change than one with shorter maturity when interest rate (YTM) changes. All other features are identical.

Maturity and Bond Price Volatility Long Maturity Bond Maturity and Bond Price Volatility Bond Value Consider two otherwise identical bonds. The long-maturity bond will have much more volatility with respect to changes in the discount rate Short Maturity Bond Par C Discount Rate

Bond Price versus Coupon Rate Which one is more risky, a bond with high or low coupon rate? A lower coupon bond has a higher relative price change than a higher coupon bond when YTM changes. All other features are identical.

Coupon Rate and Bond Price Volatility Low Coupon Bond Coupon Rate and Bond Price Volatility Bond Value Consider two otherwise identical bonds. The low-coupon bond will have much more volatility with respect to changes in the discount rate High Coupon Bond Discount Rate

Valuation of Stocks

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 market capitalization rate.

Dividend Yield + Capital Appreciation Valuing Common Stocks The formula can be broken into two parts. Dividend Yield + Capital Appreciation

Valuing Common Stocks Dividend + growth of dividend Capitalization Rate can be estimated using the perpetuity formula, given minor algebraic manipulation. Dividend + growth of dividend

Valuing Common Stocks How is g estimated? From financial analyst’s information Plowback ratio * ROE assuming constant payout ratio plowback ratio = 1 - DIV/EPS ROE = EPS / book equity value per share

An example Assume constant payout ratio (40%), dividend is growing at the same rate of earnings. EPS0 = $1. what would be EPS1? Without additional investment, EPS is expected to be the same. Additional inv. = 0.6, what is the earnings generated by this inv? 0.6* ROE (20%) = 0.12 Next-period earnings will be 0.12 + 1 = 1.12 EPS (div.) grows at 12%

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.

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 $94.48. What is the price of the stock given a 12% expected return?

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 $94.48. What is the price of the stock given a 12% expected return? What is the long-term growth rate to support the share price of $75?

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?

Valuing Common Stocks No Growth With Growth 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 Growth With Growth

Valuing Common Stocks No Growth With Growth 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 Growth With Growth

Valuing Common Stocks Example - continued If the company did not plowback some earnings, the stock price would remain at $41.67. With the plowback, the price rose to $75.00. The difference between these two numbers (75.00-41.67=33.33) is called the Present Value of Growth Opportunities (PVGO).

Growth Opportunities The value of a firm can be conceptualized as the sum of the value of a firm that pays out 100-percent of its earnings as dividends and the net present value of the growth opportunities. Growth stock versus Income stock

Price Earnings Ratio (本益比） Many analysts frequently relate earnings per share to price. The price earnings ratio is a.k.a the multiple Calculated as current stock price divided by annual EPS The Wall Street Journal uses last 4 quarter’s earnings

The idea of price-earning ratio (本益比) Is high price-earning ratio a good news ? What does high P-E ratio imply? P0 = EPS1/r + PVGO ====> P0/EPS = 1/r + PVGO/EPS High PVGO, Lower risk , or both The practical view: overvalued? EPS focuses on accounting data Use P-E ratio to estimate the value of an unlisted firm

Other Price Ratio Analysis Many analysts frequently relate earnings per share to variables other than price, e.g.: Price/Cash Flow Ratio cash flow = net income + depreciation = cash flow from operations or operating cash flow Price/Sales current stock price divided by annual sales per share Price/Book (a.k.a Market to Book Ratio) price divided by book value of equity, which is measured as assets - liabilities No, it’s not exactly in the book, but it’s a great big world out there and you don’t want your students to learn this voodoo on the streets do you? Just delete the slide if you want to ignore it (I will).

Stock Market Reporting Gap has been as high as $52.75 in the last year. Gap has been as low as $19.06 in the last year. Given the current price, the dividend yield is ½ % Gap pays a dividend of 9 cents/share Given the current price, the PE ratio is 15 times earnings 6,517,200 shares traded hands in the last day’s trading Gap ended trading at $19.25, down $1.75 from yesterday’s close

Stock Market Reporting Gap Incorporated is having a tough year, trading near their 52-week low. Imagine how you would feel if within the past year you had paid $52.75 for a share of Gap and now had a share worth $19.25! That 9-cent dividend wouldn't’t go very far in making amends. How is Gap doing today?