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MBA 643 Managerial Finance Lecture 6: Valuing Bonds and Stocks

MBA 643 Managerial Finance Lecture 6: Valuing Bonds and Stocks. Spring 2006 Jim Hsieh. Bond Valuation. Pricing and valuation are the core issues in finance. We will apply present value techniques to price bonds and stocks. Standard Terminologies on Bonds.

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MBA 643 Managerial Finance Lecture 6: Valuing Bonds and Stocks

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  1. MBA 643Managerial FinanceLecture 6: Valuing Bonds and Stocks Spring 2006 Jim Hsieh

  2. Bond Valuation • Pricing and valuation are the core issues in finance. • We will apply present value techniques to price bonds and stocks.

  3. Standard Terminologies on Bonds • C: coupon payments = interests paid in each period • Semi annual for most US corporate bonds • C = coupon rate * par value • F: face or par value = amount of money to be repaid at the end of the loan = the principal • $1,000/bond • T: time to maturity (or year to maturity) = number of years from the issue date until the principal is paid • r: bond’s market rate of interest • Note: r does NOT always equal the bond’s coupon rate.

  4. Bond Valuation – The General Approach • Discounted Cash Flow Valuation • Bond Price = PV (promised cash flows) = PV (coupon payments + face value) • Special cases: • Zero coupon bonds: P=F/(1+r)T • Consols: P=C/r This is an annuity!

  5. Example 1 • What is the price of a 4-year bond with 5% annual coupon rate and with a $1,000 face value? The required rate of return for this bond is 6.6%. Coupon = 1,000*0.05 = 50 Interest rate = 6.6%

  6. Example 1 (cont’d) • What is the price of the bond if the required rate of return for this bond is 6.6% AND the coupons are paid semi-annually? Semi-annual coupon = 1,000*0.05/2 = 25 Interest rate = 0.066/2 = 0.033 Number of compounding period = 2*(4 years) = 8 times

  7. Example 1 (cont’d) • What is the price of the bond if the required rate of return for this bond stays at 6.6%, but the annual coupon rate is 10%? The coupons are paid annually. Annual coupon = 1,000*0.1 = 100 Interest rate = 0.066

  8. Bond Price Movement • The Premium Bond: When the bond would sell above par. • The rate of return The coupon rate • The Discount Bond: When the bond would sell below par. • The rate of return The coupon rate • What do you think about the future price movement for a premium bond? How about a discount bond? < > Bond Price ($) Premium bond F=$1,000 Discount bond Year to maturity Years

  9. Yield To Maturity (YTM) • YTM is the required market interest rate that makes the discounted cash flows of the bond equal to its price. • It is the bond’s IRR. • YTM is the interest rate that we use in the bond valuation equation. • Risk-free market interest rate versus YTM • YTM takes into consideration the risk of the cash flows.

  10. Bond Returns • Total rate of return = Total income / Investment = (Coupon income + Price change) / Initial bond price = Current yield + Capital gains yield = C/P0 + (P1 – P0)/P0(for one period)

  11. Bond Returns – Example 2 • If you purchased the bond as in Example 1 and then sold it one year later with r still at 6.6%. What is your total rate of return on this bond? Bond price one year later = $957.70 (Verify!!) Total rate of return = current yield + capital gains yield = 50/945.31 + (957.70 – 945.31)/945.31 = 0.066 = 6.6% • If you purchased the bond as in Example 1 and then sold it one year later with r=7%. What is your total rate of return on this bond? Bond price one year later = $947.51 Total rate of return = current yield + capital gains yield = 50/945.31 + (947.51 – 945.31)/945.31 = 0.055 = 5.5%

  12. Interest Rate Risk • Bond prices are sensitive to changes in interest rates (required rates of return). The amount of the sensitivity depends on two factors: • Time to maturity: The longer the time to maturity, the greater the interest rate risk. • Coupon rate: The lower the coupon rate, the greater the interest rate risk.

  13. Interest Rate Risk – Example 3 • Consider the following two bonds, A and B: AB Face value $1,000 $1,000 Annual coupon rate 9% 9% YTM 9% 9% Time to maturity 2 years 10 years PriceA = PriceB = $1,000 $1,000

  14. Interest Rate Risk – Example 3 (cont’d) • What happens to the prices of the bonds if interest rates increase, leading to an increase in required returns to 12%? For Bond A: Price change = (949.29-1,000)/1,000 = -0.05 => 5% drop in price For Bond B: Price change = (830.49-1,000)/1,000 = -0.17 => 17% drop in price

  15. Interest Rate Risk – Example 4 • Consider the following two bonds, C and D: CD Face value $1,000 $1,000 YTM 9% 9% Time to maturity 10 years 10 years Annual coupon rate 10% 4% PriceC = $1,064 PriceD = $679 Verify!!

  16. Interest Rate Risk – Example 4 (cont’d) • What happens to the prices of the bonds if interest rates increase, leading to an increase in required returns to 14%? For Bond C: Price change = (791.35-1,064)/1,064 = -0.26 => 26% drop in price For Bond D: Price change = (478.38-679)/679 = -0.30 => 30% drop in price

  17. Stock Valuation • Definition: The expected return is the percentage yield that an investor forecasts from a specific investment over a period of time. It is also called the holding period return. • If you buy KKR stock with current price (P0), and in the following year, KKR pays out a dividend (D1) and its stock price moves to P1, then the expected return in one year is: r = (D1+P1-P0)/P0 = D1/P0 + (P1 – P0)/P0 = Dividend yield + Capital gains yield • Growth (glamour) stocks versus Income (value) stocks

  18. Dividend Discount Model • We know r = (D1+P1-P0)/P0 => rP0 = D1+P1-P0 => (1+r)P0 = D1+P1 => P0 = (D1+P1)/(1+r) • How about P1? • P1 = (D2+P2)/(1+r) • So we can substitute this formula into the one for P0 • We can repeat the process for P2, P3, P4, … This is P1

  19. Dividend Discount Model (DDM) • If we continue the above process for all future prices, • The price of a stock today simply equals the present value of all of the firm’s forecasted future dividends!

  20. DDM Special Case (1) -- Future dividends have zero growth rate • Firms’ dividend policies tend to be “sticky”. • If dividends are constant: D1 = D2 = D3 = … = D • Example 5: Mini-Mart Company (MM) has a policy of paying out a $2.5 per-share dividend each year. The company expects to continue the policy indefinitely. What is MM’s expected stock price if the required return is 8%? • P0 = D/r = 2.5/0.08 = $31.25

  21. DDM Special Case (2) -- Future dividends have a constant growth rate • D1=D0(1+g), D2=D1(1+g)=D0(1+g)2, …Dt=D0(1+g)t

  22. Example 6 • BioTech Corp. just paid out a dividend of $3 per share. BioTech’s dividend is expected to increase by 5% per year. Investors require a 12% return on companies such as BioTech. What is the expected stock price today? What is the expected price in 7 years? D0 = 3, g = 0.05, r = 0.12 P0 = D1/(r-g) = 3*(1.05)/(0.12-0.05) = $45 P7 = D8/(r-g) = 3*(1.05)8/(0.12-0.05) = $63.32

  23. Example 7 – Irregular Dividend Payments • You expect Gordon Growth Company to pay out dividends based on the following schedule: $1.00 in year 1, $2.00 in year 2, $2.5 in year 3. After the third year, the dividend will grow at a constant rate of 5% per year. The required return is 10%. What is the expect value of the stock today? 0 1 2 3 4 5 2 2.5 2.5(1.05) DIV $1 g = 0.05

  24. Estimating “g” in the DDM • How can a company grow its dividends? • It must invest in new projects (or grow existing ones). • This can occur only if the company does not pay out all of its earnings as dividends. • It retains some earnings, invests them, and earnings grow. • Payout ratio: Percent of earnings paid out to shareholders • Retention ratio: Percent of earnings remained in the firm • Payout ratio + Retention ratio = 1

  25. Estimating “g” in the DDM (cont’d) • Earnings next year = Earnings this year + Retained Earnings this year*Return on Retained Earnings • => E1 = E0 + N0 * ROE • => E1/E0 = 1 + (N0/E0) * ROE • => 1 + g = 1 + retention ratio * ROE • => g = retention ratio * ROE • Example 8:Simon Corp. just reported earnings of $2 million. The company plans to retain $800,000 of its earnings and pay the remaining as a dividend. The historical ROE for the company is 16% per year. What is the expected growth in earnings (g)? • g = retention ratio * ROE = 0.8/2 * 0.16 = 0.064 = 6.4% Expected growth in earnings = Expected growth in dividends

  26. Estimating “g” in the DDM (cont’d) • Limitations in the previous model: • It assumes earnings are constant over time. • It assumes projects are financed internally by earnings. • No issuance of stocks or bonds • An alternative way to estimate “g” is to estimate it directly from historical data. • It’s easy because firms’ dividend policies are sticky.

  27. Estimating “r” from the DDM -- First Simple Estimation of Expected Returns on Stock • From the DDM with a constant dividend growth rate: • P0 = D1/(r-g) • => r-g = D1/P0 • => r = D1/P0 + g • Expected return on a stock = Dividend yield + Dividend growth rate • Example 9: Skippy Corp. is selling for $50 and is expected to pay a dividend of $3 next year, growing at 4% per year. What is the expected return on Skippy’s stock? r = $3/$50 + 4% = 10%

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