Bond & Stock Valuation Spring / Summer 2007

1. Bond & Stock ValuationSpring / Summer 2007 Executive MBA Jeffrey Allen, Ph.D.

2. Bond Financing • Bonds are a legal contract (called an ‘indenture’) to repay principal plus accrued interest. • Violation of any provision of the indenture results in a default which is a precursor to a bankruptcy filing, renegotiation or other type of restructuring • Bondholders have minimal influence over management – no voting power • Advantages to issuer: 1) Debt always has a lower expected return vs. equity, and 2) Interest expense is tax deductible

3. Definitions • Face or par value: the terminal cash flow of the bond at maturity, generally $1,000 • Maturity date: the date at which the indenture expires and all obligations must be met • Coupon rate: the annual percentage rate of the par value paid as interest. Corporate bonds generally pay coupons semi-annually • Pure discount bonds: The only cash inflow on these bonds is the par value paid at maturity – no coupon payments • Yield to maturity: The rate of return from holding a bond from today through the maturity date • Premium vs. discount bonds: Bonds with a value greater than par are sold at a “premium” while bonds sold less than par are at a “discount”

4. Determining Bond Prices and Yields • Bonds are pure financial instruments, so they are priced according to their cash flows at an appropriate discount rate. The cash flows are known, but the correct rate or “yield” is determined independently based on: • Risk associated with the cash flows, e.g. default risk • Potential devaluation of the cash flows due to inflation or changes in interest rates • Securitization of the bond with the assets of the firm (lowers risk) • Subordination or seniority of the bond vs. other claims • Callability or convertibility of the bond (more later) • Tax status, e.g. municipal bonds are non-taxable

5. Important decision points • Maturity-length of contract • Measured in terms of duration (average life of loan) • Fixed or Floating rate • Floating rates are quoted as a basis point spread over treasuries or LIBOR, often subject to caps or floors on rate movements • Security • Secured debt - specific assets pledged as collateral. Examples include mortgage bonds or senior secured notes • Subordinated debentures - backed by assets, but claims on assets are junior to secured (senior) debt • Unsecured debentures - not backed by assets

6. Important decision points (cont’d) • Currency-issuing debt across borders has become more common due to improved access to information, the establishment of some standard accounting principles, and greater international trade. Can be used as a hedge against exchange rate risk • Repayment • Sinking funds - portion set aside per year to repay debt • Serial bonds - a fraction of bonds outstanding mature annually • Partial amortization – repayments prior to maturity after a “blind spot” of only coupon payments • Balloon - no principal repayments until maturity

7. Pricing a coupon bond P = price (pv) C = coupon payment PR = principal payment N = number of periods Y = periodic yield

8. Notes on the Bond Pricing Formula • To solve for YTM: Similar to IRR…solve by iteration. Use XL or financial calculator • To solve for price: Simple TVM calculation using four inputs (FV, N, r (yield), PMT) • Generally semi-annual coupons, e.g. 10-year bond with 6.5% coupon rate paid semi annually • Convert the coupon rate to a payment amount, e.g. $32.50 semi-annually • Double the number of periods, e.g. 20

9. Two Key Questions in Bond Pricing • Q1: Given a specific market rate of interest or yield (based on remaining time to maturity and risk), what is the value of the bond? • Q2: At a specified transaction price, what is the percentage yield earned by holding the bond to maturity? • WSJ examples…

10. Par, Discount and Premium Bonds • Par bonds: • Price = Face Value • YTM = Coupon Rate • Discount: • Price < Face Value • YTM > Coupon Rate • Premium: • Price > Face Value • YTM < Coupon Rate

11. Determinants of Interest Rate Risk • Time to Maturity: • All else equal, longer time to maturity results in greater interest rate risk • Higher N in formula has a greater compounding effect - -therefore changes in yields result in significant price changes • Example: 10% coupon: 2-year and 15-year bonds • 15 year bond’s price will change more with a change in the YTM. • Example: Assume the current YTM is 10%, so both bonds are worth $1000 today. What if the YTM decreases by 100 basis points – what happens to the price of each bond?

12. Interest Rate Risk Determinants (cont’d) • Coupon rate: • The lower the coupon rate, the greater the interest rate risk, all else equal • Low coupon => more of the bond’s value comes from the face amount • Example: 1% coupon versus 10% coupon on 8-year, $1000 par bonds • Most of the 1% coupon bond’s price comes from face amount so it’s value is more sensitive to YTM changes. • Example: With a current YTM of 10%, the 1% coupon bond is worth $512.30 and the 10% coupon bond is worth $1000 (par = price since YTM = coupon rate). What happens to the prices if the yield falls by 100 basis points?

13. Stock Valuation

15. Valuing Stocks is a Practical Challenge • Highly uncertain cash flows • Equity is the residual claim on the firm’s cash flows • Subject to wide variations and uncertainties • Firms are assets with long expected time horizons • The appropriate rate of return by investing in equities is not easy to determine and likely not constant over time

16. Discounted Cash Flow Approach • You own a share of stock today. What do you get for holding it for one period? • Dividend • Price when you sell the stock • What determines P1?

17. DCF Approach (cont’d) Substitute the above formula into the formula for P1.

18. DCF Approach (cont’d) • The price of a stock equals the present value of all the firm’s forecasted dividends discounted by the required rate of return, r. • Use assumptions about how dividends grow to simplify the above formula.

19. Zero Growth Dividend Model • Assume firm’s dividends are constant over time. • No growth case • Stream of constant cash flows forever • Price equity as a perpetuity • ** More relevant in pricing preferred stock since the features of preferred stock more closely align with this approach

20. Constant Growth Dividend Model • Forecast dividends grow at a constant rate • Assumption is that we forecast the dividend growth rate rather than an indefinite number of dividends • Stream of constant growing cash flows forever • Price equity as a growingperpetuity

21. Constant Growth (cont’d) • Example: A firm just paid a $6.50 per share annual dividend. Future dividends are expected to grow at an annual rate of 5% per year. The required rate of return is 12% per year. What is the expected price of the stock? Price = D1/(r – g) = $6.50(1+0.05)/(0.12-0.05) = $97.50

22. Required Return • Assume constant growth dividend model • Rearranging for r: r = dividend yield + capital gain yield • Suppose a stock pays $1 annual dividend, g = 4% and the price is $10. • r=($1/$10)+0.04 = 14.0%

23. EPS and Dividends • Dividends (or share repurchases) are a function of… • Ability to pay: Cash flow uncertainty • Decision to pay: Managerial discretion • Why do management teams retain earnings? • Company holds superior investment opportunities – cheaper source of funds vs. external capital • Agency costs – surplus cash flow is retained for personal benefits rather than maximizing shareholder wealth • What is a “superior investment opportunity”? • NPV > 0 or IRR in excess of the hurdle rate

24. Valuing a Firm that Retains Earnings • Fundamentals: Sum of discounted cash flows • First component: Present value of current earnings stream • Second component: PV of future growth

25. Investment Opportunity • A firm expects $1 million in earnings in perpetuity without new investments. The firm has 100,000 shares outstanding and has an opportunity to invest $1 million in a project expected to increase future cash earnings by $210,000 per year. The firm’s discount rate is 10%. What is the expected share price with and without the project?

26. Constant Growth & Investment • Firm Q has EPS of $10 at the end of the first year and a dividend pay-out ratio of 40% (plowback = 60%). The firm has a required return of 16% and a steady return on investment of 20%. Q takes advantage of its growth opportunities each year by reinvesting retained earnings. • PV(GO) model –> finding the growth rate • Investment = plowback x EPS → 0.6 × $10 = $6.00. This generates $1.20 in new EPS via a 20% return on investment (.2 x $6) • PVGO1 per share = -6 + (1.20/0.16) = $1.50 • 2nd investment = 0.6 × $11.20 = $6.72, generating 0.2 × $6.72 = $1.344 EPS • Per share PVGO2 = -6.72 + (1.344/0.16) = $1.68

27. Constant Growth & Investment (cont’d) • Relationship between PV(GO) • $1.68 = (1+g) × $1.50 therefore g=0.12 • Is there an easier way to estimate g? Yes! • g = ROI x plowback ratio → 0.20 x 60% = 0.12 • PVGO0 = $1.50 / (0.16 - 0.12) = $37.50 • Current dividend value: $10/0.16 = $62.50 • P = $62.50 + $37.50 = $100.00

28. Another Example Firm X currently has expected earnings of $100,000 per year in perpetuity. Firm X is switching its policy and wants to invest 20% of its earnings in projects with an expected 10% return. The discount rate is 18%. • No-growth firm value: P=$100,000/0.18 = $555,555 • PV(GO) is a constant growth perpetuity • g = plowback ratio x ROI = 0.20 × 10% = 2.0% • What is the first year’s cash flow from investing? • Invest $20,000 and receive $2,000 forever • -$20,000+($2,000/0.18) = ($8888.89) • PV(GO) = ($8,888.89)/(0.18-0.02) = ($55,555) • Why is value destroyed? • Impact of New Policy: P=$555,555 - $55,555 = $500,000

29. P/E Ratios • Today’s earnings versus future expected earnings? • High P/E ratio • Overvalued …or High PV(GO) • Low P/E ratio • Undervalued…or Low PV(GO)

30. Summary: Bond and Stock Valuation • Application of present value techniques • Bond pricing: Need the appropriate yield…expected cash flows are known • Determining the risk of bond issues is a multi-billion $ industry • Pricing common stock • zero growth dividend • constant growth dividend • PV(GO) • Significant challenges in estimating r and g