Valuation Models Bonds Common stock

Key Features of a Bond Par value: face amount; paid at maturity. Assume $1,000. Coupon interest rate: stated interest rate. Multiply by par value to get dollar interest payment. Generally fixed.

Maturity: years until bond must be repaid. Declines over time. Issue date: date when bond was issued.

Value = How can we value assets on the basis of expected future cash flows? CF 1 (1 + k) 1 CF 2 (1 + k) 2 CF n (1 + k) n

The discount rate k is the opportunity cost of capital and depends on: riskiness of cash flows. general level of interest rates. How is the discount rate determined?

An annuity (the coupon payments). A lump sum (the maturity, or par, value to be received in the future). Value = INT(PVIFA i%, n ) + M(PVIF i%, n ). The cash flows of a bond consist of:

,000 Value = = $1,000. Find the value of a 1-year 10% annual coupon bond when k d = 10%. $1,

, Find the value of a similar 10-year bond.

Way to Solve Using tables: Value = INT(PVIFA 10%,10 )+ M(PVIF 10%,10 ). = 100* * = 1000 (approx.)

Rule: When the required rate of return (k d ) equals the coupon rate, the bond value (or price) equals the par value.

What would the value of the bonds be if k d = 14%? 1-year bond Using tables: Value = INT(PVIFA 14%,1 )+ M(PVIF 14%,1 ). = 100* * =

10-year bond When k d rises above the coupon rate, bond values fall below par. They sell at a discount. Using tables: Value = INT(PVIFA 14%,10 )+ M(PVIF 14%,10 ). = 100* * =

What would the value of the bonds be if k d = 7%? 1-year bond Using tables: Value = INT(PVIFA 7%,1 )+ M(PVIF7 %,1 ). = 100* * =

10-year bond When k d falls below the coupon rate, bond values rise above par. They sell at a premium. Using tables: Value = INT(PVIFA 7%,10 )+ M(PVIF 7%,10 ). = 100* * =

Value of 10% coupon bond over time: M k d = 10% k d = 7% k d = 13% Years to Maturity

Summary If k d remains constant: At maturity, the value of any bond must equal its par value. Over time, the value of a premium bond will decrease to its par value. Over time, the value of a discount bond will increase to its par value. A par value bond will stay at its par value.

Semiannual Bonds 1.Multiply years by 2 to get periods = 2n. 2.Divide nominal rate by 2 to get periodic rate = k d /2. 3.Divide annual INT by 2 to get PMT = INT/2. INPUTS OUTPUT 2nk d /2 OK INT/2OK NI/YR PV PMT FV

2(10) 14/2 100/ NI/YR PV PMTFV Find the value of 10-year, 10% coupon, semiannual bond if k d = 14%. INPUTS OUTPUT Using tables: Value = INT(PVIFA 7%,20 )+ M(PVIF 7%,20 ). = 50* * =

What is the cash flow stream of a perpetual bond with an annual coupon of $100?

A perpetuity is a cash flow stream of equal payments at equal intervals into infinity. V perpetuity =. PMT k

V 10% = = $1000. V 13% = = $ V 7% = = $ V 10% = = $1000. V 13% = = $ V 7% = = $ $ $ $ $ $ $

P 0 = ^ D 1 (1 + k) D 2 (1 + k) 2 D n (1 + k) n Stock value = PV of dividends

D 1 = D 0 (1 + g) D 2 = D 1 (1 + g) Future Dividend Stream:

P 0 = =. ^ D 1 k s - g D 0 (1 + g) k s - g If growth of dividends g is constant, then: Model requires: k s > g (otherwise results in negative price). g constant forever.

D 0 = 2.00 (already paid). D 1 = D 0 (1.06) = $2.12. P 0 = = =$ Last dividend = $2.00; g = 6%. What is the value of Bon Temps’ stock given k s = 16%? ^ D 1 k s - g $

P 1 = D 2 /(k s - g) = 2.247/0.10 = $ ^ What is Bon Temps’ value one year from now? Note: Could also find P 1 as follows: P 1 = P 0 (1 + g) = $21.20(1.06) = $ ^ ^

k s = + g = = 16%. D1P0D1P0 $2.12 $21.20 Constant growth model can be rearranged to solve for return: ^

V= = = $ Pmt k If a stock’s dividends are not expected to grow over time (g = 0), then it is a perpetuity. $ Zero growth

Subnormal or Supernormal Growth Cannot use constant growth model Value the nonconstant & constant growth periods separately

If we have supernormal growth of 30% for 3 years, then a long-run constant g = 6%, what is P 0 ? ^ 0 k s =16% g = 30% g = 30% g = 30% g = 6% D 0 = P 3 = = = P

$2.00 $2.12 0% 6%... Suppose g = 0 for 3 years, then g is constant at 6%. ฅ

(1) PV 3-year, $2 annuity, 16% PV = PMT(PVIFA 16%,3 ) = 2 * = $ (2)P 3 = = $ PV(P 3 ) = $ P 0 = $ $13.58 = $ $ What is the price, P 0 ?