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BOND VALUATION

DICTIONARY

intrinsic value ( V ) - represents the real or true worth of an asset, separate from its market price. ( I )- Periodic Interest Payment in Value not %; or it is the actual amount paid by the issuer. ( Kd ) - required rate of return or discount rate per period.

Perpetual Bonds

A Perpetual Bond is a bond that never matures, it has an infinite life. V=I/Kd

Example: Bond P has $1k face value and provides an 8% annual coupon. The appropriate discount rate is 10%. What is the value of the perpetual bond?

I=$1k (8%) = $80

Kd = 10%

V = I/Kd = $80/10% = 800

Nonzero Coupon Bonds

A Nonzero Coupon Bond is a coupon paying bond with a finite life (MV). V= I (PVIFAKd,n) + MV (PVIFKd,n)

Example: Bond C has a $1k face value and provides and 8% annual coupon for 30 years. The appropriate discount rate is 10%. What is the value of the coupon bond?

V or PV= $80 (PVIFA10%,30) + $1000 (PVIF10%,30) = $80 (9.427) + $1000 (.057)

Semiannual Compounding

A non-zero coupon bond adjusted for semi-annual compounding. V= I/2 (PVIFAKd/2, 2*n) + MV (PVIFKd/2, 2*n)

Example: Bond C has a $1k face value and provides an 8% semi-annual coupon for 15 years. The appropriate discount rate is 10% (annual rate). What is the value of the coupon bond?

V = $40 (PVIFA5%,30) + $1000 (PVIF4%,30)

Zero Coupon Bonds

Zero coupon bonds are bonds that do not pay interest during the life of the bonds. V=MV (PVIFKd,n)

Example: Bond Z has a $1k face value and a 30 year life. The appropriate discoutn rate is 10%. What is the value of the zero-coupon bond?

V = $1000 (PVIF10%,30)

STOCK VALUATION

DICTIONARY

Div p - the annual dividend payment per preferred share.  Div t - cash dividend at the time t. K e - Equity investor's required return. (1) n - the year in which the firm's shares are expected to be sold Pricen - the expected share price in year n. D 1 - dividend paid at time 1. g - the constant growth rate. K e - Investor's required return.

Preferred Stock Valuation

Preferred stock has no stated maturity date, given the fixed nature of its payments, is similar to a perpetual bond. So, the same approach of valuation is used. V = Divp / Kp

Example: Stock PS has an 8%, $100 par value issue outstanding. The appropriate discount rate is 10%. What is the value of the preferred stock?

Div p = $100 (8%) = $8.00

Kp = 10%

V = $8/10% = $80

Dividend Valuation Model

Basic dividend valuation model accounts for the PV of all future dividends. V = Div1 / (1 + Kr)^1 + Div2 (1+Ke)^2 + ... + Div (inf.) / (1+Ke)^(inf.)

Adjusted Dividend Valuation Model

The basic dividend valuation model adjusted for the future stock sale. V = Div1 / (1 + Ke)^1 + Div2 / (1 + Ke)^2 + ... + Div n + Price n/ (1+Ke)^n

Constant Growth Model

The constant growth model assumes that dividends will grow forever at the rate g. V = D1/(Ke-g) where D1=D0(1+g)

Example: Stock CG has an expected dividend growth rate of 8%. Each share of stock just received an annual $3.24 dividend. The appropriate discount rate is 15%. What is the value of the common stock?

D1 = $3.24 ( 1 + 0.08 ) = $3.50

Vcg = D1/(Ke-g) = #3.50 / (0.15 - 0.08)

Zero Growth Model

The zero growth model assumes that dividends will grow forever at the rate g = 0. V = D1/Ke

Growth Phases Model

The growth phases model assumes that dividends for each share will grow at two or more different growth rates.

Determining Bond YTM

Determine the Yield-to-Maturity (YTM) for the annual coupon paying bond with finite life. Kd = YTM