Supplement of Formulae and Present Value Tables Formulae
1. CAPITAL STRUCTURE a) After-Tax Marginal Cost of Debt:

kb = k(1− T) or where b)

(1− T)I F

k = interest rate; T = corporate tax rate; I = annual interest payment on debt; F = face value of debt

Cost of Preferred Shares: kp = Dp NPp

where c)

Dp = stated annual dividend payment on shares; NPp = net proceeds on preferred share issue

Cost of Common Equity: i) Cost of Common Shares (Capitalization of Dividends with Constant Growth Rate): ke = D 1 +g NP e

where ii)

D1 = dividend expected for period 1; NPe = net proceeds on common share issue; g = annual long-term dividend growth rate

Cost of Retained Earnings: kre = re = D 1 +g P e

where

Pe = market price of a share; re = expected return on common equity

iii)

Capital Asset Pricing Model:
Rj = Rf + β j Rm − Rf

(

)

where d)

Rj = expected rate of return on security j; Rf = risk-free rate; Rm = expected return for the market portfolio βj = beta coefficient for security j (measure of systematic risk)

Weighted Average Cost of Capital:
 E  P  B k =   kb +   kp +   ke  V  V  V

where

B = amount of debt outstanding; P = amount of preferred shares outstanding; E = amount of common equity outstanding V = B + P + E = total value of firm

2.

PRESENT VALUE OF TAX SHIELD FOR AMORTIZABLE ASSETS a) Present Value of Total Tax Shield from CCA for a New Asset Present Value = b)

CTd  2 + k  CdT  1 + 0.5k   =   (d + k )  2(1 + k )  (d + k )  1 + k   

Present Value of Total Tax Shield from CCA for an Asset that is Not Newly Acquired

 dT  Present Value = UCC  d +k 
c) Present Value of Total Tax Shield Lost From Salvage Present Value =

Sn (1 + k )n

Sn  dT    or n −1  d + k  (1 + k )

 dT   , depending on cash flow assumptions d +k 

Notation for