, Summary of Discrete Compounding Formulas with Discrete Payments
- - = -
Factor Excel Cash Flow -
Flow Type Notation Formula Command Diagram i
S Compound
I amount = FV(i,N . P . , 0 )
N (F/e i, N )
G Present
i L worth = PV(i, N , F , -0)
E (PIE i, N
E Compound
: Q amount
= u i, N ) = P V ( i , N , A , . 0)
- A
L
Sinking
P fund
A ( M E i. N )
Y
i M AAA AA /
r E
5
I N Present i.
+ illv - 1 I
f
i;
i
T
s
worth
(P/A,i, N )
= .[(I
i ( 1 + i)" I
D E
$ R Capital
i I recovery A = P[
E ( M e i, N ) (1 + ilN - 1
r S
Linear
gradient
"
"r
8
I
Present
worth
+ i)" - iN - 1
I E (P/G,i, N)
Conversion fact01
j T (AIG,i, Rr)
S Geometric
E gradient
R
I Present
E worth
s ,,
(PIA g, i, N )
--.----
, Summary of Formulas
Effective Interest Rate per Payment Period
Discrete compounding i = [ ( I + ~ / ( c K ) ] '- 1
Continuous compounding i erlK - 1 - Recovery Period (Year
where i -effective interest rate per payment period
r =nominal interest rate or APR
C = number of interest periods per payment
period
K = number of payment periods per year
r / K = nominal interest rate per payment period
Market Interest Rate
i - i' + f + i'f
where i = market interest rate
if = inflation-free interest rate
-
,f = general inflation rate
Present Value of Perpetuities
p = market related risk index
r, = market rate of return
Capital Recovery with Return Cost of Debt
CR(i) = ( I - S ) ( A / P ,i, N ) + iS
Book Value
= I - x
11
1'1
D, where id
c,
=
-
cost of debt
the amount of term loan
Straight-Line Depreciation c,, = the amount of bond financing
-
(I - S)
D,? -
N
c,, = total debt = c, t c,,
k, = the before-tax interest rate on the term loan
kh = the before-tax interest rate on the bond
Declining Balance Depreciation
D,, - aI(1 - a)"-'
t,,, = the firm's marginal
-
Weighted-Average Cost of Capital
tax rate
1
where a = declining balance rate. and 0 < a 5
N
Cost of Equity
where k = cost of capital
where i, = cost of equity c,, = total equity capital
rf = risk-free interest rate V = Cd + C,
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