needed to generate $1 in sales = Total Assets / Sales
External Financing Needed (EFN)
–
The amount of financing required to balance both sides of
the balance sheet
External Financing and Growth
Symbols
S = Previous year’s sales
A = Total Assets
D = Total Debt
E = Total equity
p = Profit Margin
R = Retention Ratio
ROA = Return on Assets
ROE = Return on Equity
D/E = Debt/Equity Ratio
g = Growth rate in sales

FIN 300
Blawal Aleem
Increase in Total Assets =
A x g
Addition to retained earnings
= p(S)R x (1+g)
EFN =
Increase in total assets
–
Addition to retained earnings = A(g)
–
p(S)R x (1+g)
EFN =
-p(S)R + [A-p(S)R] x g
Internal Growth Rate
–
The growth rate a firm can maintain with only internal financing = (ROA
x R) / (1
–
ROA x R)
Debt Capacity
–
The ability to borrow to increase firm value
Sustainable growth rate
–
The growth rate a firm can maintain given its debt capacity, ROE, and
retention ratio
D/E =
New borrowing / Addition to retained earnings
New Borrowing =
D/E[p(S)R(1+g)]
EFN* =
Increase in total assets
–
Addition to retained earnings
–
New borrowing = A(g)
–
p(S)R x
(1+g)[D/E] = 0
g* =
ROE x R/[1
–
ROE x R]
ROE =
Profit Margin x Total Asset Turnover x Equity Multiplier = p(S/A)(1+D/E)
Chapter 5
Future Value and Compounding
Future Value (FV)
–
The amount an investment is worth after one or more periods. Also
compound value. = $1 x (1+r)
t
Compounding
–
The process of accumulating interest in an investment over time to earn more
interest
Interest on interest
–
Interest earned on the reinvestment of previous interest payments
Compound Interest
–
Interest earned on both the initial principal and the interest reinvested
from prior periods
Simple interest
–
Interest earned only on the original principal amount invested
Present Value and Discounting

FIN 300
Blawal Aleem
Present Value (PV)
–
The current value of future cash flows discounted at the appropriate
discount rate = $1 x [1/(1+r)
t
] = $1/(1+r)
t
Discount
–
Calculate the present value of some future amount
Discount rate
–
The rate used to calculate the present value of future cash flows
More on Present and Future Values
FV =
PV x (1+r)^t
PV =
FV
t
/ (1+r)
t
= FV
t
x [1/(1+r)
t
]
Symbols
PV = Present Value
FV
t
= Future Value
r = Interest rate
t = Number of periods
C = Cash amount
TIME VALUE CALCULATIONS
FV
t
=
C x (1+r)
t
PV =
C / (1+r)
t
PV =
FV
t
/ (1+r)
t
Chapter 6
Valuing Level Cash Flows: Annuities and Perpetuities
Annuity
–
A level stream of cash flows for a fixed period of time
Annuity present value =
C x (1-Present Value Factor/r) = C x ((1-1/(1+r)
t
)/r)
Annuity FV factor =
(Future Value Factor
–
1)/r = ((1+r)
t
-1)/r
Annuity Due
–
An annuity doe which the cash flows occur at the beginning of the period
Annuity due value =
Ordinary annuity value x (1+r)
Perpetuity
–
An annuity in which the cash flows continue forever

FIN 300
Blawal Aleem
Consol
–
A time of perpetuity
Cash flow =
Perpetuity present value x Rate
Perpetuity PV =
C/r = C x (1/r)
ANNUITY AND PERPETUITY CALCULATIONS
FV
t
= C x {[1+r)
t
–
1]/r}
PV
= C x {1-[1/(1+r)
t
]}/r
PV =
C/r
Growing Perpetuity
–
A constant stream of cash flows without end that is expected to rise
indefinitely = PV = C/r-g
Growing Annuity
–
A finite number of growing annual cash flows = PV = (C/r-g)(1-(1+g/1+r)
t
)
Comparing Rates: The effect of compounding
Stated Interest Rate
–
The interest rate expressed in terms of the interest payment made each
period. Also, quoted interest rate
Effective Annual Rate (EAR)
–
The interest rate expressed as if it were compounded once per
year = [1+(Quoted rate/m]
m
-1 (m=number of time interest is compounded during the year)
Annual Percentage Rate (APR)
–
The interest rate charged per period multiplied by the number
of periods per year
EAR =
e
q
–
1 (q=quoted rate) (continuous compounding)
Loan Types and Loan Amortization
Pure Discount Loans
Interest-Only Loans
Amortized Loans