Bus 342
Fundamentals of Corporate
Finance
Chapter 6
Discounted Cash Flow Valuation
Timeline and Cash Flows
– $150
Now
$100
$100
1 year later
Cash Flows
2 years later
3 years
Timeline
Positive Cash Flow :
Cash You Receive, Up Arrows
Negative Cash Flow: Cash You Pay,
Down Arrows
Present Value
with Multiple Cash Flows
1
A Second Way of
Calculating the Present Value
Financial Calculators
PV
I/YR
PMT
N
FV
Annuities
A series of constant or level cash flows that occur at
the end of each period for some fixed number of
periods is called an ordinary annuity.
Constant cash flow, at the beginning of each period:
annuity due.
2
Annuities – Finding Present Value
Annuities – Finding Payments
Annuities – Finding Interest Rate
3
Annuities – Finding
the Number of Payments
Annuities – Finding Future Value
Perpetuities
• Just like an annuity, except that the cash
flow stream continues forever. Also
called consols.
• Payment each period: C. Interest rate: r .
4
Ordinary Annuity
Present Value and Future Value
C: constant cash flow every period;
r: interest rate; t: number of periods.
PV
=
C
⎡
⎢ 1 −
⎢
⎢
⎢⎣
FV
=
C
⎡ (1 +
⎢
⎣
1
(1 +
r
r )
r
r )
t
t
⎤
⎥
⎥
⎥
⎥⎦
− 1 ⎤
⎥
⎦
Effective Annual Rates
and Compounding
• Quoted as “10% per annum compounded
semiannually”, or “10% compounded
semiannually”.
• Means paying 5% every six months.
Effective Annual Rates
and Compounding
• Quoted as “12% per annum compounded
monthly”, or “12% compounded monthly”.
• Means paying 1% every month.
5
Effective Annual Rates
and Compounding
• Quoted as “q per annum compounded m
times a year”.
• Means paying q / m each time for m
times in a year.
From EAR to Quoted Rate
APR and APY
• Annual Percentage Rate (APR): The
interest rate charged per period multiplied
by the number of periods per year.
Quoted to borrowers.
• Annual Percentage Yield (APY): The
effective annual rate a deposit earns.
6
Continuous Compounding
Continuous Compounding: EAR = eq – 1
=2.71828.10 – 1 = 10.51709%
Loan Types and Loan Amortization
• Pure Discount Loans
• Interest-Only Loans
• Amortized Loans
Pure Discount Loans
• The borrower receives money today and
repays a single lump sum at some time in
the future.
7
Interest – Only Loans
• The borrower pays interest each period,
and repay the entire principal at some
point in the future.
Amortized Loans
• A loan to be paid off by making regular
principal reductions.
My Own Story
• “Paying mortgage on a home you
purchased is building up your own equity
in the home, while paying rent is just
pouring money down the drain.”
8
My Own Story
My Own Story
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