Fundamentals of Corporate Finance (Brealey)
Weiting Xu
Professor: Andreanne Tremblay
Chapter Reading Notes
FINE 2000
CHAPTER 5 – TIME VALUE OF MONEY (“TVM”)*
1.
FUTURE VALUES AND COMPOUND INTEREST
Future Value (FV):
amount to which an investment will grow after earning interest
Compound Interest:
interest earned on interest
Simple Interest:
interest earned only on original investment; no interest is earned on interest
FMV of $I investment = I (1 + r)
t
Future Value Interest Factor or Future Value Factor:
future value of current cash flow of $1
FV = I x Future Value Factor = I x FVIF(r,t) = I x (1+r)
t
Compound growth means that value increases each period by factor (1 + growth rate). The value after t periods will
equal the initial value times (1+ growth rate)
t

When money is invested at compound interest, the growth rate is the interest rate
2.
PRESENT VALUES
Present Value (PV):
value today of a future cash flow
PV =

PV are always calculated using compound interest

Thus, PV decline, other things being equal, when future cash payments are delayed
PV = I x discount factor = I x PVIF(r,t) = I x
Finding the Interest Rate

Solve for the r in the equation
Finding the Investment
Period

Finding the t in the equation
3.
MULTIPLE CASH FLOWS
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Fundamentals of Corporate Finance (Brealey)
Weiting Xu
Professor: Andreanne Tremblay
Chapter Reading Notes
FINE 2000
Future Value of Multiple Cash
Flows

Stream of cash flows:
when there are many payments
To find value at some future date of a stream of cash flows, calculate what
each CF will be worth at that future date, then add up these FV
PV of Multiple Cash Flows

If there is more than one future CF, we simply need to work out what each
flow would be worth today and then add these PVs
4.
LEVEL CASH FLOWS: PERPETUITIES AND ANNUITIES
Annuity:
equally spaced and level stream of cash flows
Perpetuity:
stream of level cash payments that never ends
How to Value
Perpetuities
e.g. British gov’t borrowed by issuing perpetuities. Instead of repaying these loans,
British gov’t pays investors holding these securities a fixed annual payment in
perpetuity
PV of Perpetuity =
Warnings about the formula:
1.
A payment of $1 at end of one year has a PV 1/(1+r) the perpetuity has a value of 1/r
2.
Tells us the value of a regular stream of payments starting one period from now
How to Value Annuities
Two ways:
1.
Slow – value each cash flow separately and add up PVs
2.
Simplification process
PV of tyear annuity = C x []
Or,
PV of tyear annuity = payment x annuity factor = C x PVA(r,t)
Annuities Due
Level stream of cash flows starting immediately

In general, PV of an annuity due of t payments of $1 per period is the same as $1 plus
the PV of an ordinary annuity providing the remaining t – 1 payments
PV Annuity Due = 1 + PV Ordinary Annuity of t – 1 payments = 1 + []
Future Value of an
Annuity
FVA(r,t) = PV of Annuity of $1 per year x (1 + r)
t
of $1 per year, FVA (r,t)
FVA(r,t) =
If the first cash flow comes immediately, FV of CF stream is greater, since each flow