INSTRUCTOR MANUAL
Instructor’s Manual for Principles of Finance
03/21/22 1
, Instructor’s Manual for Principles of Finance
Chapter 8
Time Value of Money II: Equal Multi ple Payments
Chapter Summary
This chapter deals with cash flows that are uniform and predictable in nature, either in the form
of perpetuities, or payments that continue into infinity, or annuities, which are uniform
payments with a finite end.
Lecture Notes
8.1 Perpetuities
A perpetuity is a series of uniform discrete payments or receipts that continue forever, or into
infinity (i.e., perpetually). An annuity also consists of uniform discrete payments, but these
payments come to a finite end.
The present value formula for a growing perpetuity is the starting point for calculating the
present value of a constant perpetuity.
PMT
The present value of a growing perpetuity is calculated as follows: PV =
i
.
PV = (PMT × (1 + g)) / (g – i)
Where:
PMT = payment
i = interest rate
g = growth rate
To determine the present value of a constant perpetuity, equating g to zero in the above
formula gives you:
( 1+ g )
PV =PMT ×
(g−i )
8.2 Annuities
An annuity consists of fixed regular payments into the future for a finite period of time.
In contrast, perpetuities have payments that don’t come to an end but continue forever.
Examples of annuities:
A lottery payout consisting of uniform annual payouts for a specified of time is a
common annuity.
Mortgage loans to fund a home purchase that are paid back through uniform monthly
installment payments—for example, for 30 years—are also annuities.
US Treasury bonds are US government debt obligations that promise to pay a fixed bond
coupon payment for as long as the bond is outstanding. The fixed coupon payments on
such bonds are annuities.
03/21/22 2
Instructor’s Manual for Principles of Finance
03/21/22 1
, Instructor’s Manual for Principles of Finance
Chapter 8
Time Value of Money II: Equal Multi ple Payments
Chapter Summary
This chapter deals with cash flows that are uniform and predictable in nature, either in the form
of perpetuities, or payments that continue into infinity, or annuities, which are uniform
payments with a finite end.
Lecture Notes
8.1 Perpetuities
A perpetuity is a series of uniform discrete payments or receipts that continue forever, or into
infinity (i.e., perpetually). An annuity also consists of uniform discrete payments, but these
payments come to a finite end.
The present value formula for a growing perpetuity is the starting point for calculating the
present value of a constant perpetuity.
PMT
The present value of a growing perpetuity is calculated as follows: PV =
i
.
PV = (PMT × (1 + g)) / (g – i)
Where:
PMT = payment
i = interest rate
g = growth rate
To determine the present value of a constant perpetuity, equating g to zero in the above
formula gives you:
( 1+ g )
PV =PMT ×
(g−i )
8.2 Annuities
An annuity consists of fixed regular payments into the future for a finite period of time.
In contrast, perpetuities have payments that don’t come to an end but continue forever.
Examples of annuities:
A lottery payout consisting of uniform annual payouts for a specified of time is a
common annuity.
Mortgage loans to fund a home purchase that are paid back through uniform monthly
installment payments—for example, for 30 years—are also annuities.
US Treasury bonds are US government debt obligations that promise to pay a fixed bond
coupon payment for as long as the bond is outstanding. The fixed coupon payments on
such bonds are annuities.
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