FIN 614: Financial Management
Larry Schrenk, Instructor
1. What are Perpetuities?
2. Valuing Perpetuities
1. Constant Perpetuities
2. Growing Perpetuities
Cash Flows that are:
Infinite
Constant (or Growing at a Constant Rate)
At Regular Intervals
Examples:
I promise to pay you $100 per year forever.
I promise to pay you $10 per week forever.
Formula
PVPerpetuity
C

r
PVPerpetuity = Present Value of a Perpetuity
C = Period Cash Flow
r = Discount Rate
Notes:
No Financial Calculator Function
No Future Value
C and r are per Period
What is the present value of $1,000 per
year forever? (r = 10%)
PVPerpetuity
1,000

 $10,000
0.10
Example: I promise to pay you $100 per
year growing at 3% forever.
I am promising you the following cash
flow:
100 100(1.03) 100(1.03)2 100(1.03)3…
or
100 103.00
106.09
109.27…
Formula
PVGrowing Perpetuity
C1

r g
PVGrowing Perpetuity = Present Value of a Growing Perpetuity
C1 = Cash Flow in Period 1
Notes:
r = Discount Rate
g = Growth Rate of Cash Flow
Same as Constant Perpetuity
Growth can be Positive or Negative
C1 is Next Period’s Cash Flow
‘g’ will never be greater then ‘r’
What is the present value of receiving forever
$1,000 per year growing at 3% per year? (r =
10%)
PVGrowing Perpetuity
1,000

 $14,285.71
0.10  0.03
What is the present value of receiving forever
$1,000 per year declining at 3% per year? (r =
10%)
PVGrowing Perpetuity
1,000

 $7,692.31
0.10   0.03 
It might be better to call them ‘changing’
perpetuities, since the growth rate can be
negative.
A perpetuity is valued at $5,000 and the
interest rate is 7%. What is its cash flow?
Solve the formula for ‘C’
C
PV   C  PV  r  5,000 x.07  $350.00
r
A perpetuity valued at $5,000 has a cash
flow of $400. Find the discount rate.
Solve the formula for ‘r’
C
C
5000
PV   r 

 12.50%
r
PV
400
Perpetuity Assets
British ‘consol’
Real Estate
Perpetuity as a Cash Flow Pattern
Stocks
Long Term Value of Projects
FIN 614: Financial Management
Larry Schrenk, Instructor