Rate of Return to Investment
The Concept of Investment
For a one period investment,the ROR can be
evaluated each year.
For investments that generate returns in many
periods,there are two ways of describing the rate
of return.
– ROR in year t = yield/investment.
– Often ask,What is rate of return to an investment
project?
1tt
t
t
ppR
p
The Example of Consol
A consol (or perpetuity) that pays $100
annually can be bought and sold at the
market for $1000,
Want to compare the investment in the bond
($1000) with alternative investment
opportunities (e.g.,bank deposit).
Q,What is the interest rate R (or effective
yield) consistent with this price?
Effective Yield of a Bond
A,The R that equates the bond price with the
present value of the bond.
Present value of the bond is
Letting bond price equal to the PV,
R=100/1000=10%
1001000
R?
234
1 0 0 1 0 0 1 0 0 1 0 0 1 0 0...
( 1 ) ( 1 ) ( 1 ) ( 1 )PV R R R R R
Generalize to All Investment
Effective yield (or rate of return) is the R
that makes the present value of investment
returns equal to the present value of the cost.
Our example,cost=1000 in period 1;
return=100 each year starting from period 2.
Education example is a little more complex.
Consider Investment in College Education
You graduate from high school at 18
You earns if quitting school after high
school
If you go to college,
– pays direct cost H
– delays labor market entry by 4 years
– earns after college
HSW
COLW
18 22 65
Goes to College
Quits after highs
school
Age
Dollars
HSW
COLW
-H
Potential Earnings Stream Faced by a High School Graduate
The College Investment
465432 )1(...)1()1()1()1()1( r
W
r
W
r
W
r
H
r
H
r
HHPV C O LC O LC O L
C O L
462 )1(...)1()1( r
W
r
W
r
WWPV HSHSHS
HSHS
Effective yield of college education is the r when
This is also called,internal rate of return”.
HSC O L PVPV?
Benefits and Costs of College
Alternative Illustration:
Benefits of College:
Costs of College
4654 )1(...)1()1( r
WW
r
WW
r
WWP V B HSC O LHSC O LHSC O L
C O L?
32 )1()1()1()( r
WH
r
WH
r
WHWHP V C HSHSHS
HSC O L?
The College Decision
A person chooses to go to college if
Or,equivalently,the rate of return is larger than returns
from alternative investment.
HSC O L PVPV?
The Concept of Investment
For a one period investment,the ROR can be
evaluated each year.
For investments that generate returns in many
periods,there are two ways of describing the rate
of return.
– ROR in year t = yield/investment.
– Often ask,What is rate of return to an investment
project?
1tt
t
t
ppR
p
The Example of Consol
A consol (or perpetuity) that pays $100
annually can be bought and sold at the
market for $1000,
Want to compare the investment in the bond
($1000) with alternative investment
opportunities (e.g.,bank deposit).
Q,What is the interest rate R (or effective
yield) consistent with this price?
Effective Yield of a Bond
A,The R that equates the bond price with the
present value of the bond.
Present value of the bond is
Letting bond price equal to the PV,
R=100/1000=10%
1001000
R?
234
1 0 0 1 0 0 1 0 0 1 0 0 1 0 0...
( 1 ) ( 1 ) ( 1 ) ( 1 )PV R R R R R
Generalize to All Investment
Effective yield (or rate of return) is the R
that makes the present value of investment
returns equal to the present value of the cost.
Our example,cost=1000 in period 1;
return=100 each year starting from period 2.
Education example is a little more complex.
Consider Investment in College Education
You graduate from high school at 18
You earns if quitting school after high
school
If you go to college,
– pays direct cost H
– delays labor market entry by 4 years
– earns after college
HSW
COLW
18 22 65
Goes to College
Quits after highs
school
Age
Dollars
HSW
COLW
-H
Potential Earnings Stream Faced by a High School Graduate
The College Investment
465432 )1(...)1()1()1()1()1( r
W
r
W
r
W
r
H
r
H
r
HHPV C O LC O LC O L
C O L
462 )1(...)1()1( r
W
r
W
r
WWPV HSHSHS
HSHS
Effective yield of college education is the r when
This is also called,internal rate of return”.
HSC O L PVPV?
Benefits and Costs of College
Alternative Illustration:
Benefits of College:
Costs of College
4654 )1(...)1()1( r
WW
r
WW
r
WWP V B HSC O LHSC O LHSC O L
C O L?
32 )1()1()1()( r
WH
r
WH
r
WHWHP V C HSHSHS
HSC O L?
The College Decision
A person chooses to go to college if
Or,equivalently,the rate of return is larger than returns
from alternative investment.
HSC O L PVPV?
