1
Finance School of Management
Chapter 5,Life-Cycle
Financial Planning
Objective
Human
capital,permanent income
decisions over
life cycle
2
Finance School of Management
Consumption over the Life Cycle
u You are currently 35 years old,expect to retire
in 30 years at age 65,and then to live for 15
more years until age 80
u You current income is $30,000 per year,and
you real labor income adjusted for inflation
remains at $30,000 per year until age 65
u The real rate of interest is 3% per year
u Assume you plan to consume a constant stream
of the same amount in each of the next 45 years,
denoted by C
3
Finance School of Management
Target Replacement Rate of
Preretirement Income
u You should aim for a replacement rate equal to
75% of your preretirement income,That is
0.75*$30000=$22,500,
n i PV FV PMT Rsult
15 3？ 0 -22,500 $268,604
n i PV FV PMT Rsult
30 3 0 $268,604? $5,646
4
Finance School of Management
n i PV FV P M T R e s u l t
30 3% 0? 1 $ 4 7, 5 8
n i PV FV P M T R e s u l t
15 3%? 0 1 $ 1 1, 9 4
Consumption over the Life Cycle
5
Finance School of Management
CC 94.11)0 0 0,30(58.47 ??
Consumption over the Life Cycle
982,23$?C
— Permanent income
— Human capital
? ?
? ? ?
?
?
45
1
30
1 )1()1(t t
t
t
t i
Y
i
C
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Finance School of Management
L a b o r I n c o m e a n d C o n s u m p t i o n
- 5 0 0 0
0
5000
10000
15000
20000
25000
30000
35000
35 40 45 50 55 60 65 70 75 80
A g e
R
e
a
l
$
l a b _ i n c
c o n s u m p
7
Finance School of Management
H u m a n C a p i t a l a n d W e a l t h
- 1 0 0 0 0 0
0
100000
200000
300000
400000
500000
600000
700000
35 45 55 65 75
A g e
R
e
a
l
$
f u n d
H u m a n C a p
C a p i t a l
See Excel
8
Finance School of Management
The Inter-temporal Budget
Constraint
? ? ? ? ? ?
??
?? ?
??
?
?
?
R
t
t
t
T
T
t
t
t
i
Y
W
i
B
i
C
1
0
1 111
i = real interest rate
R = number of years to retirement
T = number of years of remaining life
W0 = initial wealth
B = bequest
9
Finance School of Management
The Optimal Choice,
Optimization Model
u The economists usually research the optimal
choice of agents under intertemporal budget
constraint,
– a feasible plan
10
Finance School of Management
Omar’s Problem
u Dr,Omar has just graduated from medical school
at age 30 and has started training to be a surgeon,
u His real salary for the next five years will be
$25,000 per year,After completing his residency,
Omar expects to earn $300,000 per year in real
terms until he retires at age 65,Assume that the
real interest rate is 3%,
u If he wants to maintain the same level of
consumption until his life expectancy 85 years old,
should Omar allocate his wealth?
11
Finance School of Management
-300,000
-200,000
-100,000
0
100,000
200,000
300,000
400,000
30 31 32 33 34 35 36 37 38 39 40 45 49 54 58 63 67 72 76 81 85
Salary
consumption
Saving
12
Finance School of Management
-2,000,000
-1,000,000
0
1,000,000
2,000,000
3,000,000
4,000,000
5,000,000
6,000,000
7,000,000
30 31 32 33 34 35 36 37 38 39 40 45 49 54 58 63 67 72 76 81 85
Human capital
Tatal wealth
Other A & L
See excel
13
Finance School of Management
Taking account of social security
u In many countries the government obliges
citizens to participate in a mandatory
retirement system called security,
– Pay a tax during their working time and in turn
a lifetime annuity in their old age,
– Influence voluntary saving,
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Finance School of Management
Age Salary Consumption Saving
Human
capital Cum,Saving
35 30,000 23,982 4018+2000 588,013 0
65 30,000 23,982 4018+2000 0 16012+7970
70 0 23,982 -23,982 0 204,573
80 0 23,982 -23,982 0 0
15
Finance School of Management
u The tax-deferred plan
u You face a tax rate of 20%
and interest is 8%,
u You are 30 years before
retirement and contribute
$1000 to IRAs,Your total
before-tax cum,account
will be,
$1000*1.0830 =$10,063
u You will pay taxes,
0.2*$10,063=$2,012
u You will be left with
$8,050
u The ordinary saving plan,
u You have to pay $ 200 in
taxes,The remaining $800
go into ordinary saving plan,
and interest earnings will be
taxed,so after-tax int,rate,
(1-0.2)*8%=6.4%
u The cum,account will be
$800*1.06430=$5,144.45
16
Finance School of Management
Should you buy or rent?
u You are currently renting a house for $10,000 per year
and can buy a house for $200,000,
u Property taxes are deductible for income tax purposes,and
your tax rate is 30%,
u The maintenance and property taxes are estimated to be,
u Should you buy or continue to rent?
Maintenance $1,200
Property taxes $2,400
Total $3,600
To be continued
17
Finance School of Management
u If you buy the house,you have to pay $200,000
now,Because the after-tax outflow for property
taxes is 0.7*$2,400=$1,680,so the payout each
year will be,
u The NPV of two alternatives will be,
880,2$680,1$200,1y ear ti n O u t f l o wC a s h ??? $
? ?
? ?
2 8 8 0
C o s t o f O w n i n g 2 0 0 0 0 0
07
1 0 0 0 0
C o s t o f R e n t i n g
07
$,
P V $,
.i
$,
PV
.i
??
?
Continue…
To be continued
18
Finance School of Management
u Assume no inflation so that the real and nominal
before-tax discount rate is 3%,so
u Rent costs at which would you be indifferent
between buying and renting,
047,139$143,337$190,476$
)R e n t i n g(190,476$)O w n i n g(143,337$
???
?
N P V
$ 2 8 8 0
$ 2 0 0 0 0 0
0 0 2 1 0 0 2 1
$ 7,0 8 0
X,
,
..
X
??
??
Continue…