Corporate finance chapter 06 life cyle financial planning

Chapter 5: Life Cycle
Financial Planning

Objective
1

Financial decisions in an
uncertain world; Human
capital, permanent income
decisions over
life cycle


Objectives
– How much to save for retirement
– Whether to defer taxes or pay them now
– Whether to get a professional Degree
– Whether to buy or rent an apartment

2


Labor Income and Consumption
35000
30000
25000

Real $

20000

lab_inc
consump

15000
10000
5000
0
35

40

45

50

55

60

65

-5000

Age

3

70

75

80


Human Capital and Wealth
700000
600000
fund
HumanCap
Capital

500000

Real $

400000
300000
200000
100000
0
35

45

55

65

-100000
Age

4

75


The Inter-temporal Budget
Constraint
T

R

Ct
Yt
B
+
= W0 + ∑
∑
t
T
t
(1 + i )
t =1 (1 + i )
t =1 (1 + i )
i = real interest rate
R = number of years to retirement
T = number of years of remaining life
W0 = initial wealth
B = bequest
5

Solution by Real Conversion
We are almost done. All that remains is to assemble the
parts, and solve the resulting equation

PV = 391816.3459
− 8.208829897 * X
− 19876.29308
− 391816.3459 + 19876.29308
X=
= $45,309.75
− 8.208829897
6


Solution by Growing Annuity
• Equation

 1+ g 
Xa
1 − 
PV =

a −1 
( r − g )(1 + r )   1 + r 

7

b − a +1







Solution by Growing Annuity
j

a j bj

gj

Xaj

PVj

1 1

10 10% 35,000

?

2 1

13 3%

?

3 11 13 3%

X1
15,000*1.03

8

10

?


Algebra
  1.15 10 
  1.03 13 
35000
x
1 − 
1 − 
PV = 0 = +
  −
 
1−1 
1−1 
( 0.1 − 0.15)(1.1)   1.1   ( 0.1 − 0.03)(1.1)   1.1  
10
  1.03 13−11+1 
15000(1.03)
1 − 


−

11−1 

( 0.1 − 0.03)(1.1)   1.1 


⇒
0 = 391816.3459 − 8.208829897 x − 19876.29308
⇒
x = 45309.75

9


Year

NetSalary Fees
0
1
2
3
4
5
6
7
8
9
10
11

12
13

StartExp

35000
40250
46288
53231
61215
70398
80957
93101
107066
123126
-20159
-20764
-21386

Expend
-45310
-46669
-48069
-49511
-50997
-52526
-54102
-55725
-57397
-59119

-60893
-62719
-64601

45309.75
10

Sum
-10310
-6419
-1782
3719
10219
17871
26855
37375
49669
64007
-81051
-83483
-85987

Account
-10310
-17760
-21317
-19730
-11484
5239
32618

73255
130249
207281
146957
78170
0


How Much Must I Save? The
Nominal Approach
n
n


X 0 (1 + g )   1 + g  
1+ g 
PV =
1− 
= P
⇒


( r − g )   1 + r    1 + r 
P( r − g )
20000( 0.12 − 0.03)
X0 =
=
n
 1+ r 


  1.12 8 

(1 + g ) 1.03 

−
1


−
1
  1.03 

  1 + g 





X 0 = $1,830.79

11