1 Finance School of Management Chapter 5: Life-Cycle Financial Planning Objective To analyze how much to save for retirement To determine whether to defer

1

FinanceFinance School of Management School of Management

Chapter 5: Life-Cycle Financial Chapter 5: Life-Cycle Financial PlanningPlanning

Objective To analyze how much to save for retirement

To determine whether to defer taxes or pay then now, and to get a professional degree, and to buy or rent an apartment

2


Chapter 5 ContentsChapter 5 Contents

Analyze how much to save for retirement. Determine whether to defer taxes or pay them

now. Determine whether to get a professional degree. Determine whether to buy or rent an apartment.

3


Consumption over the Life CycleConsumption over the Life Cycle

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.

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.

The real rate of interest is 3% per year. How much should you spend for consumption now and

how much should you save for retirement ?

4


Two ApproachesTwo Approaches

Aim for a target replacement rate of preretirement income.

Aim for maintaining the same level of consumption spending before and after retirement.

5


Target Replacement Rate of Target Replacement Rate of Preretirement IncomePreretirement Income

Recommendation: You should aim for a replacement rate equal to 75% of your preretirement income.

That is 0.75×$30,000 = $22,500.

n i PV FV PMT Result15 3% ？ 0 -22,500 $268,604

n i PV FV PMT Result30 3% 0 $268,604 ? $5,646

6


Maintaining the Same Level of Maintaining the Same Level of ConsumptionConsumption

Assume you plan to consume a constant stream of the same amount in each of the next 45 years, denoted by C.

n i PV FV PMT Result

30 3% 0 ? 1 $47.58


15 3% ? 0 1 $11.94

7


CC 94.11)000,30(58.47

982,23$C — — Permanent Permanent incomeincome

— — Human capitalHuman capital

45

1

30

1 )1()1(t tt

tt i

Y

i

C

8


Labor Income and Consumption

-5000

0

5000

10000

15000

20000

25000

30000

35000

35 40 45 50 55 60 65 70 75 80

Age

Rea

l $ lab_incconsump

9


Human Capital and Wealth

-100000

0

100000

200000

300000

400000

500000

600000

700000

35 45 55 65 75

Age

Rea

l $

fundHumanCapCapital

10


The Intertemporal Budget ConstraintThe Intertemporal Budget Constraint

R

tt

tT

T

tt

t

i

YW

i

B

i

C

10

1 111

i = real interest rate

R = number of years to retirement

T = number of years of remaining life

W0 = initial wealth

B = bequest

11


The Effect of Changes in Real IncomeThe Effect of Changes in Real Income

Dr.Omar Ben Holim’s has just graduated from medical school at age 30 and has started training to be a surgeon.

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%. If he wants to maintain the same level of consumption

for the rest of his life and his life expectancy is 85 years, how much should he allocate his wealth?

12


-300,000

-200,000

-100,000

0

100,000

200,000

300,000

400,000

30 35 40 45 50 55 60 65 70 75 80

Age

Con

stan

at D

olla

rs

Salary Consumption Saving

13


Taking Account of Social SecurityTaking Account of Social Security

In many countries governments oblige citizens to participate in a mandatory retirement system called social security.– Pay a tax during their working years and in turn qualify

for a lifetime annuity in their old age.

– The influence of mandatory saving on voluntary saving.

14


The Influence of Mandatory Saving on The Influence of Mandatory Saving on Voluntary SavingVoluntary Saving

Suppose that social security benefits are equal to what you would have if– you had saved each year an amount equal to the amount you pay in

social security taxes, and – earned a real interest rate of 3% per year.

Suppose that you are required to pay $2,000 per year in social security taxes for 30 years.


30 3% 0 ? 2000 $95,151


15 3% 95,151 0 ? $7,970

15


Age Salary Consumption SavingHuman capital Cum. Saving

35 30,000 23,982 4018+2000 588,013 0

65 30,000 23,982 4018+2000 0 191,147+95,151

70 0 16012+7970 -23,982 0 204,573

80 0 16012+7970 -23,982 0 0

The real interest rate implied in social security account vs. that earned in your bank account.

Lifetime annuity implies that the longer you live, the higher your actual rate of return.

16


Deferring Taxes through Voluntary Deferring Taxes through Voluntary Retirement PlansRetirement Plans

In many countries governments encourage voluntary saving for retirement through provisions of the tax code.

Tax-advantage accounts: IRAs (Individual Retirement Accounts).– Contributions are deductible, and

– interest on the contributions is not taxed until the money is withdrawn.

17


The tax-deferred plan– You face a tax rate of 20%

and interest rate is 8%.

– You are 30 years before retirement and contribute $1000 to IRAs.

– Your total before-tax cum. account will be:

$1000×1.0830 =$10,063

– You will pay taxes:

0.2×$10,063=$2,012

– You will be left with $8,050.

The ordinary saving plan:– You have to pay $ 200 in

taxes.

– The remaining $800 goes into ordinary saving plan, and interest earnings will be taxed, so after-tax int. rate:

(1-0.2) ×8%=6.4%

– The cum. account will be

$800×1.06430=$5,144.45

The Advantage of The Advantage of Tax-deferred SavingTax-deferred Saving

18


Should You Invest in a Professional Degree?Should You Invest in a Professional Degree? Joe Grad has just graduated from college and is deciding whether to

go on for his master’s degree. If he takes job immediately, he can earn $30,000 per year in real

terms. If he goes on for two more years of graduate study, he can increase

his earnings to $35,000 per year. The cost of tuition is $15,000 per year in real terms, and the real

interest rate is 3% per year. Joe is now 20 years old and expects to retire at age 65.


2 3% ? 0 45,000 $86,106


43 3% ? 0 5,000 $119,910

2 3% ? 119,910 0 $113,026

19


Should You Buy or Rent?Should You Buy or Rent? You are currently renting a house for $10,000 per year and

can buy a house for $200,000. Property taxes are deductible for income tax purposes, and

your tax rate is 30%. The maintenance and property taxes are estimated to be:

Should you buy or continue to rent?

Maintenance $1,200

Property taxes $2,400

Total $3,600

20


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, the cash outflow each year will be:

The NPV of two alternatives will be:

Cash Outflow in year $1,200 $1,680 $2,880t

2 880 Cost of Owning 200 000

0 710 000

Cost of Renting0 7

$ ,PV $ ,

. i$ ,

PV. i

21


Assume no inflation so that the real and nominal before-tax discount rate is 3%. Thus,

Rent costs at which would you be indifferent between buying and renting:

$337,143(Owning) $476,190(Renting)

$476,190 $337,143 $139,047NPV

$2 880$200 000

0 021 0 021$7,080

X ,,

. .X

Documents

1 Finance School of Management Chapter 5: Life-Cycle Financial Planning Objective To analyze how much to save for retirement To determine whether to defer