Financial Economics: Household Saving and Investment Decisionshellenzsx.weebly.com/uploads/4/8/2/0/48206823/chap5.pdf · A Life-Cycle Model of Saving Human Capital and Permanent Income

Financial Economics: Household Saving and

Investment Decisions

Shuoxun Hellen Zhang

WISE & SOE

XIAMEN UNIVERSITY

Oct, 2016

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Outline

1 A Life-Cycle Model of Saving

2 Taking Account of Social Security

3 Deferring Taxes Through Voluntary Retirement Plans

4 Should You Invest in a Professional Degree?

5 Should You Buy or Rent

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A Life-Cycle Model of Saving

Outline






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Example 1:

Assume that you are currently 35 years old, expect to retire in30 years at 65, and then live for 15 more years until 80

Your real labor income is $30,000/year until age 65

Interest rates exceed inflation by 3%/ year (interest rates in realterm)

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How Much Should I Save and Consume?

Consider two approaches:

Target replacement rate of pre-retirement income

Maintain the same level of consumption spending

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Target replacement rate of pre-retirement income

1 compute the retirement income. Many experts recommend arate of 75% of the pre-retirement income.$30, 000 ∗ 0.75 = $22, 500/year

2 using your calculator compute the present value of theretirement funds as an regular annuity

n = 15, i = 3,FV = 0,PMT = −22, 500 =⇒ PV = 268, 604

3 compute the retirement income

4 compute how much you need to save each year

n = 30, i = 3,PV = 0,FV = −268, 604 =⇒ PMT = 5, 646

To obtain a real $22,500 you need to save $5,646 per year

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Target replacement rate Conclusion

You will have noticed that your pre-retirement consumption is$30,000 - $5,646 = 24,354; but the real retirement income isonly $22,500

The next method equates consumption

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Maintain the same level of consumption spending

Assume that your level of real consumption is C

The present value of consumption over the next 45 years mustequal the present value of earnings over the next 30 years

n = 30, i = 3,FV = 0,PMT = 30, 000⇒ PV = 588013.2

n = 45, i = 3,FV = 0,PV = 588013.2⇒ PMT = $23, 982

The savings are then $30,000 - $23,982 = $6,018

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Human Capital and Permanent Income

4∑t=1

5C

(1 + 0.03)t=

3∑t=1

030, 000

(1 + 0.03)t

Human capital :The present value of one’s future labor income

Permanent income: The constant level of (real) consumptionspending that has a present value equal to one’s human capital

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The Inter-temporal Budget Constraint

T∑t=1

[Ct

(1 + i)t+

Bt

(1 + i)t] = W0 +

R∑t=1

Yt

(1 + i)t

i = real interest rate

R = number of years to retirement

T = number of years of remaining life

W0 = initial wealth

Bt = bequest received in year t

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Omar’s Life-Cycle Savings Plan

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Example 2

Suppose that you are 30 years old, plan to retire at age 65, andexpects to live to age 85. Your salary is $25,000 per year, and youintend to maintain a constant level of real consumption spending overthe next 55 years. Assume no taxes, no growth in real labor income,and a real interest rate of 3% per year.

What is the value of your human capital?

What is your permanent income?

What effect would a $1 million inheritance that you expect toreceive 30 years from now have on your permanent income?

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Several Formula

Annuity Present Value factor

PV (PMT , i , n) = PMT1− (1 + i)−n

i

Sinking Fund Factor

PMT (FV , i , n) = FVi

(1 + i)n − 1

Capital Recovery Factor

PMT (PV , i , n) = PVi

1− (1 + i)−n

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Taking Account of Social Security

Outline






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In many countries the government obliges citizens to participatein a mandatory retirement income system called social security

Contributors pay a tax during their working years, and in returnqualify for a lifetime annuity in their old age

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Social Security as Investment Substitute

If social security pays a return equal to 3% in the last example,then just reduce the savings by the social security tax—In Example 1, if you pay $2000 per year in social securitytaxes for 30 years, how much will you receive in benefits per yearfor 15 years starting at age 65.

n = 30, i = 3%,PMT = 2000⇒ FV = 95, 151

n = 15, i = 3%,PV = 95, 151⇒ PMT = $7970

What impact will social security have on your savings?You will reduce your voluntary saving by $2,000, that is, yoursaving falls from $6,018 to $4,018 per year.

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n = 30, i = 3%,PMT = 2000⇒ FV = 95, 151

n = 15, i = 3%,PV = 95, 151⇒ PMT = $7970


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n = 30, i = 3%,PMT = 2000⇒ FV = 95, 151

n = 15, i = 3%,PV = 95, 151⇒ PMT = $7970


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Deferring Taxes Through Voluntary Retirement Plans

Outline






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Deferring Taxes Through Voluntary Retirement

Plans

Many countries encourage voluntary savings for retirementthrough provisions of the tax code.

In the U.S., employees are permitted to set up IndividualRetirement Accounts (IRA) that defer payment of taxes untilretirement

The rules are a little complex, but an IRA may be used by aninvestor to save money for retirement. Payments into the planare tax-deductible, but the flows from the plan after retirementare taxed. The interest on these contributions is not taxed untilthe money is withdrawn.

It is usual for marginal tax rates to be lower after retirement, butthis is not the key benefit

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IRA Benefits

The major benefits are more subtle. Assume:

You can contribute $1,000 of pre-taxed income to the IRA plan,starting next year, for the next 30-years.

That the plan will return 8%/year

The tax rate on all taxable income streams is 20%, both nowand after retirement

Analyse the benefits of IRA plan

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The Advantage of Tax-Deferred Saving

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Sheltered and Unsheltered Cases

Sheltered Case

The full $1,000 enters the plan. Accumulations are not taxed,dispersions are taxed. Result: 1st year after tax retirementbenefits =$1000 ∗ (1.0830) ∗ 0.8= $8050.12

Unsheltered Cases

Only a $1, 000 ∗ (1− 0.20) = 800, enters the plan. Earnings andrealized capital gains are taxable, dispersions are not taxed.Result: 1st year after tax retirement benefits$800 ∗ (1 + 0.08 ∗ 0.8)30 = $5144.45

Not taking into account the advantages of differential taxation, theinvestor will be 1.56 times better off using the sheltered plan

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Should You Invest in a Professional Degree?

Outline






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Education may be viewed as an investment in human capital—One purpose of additional schooling is to increase one’searning power

Example: Getting a Graduate Degree (like all of you)

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Example 3

You are 20 years old and are considering full-time study for an MBAdegree. Tuition and other direct costs will be $15,000 per year fortwo years. In addition you will have to give up a job with a salary of$30,000 per year.Assume tuition is paid and salary received at the end of the year. Buthow much does your salary have to increase (in real terms) as aresult of getting your MBA degree to justify the investment? Assumea real interest rate of 3% per year and ignore taxes. Also assume thatthe salary increase is a constant real amount that starts after youcomplete your degree (at the end of the year following graduation)and lasts until retirement at age 65.

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Example 3

Ignoring uncertainty, you give up $45,000 in each of the next twoyears in order to increase earnings by $5,000 per year over theremaining 43 years.The present value of the out ow is $86,106, the present value of theinflow is $ 113,026. So the NPV of the human capital investment =$26,920. Is it worthwhile?

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Should You Buy or Rent

Outline






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Interest paid on a mortgage is tax-deductible, and this provides asubstantial tax break if you are in a higher tax bracket

This may make buying a house attractive to you when comparedto renting

Remember that this tax shield decays

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Example 4

Suppose you currently rent an apartment and have an option tobuy it for $200,000.

Property taxes are $2,000 per year and are deductible for incometax purposes.

Annual maintenance costs on the property are $1,500 per yearand are not tax deductible. You expect property taxes andmaintenance costs to increase at the rate of inflation.

Your income tax rate is 40%,

you can earn an after-tax real interest rate of 2% per year.

You plan to keep the apartment forever. What is the “break-even”annual rent such that you would buy it if the rent exceeds thisamount?

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Example 4

The after-tax annual outlay from the purchase is:1500 + (1− 40%) ∗ 2000 = $2, 700The present value of this perpetuity is: 2700

2%= $135, 000

The present value of the costs of owning are:135000 + 200000 = $335, 000The break-even rent is: 2% ∗ 335000 = $6, 700 per year.

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Financial Economics: Household Saving and Investment Decisionshellenzsx.weebly.com/uploads/4/8/2/0/48206823/chap5.pdf · A Life-Cycle Model of Saving Human Capital and Permanent Income