Financial Economics: Household Saving and Investment Decisions

Transcription

1 Financial Economics: Household Saving and Investment Decisions Shuoxun Hellen Zhang WISE & SOE XIAMEN UNIVERSITY Oct, / 32

2 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 2 / 32

3 Outline A Life-Cycle Model of Saving 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 3 / 32

4 A Life-Cycle Model of Saving A Life-Cycle Model of Saving Example 1: Assume that you are currently 35 years old, expect to retire in 30 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 real term) 4 / 32

5 A Life-Cycle Model of Saving How Much Should I Save and Consume? Consider two approaches: Target replacement rate of pre-retirement income Maintain the same level of consumption spending 5 / 32

6 A Life-Cycle Model of Saving Target replacement rate of pre-retirement income 1 compute the retirement income. Many experts recommend a rate of 75% of the pre-retirement income. $30, = $22, 500/year 2 using your calculator compute the present value of the retirement funds as an regular annuity n = 15, i = 3, FV = 0, PMT = 22, 500 = PV = 268, 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 6 / 32

7 A Life-Cycle Model of Saving 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 is only $22,500 The next method equates consumption 7 / 32

8 A Life-Cycle Model of Saving 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 must equal the present value of earnings over the next 30 years n = 30, i = 3, FV = 0, PMT = 30, 000 PV = n = 45, i = 3, FV = 0, PV = PMT = $23, 982 The savings are then $30,000 - $23,982 = $6,018 8 / 32

9 A Life-Cycle Model of Saving Human Capital and Permanent Income 4 C 3 5 ( ) = 30, t ( ) t t=1 t=1 Human capital :The present value of one s future labor income Permanent income: The constant level of (real) consumption spending that has a present value equal to one s human capital 9 / 32

10 A Life-Cycle Model of Saving 10 / 32

11 A Life-Cycle Model of Saving 11 / 32

12 A Life-Cycle Model of Saving 12 / 32

13 A Life-Cycle Model of Saving The Inter-temporal Budget Constraint T C t [ (1 + i) + B t t (1 + i) ] = W t 0 + t=1 R t=1 Y t (1 + i) t i = real interest rate R = number of years to retirement T = number of years of remaining life W 0 = initial wealth B t = bequest received in year t 13 / 32

14 A Life-Cycle Model of Saving Omar s Life-Cycle Savings Plan 14 / 32

15 A Life-Cycle Model of Saving Example 2 Suppose that you are 30 years old, plan to retire at age 65, and expects to live to age 85. Your salary is $25,000 per year, and you intend to maintain a constant level of real consumption spending over the 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 to receive 30 years from now have on your permanent income? 15 / 32

16 Several Formula A Life-Cycle Model of Saving Annuity Present Value factor Sinking Fund Factor Capital Recovery Factor PV (PMT, i, n) = PMT PMT (FV, i, n) = FV PMT (PV, i, n) = PV 1 (1 + i) n i i (1 + i) n 1 i 1 (1 + i) n 16 / 32

17 Outline Taking Account of Social Security 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 17 / 32

18 Taking Account of Social Security Taking Account of Social Security In many countries the government obliges citizens to participate in a mandatory retirement income system called social security Contributors pay a tax during their working years, and in return qualify for a lifetime annuity in their old age 18 / 32

19 Taking Account of Social Security 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 security taxes for 30 years, how much will you receive in benefits per year for 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, your saving falls from $6,018 to $4,018 per year. 19 / 32

20 Taking Account of Social Security 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 security taxes for 30 years, how much will you receive in benefits per year for 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, your saving falls from $6,018 to $4,018 per year. 19 / 32

21 Taking Account of Social Security 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 security taxes for 30 years, how much will you receive in benefits per year for 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, your saving falls from $6,018 to $4,018 per year. 19 / 32

22 Deferring Taxes Through Voluntary Retirement Plans 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 20 / 32

23 Deferring Taxes Through Voluntary Retirement Plans Deferring Taxes Through Voluntary Retirement Plans Many countries encourage voluntary savings for retirement through provisions of the tax code. In the U.S., employees are permitted to set up Individual Retirement Accounts (IRA) that defer payment of taxes until retirement The rules are a little complex, but an IRA may be used by an investor to save money for retirement. Payments into the plan are tax-deductible, but the flows from the plan after retirement are taxed. The interest on these contributions is not taxed until the money is withdrawn. It is usual for marginal tax rates to be lower after retirement, but this is not the key benefit 21 / 32

24 Deferring Taxes Through Voluntary Retirement Plans 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 now and after retirement Analyse the benefits of IRA plan 22 / 32

25 Deferring Taxes Through Voluntary Retirement Plans The Advantage of Tax-Deferred Saving 23 / 32

26 Deferring Taxes Through Voluntary Retirement Plans 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 retirement benefits =$1000 ( ) 0.8= $ Unsheltered Cases Only a $1, 000 (1 0.20) = 800, enters the plan. Earnings and realized capital gains are taxable, dispersions are not taxed. Result: 1st year after tax retirement benefits $800 ( ) 30 = $ Not taking into account the advantages of differential taxation, the investor will be 1.56 times better off using the sheltered plan 24 / 32

27 Outline Should You Invest in a Professional Degree? 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 25 / 32

28 Should You Invest in a Professional Degree? Should You Invest in a Professional Degree? Education may be viewed as an investment in human capital One purpose of additional schooling is to increase one s earning power Example: Getting a Graduate Degree (like all of you) 26 / 32

29 Example 3 Should You Invest in a Professional Degree? You are 20 years old and are considering full-time study for an MBA degree. Tuition and other direct costs will be $15,000 per year for two 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. But how much does your salary have to increase (in real terms) as a result of getting your MBA degree to justify the investment? Assume a real interest rate of 3% per year and ignore taxes. Also assume that the salary increase is a constant real amount that starts after you complete your degree (at the end of the year following graduation) and lasts until retirement at age / 32

30 Example 3 Should You Invest in a Professional Degree? Ignoring uncertainty, you give up $45,000 in each of the next two years in order to increase earnings by $5,000 per year over the remaining 43 years. The present value of the out ow is $86,106, the present value of the inflow is $ 113,026. So the NPV of the human capital investment =$ 26,920. Is it worthwhile? 28 / 32

31 Outline Should You Buy or Rent 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 29 / 32

32 Should You Buy or Rent Should You Buy or Rent Interest paid on a mortgage is tax-deductible, and this provides a substantial tax break if you are in a higher tax bracket This may make buying a house attractive to you when compared to renting Remember that this tax shield decays 30 / 32

33 Should You Buy or Rent Example 4 Suppose you currently rent an apartment and have an option to buy it for $200,000. Property taxes are $2,000 per year and are deductible for income tax purposes. Annual maintenance costs on the property are $1,500 per year and are not tax deductible. You expect property taxes and maintenance 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 this amount? 31 / 32

34 Example 4 Should You Buy or Rent The after-tax annual outlay from the purchase is: (1 40%) 2000 = $2, 700 The present value of this perpetuity is: 2700 = $135, 000 2% The present value of the costs of owning are: = $335, 000 The break-even rent is: 2% = $6, 700 per year. 32 / 32