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1、Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,1,Chapter 5:Household Saving and Investment Decisions,ObjectiveFinancial decisions in an uncertain world;Human capital,permanent income decisions over life cycle,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,2,Conten
2、ts,5.1 A Life-Cycle Model of Savings5.2 Taking Account of Social Security5.3 Deferring Taxes through Voluntary Retirement Plans5.4 Should you Invest in a Professional Degree?5.5 Should you Buy or Rent?,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,3,Objectives,How much to save for
3、 retirementWhether to defer taxes or pay them nowWhether to get a professional degreeWhether to buy or rent an apartment,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,4,5.1 A Life-Cycle Model of Saving,Assume that you are currently 35 years old,expect to retire in 30 years at 65,a
4、nd then live for 15 more years until 80Your real labor income is$30,000/year until age 65Interest rates exceed inflation by 3%/year,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,5,How Much Should I Save and Consume?,Consider two approaches:Target replacement rate of pre-retirement
5、 incomeMaintain the same level of consumption spending,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,6,Target replacement rate of pre-retirement income,First compute the retirement income.Many experts recommend a rate of 75%of the pre-retirement income.$30,000*0.75=$22,500/yearusi
6、ng your calculator compute the present value of the retirement funds as an regular annuityn=15,i=3,FV=0,PMT=-22,500-PV=268,604,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,7,Target replacement rate of pre-retirement income(Cont.),Next compute how much you need to save each yearn=
7、30,i=3,PV=0,FV=-268,604-PMT=5,646 To obtain a real$22,500 after retirement you need to save$5,646 per year from now.,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,8,Target replacement rate Conclusion,You would have noticed that your pre-retirement consumption is$30,000-$5,646=24,3
8、54;but the real retirement income is only$22,500The next method equates consumption,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,9,Maintain the same level of consumption spending,Assume that your level of real consumption is CThe present value of consumption over the next 45 year
9、s must equal the present value of earnings over the next 30 yearsUsing annuity formula we got C=$23,982The savings are then$30,000-$23,982=$6,018A more general formula:,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,10,Human Capital and Permanent Income,Human capitalThe present val
10、ue of ones future labor incomePermanent incomeThe constant level of(real)consumption spending that has a present value equal to ones human capital,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,11,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,12,Copyright 2009 Pe
11、arson Education,Inc.Publishing as Prentice Hall,13,The Inter-temporal Budget Constraint,C=consumption spending in year ti=real interest rateR=number of years to retirementT=number of years of remaining lifeW0=initial wealthB=bequest,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,14
12、,Story,Dr.Omar Ben Holim has just graduated from medical school at age 30,and has started training to be a surgeon at Mount Heaven Hospital.Omars 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 re
13、tires at age 65.He wants to maintain the same level of real consumption spending for the rest of his life and his life expectancy is 85 years,how much should he plan to save now and in the future?Assume the real interest rate is 3%per year.,Copyright 2009 Pearson Education,Inc.Publishing as Prentice
14、 Hall,15,Omars Life-Cycle Savings Plan,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,16,illustration,Omars human capital initially is$5,186,747,and his permanent income is$193,720.In order to spend$193,720 per year during the five years of his residency,he will have to borrow(“dis
15、save”)$168,720 each year to supplement his$25,000 salary.His total indebtedness will grow to maximum of$895,758 at age 35,and then decline thereafter as a result of his saving$106,280 every year from age 36 until he retires at age 65.Note that he will not have paid off his debt until age 45!,Copyrig
16、ht 2009 Pearson Education,Inc.Publishing as Prentice Hall,17,Example 1,Suppose that you are 30 years old,plans 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 ta
17、xes,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?,Copyright 2009 Pearson Education,Inc.P
18、ublishing as Prentice Hall,18,5.2 Taking Account of Social Security,In many countries the government obliges citizens to participate in a mandatory retirement income system called social securityContributors pay a tax during their working years,and in return qualify for a lifetime annuity in their o
19、ld age,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,19,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 taxFor example,the previous example(Slide 17).If you pay$2000 per ye
20、ar in social security taxes for 35 years,how much will you receive in benefits per year for 20 years starting at age 65.What impact will social security have on your savings?The analysis becomes progressively more complex as we make the assumptions more realistic.What if you dont know your date of d
21、eath.,returns are risky,et cetera?,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,20,Redistribution among the rich and the poor,In many countries,the social security system offers a higher rate of return to people in the lower end of the income distribution than to those in the upp
22、er end.But the fact that benefits are paid in the form of a lifetime annuity implies that no matter how rich or poor you are,the longer you live,the higher your actual rate of return.So,consider a bonus awaiting you if you live long enough.,Copyright 2009 Pearson Education,Inc.Publishing as Prentice
23、 Hall,21,5.3 Deferring Taxes Through Voluntary Retirement Plans,Many countries encourage voluntary savings for retirement through provisions of the tax code.In the US employees are permitted to set up Individual Retirement Accounts(IRA)that defer payment of taxes until retirementThe rules are a litt
24、le 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
25、after retirement,but this is not the key benefit,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,22,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.This will grow at the rate
26、 of inflation of 2%That the plan will return 10%/yearThe tax rate on all taxable income streams is 20%,both now and after retirement,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,23,A comparison,Using IRA:Total pre-tax amount accumulated in IRA would be Pay taxes at the rate of 20
27、%,so you would have the following amount left after taxUsing other saving accounts:You have to pay 20%of$1,000 as tax immediately,so$800 left after tax each year;The after-tax interest rate earned is,therefore,So the amount accumulated at the savings plan would be,Copyright 2009 Pearson Education,In
28、c.Publishing as Prentice Hall,24,The Advantage of Tax-Deferred Saving,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,25,5.4 Should You Invest in a Professional Degree?,Education may be viewed as an investment in human capitalOne purpose of additional schooling is to increase ones e
29、arning powerExample:Getting a Graduate Degree(like all of you),Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,26,Example 2,You are 30 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
30、 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.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 ignor
31、e 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 65.,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,27,A more complicated exampleYouve deci
32、ded to obtain practical experience for 10 years,and then get a Ph.D.In three years You want the same standard of income over the next 13 years Assume that all cash flows occur at year-endYour starting salary is$35,000.Because you are smart,this will increase by 15%/year.You have agreed to be paid th
33、is at the end of the first year,and yearly thereafterPh.D.Fees are currently$15,000 per year,and increase by 3%/year with general inflation.Fees are paid at the end of each year,so the fees for the period from 10 to 11 are paid at year 11,Copyright 2009 Pearson Education,Inc.Publishing as Prentice H
34、all,28,Con.,Taxes are 30%,and are assumed to be constant.Assume that lending and borrowing rates have been adjusted for taxA fund with acceptable risk yields 10%/yearYou may also borrow at 10%Lending rate=borrowing rate!The real reason for this is to simplify the math,but the fund could be moderatel
35、y aggressive,and the debt be consumer loansQuestion:Living Expenditure?,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,29,Data Extraction,Let the expenditure required for your standard of living be X at the end of year 0(beginning of year 1),X*1.03 in year 2,X*1.032 in year 3,et ce
36、teraThe fees start at$15,000*1.0310(year 11),and continue to grow at a rate of 3%Your net salary starts at$35,000（after-tax）in year 1,and grows at 15%for 10 yearsEverything is discounted at 10%,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,30,Salary cash flow(rate issue),The after
37、-tax nominal cash flow in the first year is$35,000,grows at a nominal 15%for 10 yearsWe treat the 15%as the combined effect of inflation and real growthApply,and“Inflation”is the 15%hereThe real rate is(0.10-0.15)/1.15=-4.35%,which is the growth rate of purchasing power of your salary,Copyright 2009
38、 Pearson Education,Inc.Publishing as Prentice Hall,31,Salary cash flow($issue),Now,remember,we have assumed that the cash flows occur at the end of each yearThe first net income occurs at time 1,and so must be discounted to year 0The real salary is not$35,000 but$35,000/1.15=$30,434.78,Copyright 200
39、9 Pearson Education,Inc.Publishing as Prentice Hall,32,Salary Cash Flow Computation,Using your financial calculators10-n;4.35“+/-”-I;PV=?;$30,434.78261-PMT;0-FVResult PV=$391,816.3459(in),Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,33,Fee cash flow($issues),The fees are already
40、expressed in real terms,but the first cash flow occurs in year 11,not 10(the evaluation point)The year 11 real cash flow must be adjusted to year 1015000/1.03=$14563.1068,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,34,Solution by Real Conversion,The real interest rate is(0.10-0.
41、03)/1.03=6.7961165%or about 6.80%,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,35,Fee Cash Flow Computation,The present value of the fees at year 10 may be obtained using your financial calculator:3-n;6.80-I;PV=?;$14563.1068-PMT;0-FVResult PV10=-$38,361.0067810-n;6.80-I;PV=?;PMT-
42、0;FV10=38,361.00678(=PV10)Result PV0=$19,876.2931(out),Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,36,Living Expenditure CF$issues,Cash flows are assumed to occur at the end of each year Let us compute the real amount today.Denote this nominal amount in terms of the unknown amou
43、nt X in year 1X/1.03=0.970873786 x,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,37,Living Expenditure CF Rate Issues,This case is easy.The real rate has been computed to be 6.7961165%in the fee section,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,38,Living Exp
44、enditure CF Computation,We do not know both the PV nor the PMT.Set the payment to$1 for now,and multiply by X laterUsing your financial calculators13-n;6.7961165-I;PV=?;$0.970873786-PMT;0-FV Result PV=$8.208829899*X(out),Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,39,Solution by
45、 Real Conversion,We are almost done.All that remains is to assemble the parts,and solve the resulting equation,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,40,Conclusion,This amount is the actual amount that will be expended for the first year,paid at the end of that yearThis is
46、a simple,but not a trivial,example,but it is loaded with traps of even the most experienced.It requires multistage logicThe use of two distinct interest rates will bother some of youSome thinkers believe that it is better to avoid quantities that can not be observed directly While we certainly feel
47、the influence of real cash flows and real rates,observation is through the inflation rateWe live in the world of the nominal,and another approach is to recognize this in our system of financial analysis,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,41,Solution by Growing Annuity,N
48、otationr is the nominal discount rate from 0 to bg is the geometric growth rate in nominal cash flowspmt is the starting cash flowN is the period,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,42,Solution by Growing Annuity,EquationWith a comparison to the regular annuity PV formul
49、a,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,43,Solution method,Just apply the equation three timesTo avoid error,you may wish to summarize the data in a table before using it,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,44,Algebra,Copyright 2009 Pearson Edu
50、cation,Inc.Publishing as Prentice Hall,45,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,46,Interpretation,The plan projects your going into debt in the early years.You are probably collaterallizing your existing human capital,or future earnings potential,Copyright 2009 Pearson Edu
