Chapter FiveHousehold Savings and Investment DecisionsThis chapter contains 28 multiple choice questions, 10 short problems, and 9 longer problems.Multiple Choice1.Getting a professional degree can be evaluated as ________.a) a social security decisionb)an investment in human capitalc)an investment in a consumer durabled) a tax exempt decisionAnswer: (b)2.Suppose you will face a tax rate of 20% before and after retirement. The interest rate is 8%.You are 30 years before your retirement date and invest $10,000 to a tax deferred retirement plan. If you choose to withdraw the total accumulated amount at retirement, what will you be left with after paying taxes?a)$51,445b)$64,000c)$80,501d)$100,627Answer: (c)3.Suppose you will face a tax rate of 20% before and after retirement. The interest rate is 8%.You are 30 years before your retirement date and have $10,000 to invest. If you invest this in an ordinary savings plan instead of a tax deferred retirement plan, what amount will you have accumulated at retirement?a)$51,445b)$64,000c)$80,501d)$100,627Answer: (a)4.When your tax rate remains unchanged, the benefit of tax deferral can be summarized in therule, “deferral earns you ________.”a)the after-tax rate of return before taxb)the pretax rate of return after taxc)the after-tax rate of return after taxd)the pretax rate of return before taxAnswer: (b)5.From an economic perspective, professional training should be undertaken if the ________exceeds the ________.a)future value of the benefit; present value of the costsb)present value of the benefits; future value of the costsc)future value of the benefits; future value of the costsd)present value of the benefits; future value of the costsAnswer: (d)6.Suppose you will face a tax rate of 30% before and after retirement. The interest rate is 6%.You are 35 years before your retirement date and $2,000 to a tax deferred retirement plan. If you choose to withdraw the total accumulated amount at retirement, what will you be left with after paying taxes?a)$7,532b)$10,760c)$12,298d)$15,372Answer: (b)7.Kecia is currently thirty years old and she plans to retire at age sixty. She is expected to liveto age eighty-five. Her labor income is $45,000 per year and she intends to maintain aconstant level of real consumption spending over the next fifty-five years. Assuming a real interest rate of 4% per year, no taxes, and no growth in real labor income, what is the value of Kecia’s human capital?a)$31,797b)$35,196c)$778,141d)$994,888Answer: (c)8.Kecia is currently thirty years old and she plans to retire at age sixty. She is expected to liveto age eighty-five. Her labor income is $45,000 per year and she intends to maintain aconstant level of real consumption spending over the next fifty-five years. Assuming a real interest rate of 4% per year, no taxes, and no growth in real labor income, what is the value of Kecia’s permanent income?a)$31,797b)$35,196c)$778,141d)$994,888Answer: (b)9.Oscar is currently thirty-five year old, plans to retire at age sixty-five, and to live to ageeighty-five. His labor income is $40,000 per year, and he intends to maintain a constant level of real consumption spending over the next fifty years. Assuming a real interest rate of 4% per year, no taxes, and no growth in real labor income, what is the value of Oscar’s human capital?a)$884,344b)$691,681c)$39,999d)$32,198Answer: (b)10.Oscar is currently thirty-five year old, plans to retire at age sixty-five, and to live to ageeighty-five. His labor income is $40,000 per year, and he intends to maintain a constant level of real consumption spending over the next fifty years. Assuming a real interest rate of 4% per year, no taxes, and no growth in real labor income, what is the value of Oscar’spermanent income?a)$884,344b)$691,681c)$39,999d)$32,198Answer: (d)11.You are currently renting a house for $12,000 per year, and you also have an option to buy itfor $240,000. Maintenance and property taxes are estimated to be $4,320, and these costs are included in your rent. Property taxes ($2,880 of the $4,320) are deductible for income tax purposes. Your tax rate is 35%. You wish to provide yourself with housing at the lowest present value of cost. If the real after-tax rate is 2.52%, should you rent or buy?a)rent the house; the PV cost of renting is $476,190b)rent the house; the PV cost of renting is $309,524c)buy the house; the PV cost of owning is $442,198d)buy the house; the PV cost of owning is $371,429Answer: (d)12.You are currently renting a house for $12,000 per year and you also have an option to buy itfor $240,000. Maintenance and property taxes are estimated to be $4,320, and these costs are included in your rent. Property taxes ($2,880 of the $4,320) are deductible for income tax purposes. Your tax rate is 35%. You wish to provide yourself with housing at the lowest present value of cost. The real after-tax rate is 2.52%. What is the break-even rent?a)$6,048b)$9,360c)$10,128d)$12,302Answer: (b)13.As one gets older, the ________ declines, so ________ falls steadily until it reaches zero atage 65.a)future value of remaining labor income; human capitalb)future value of remaining labor income; initial wealthc)present value of remaining labor income; human capitald)present value of initial wealth; optimizationAnswer: (c)14.Any lifetime consumption spending plan that satisfies your budget constraint is:a)an optimal modelb) a feasible planc) a model benefitd) a target replacementAnswer: (b)15.There is an advantage to tax deferred retirement savings plans for those ________ when themoney is withdrawn.a)who will be in a lower tax bracketb)who will be in the same tax bracketc)both (a) and (b)d)neither (a) nor (b)Answer: (c)16.In the United States, individual retirement accounts (IRAs) are called ________ rather than________ because any amounts withdrawn from the plan are taxed at the time of withdrawal.a)tax advantaged; tax deferredb)tax deferred; tax exemptc)tax advantaged; tax loopholesd)tax exempt; tax deferredAnswer: (b)17.The present value of one’s future labor income is called ________ and the constant level ofcon sumption spending that has a present value equal to one’s human capital is called________.a)human income; taxable incomeb)human capital; permanent incomec)permanent capital; taxable incomed)permanent income; human capitalAnswer: (b)18.The ________ the interest rate, the ________ the value of human capital, but the higher thelevel of permanent income.a)lower; lowerb)higher; lowerc)higher; higherd)lower; higherAnswer: (b)19.The ________ states that the present value of one’s lifetime consumption spending andbequests equals the present value of one’s initial wealth and future labor income.a)consumption budget constraintb)spending constraintc)intertemporal budget constraintd)income and spending constraintAnswer: (c)20.According to the text, many experts recommend that in making a savings plan one should aimfor a replacement rate of ________ of pre-retirement income.a)100%b)25%c)50%d)75%Answer: (d)21.Economic costs that are said to be explicit costs include items such as ________.a)tuitionb)foregone rentc)foregone earningsd)all of the aboveAnswer: (a)22.Economic costs that are said to be implicit costs include items such as ________.a)tuitionb)administrative fees while undertaking a professional degreec)foregone earningsd)all of the aboveAnswer: (c)23.In making lifetime saving/consumption decisions it is considered simpler to do the analysis________.a)in nominal termsb)in inflationary termsc)in perpetual termsd)in real termsAnswer: (d)24.In terms of a lifetime saving/consumption decision such as buying or renting an apartment ora consumer durable, the alternative you should choose is ________.a)the one with the lower present value of benefitsb)the one with the lower present value of costsc)the one with the higher present value of costsd)the one with the lower present value of benefits and the higher present costsAnswer: (b)25.Among the approaches you can use for saving for your retirement is/are ________.a)aiming to maintain the same level of consumption spending before and afterretirementb)aiming for a target replacement rate of incomec)bypassing graduate school and continuing to consume at the same leveld)(a) and (b)Answer: (d)26.In the equation known as the intertemporal budget constraint, ________.a)the present value of lifetime consumption spending equals the present value ofbequestsb)the present value of lifetime consumption spending and bequests equals the presentvalue of lifetime resourcesc)the present value of lifetime consumption spending equals the future value of laborincomed)the future value of lifetime consumption spending equals the present value of laborincomeAnswer: (b)27.Salman is currently twenty-five years old and plans to live to age eighty. His labor income is$75,000 per year and he plans to maintain a constant level of real consumption spending over the next fifty-five years. Salman plans to retire at age 60. Assume the real interest rate is 5% per year and there are no taxes and no growth in real labor income. What is the value ofSalman’s permanent income?a)$75,000b)$65,906c)$85,348d)$1,228,064Answer: (b)28.You are currently renting a house for $25,800 a year and you have an option to buy it for$350,000. Maintenance and property taxes are $6,150 per year and these costs are included in your rent. Property taxes ($4,150 of the $6,150) are deductible for income tax purposes. Your tax rate is 35%. The real after-tax rate is 3.5%. What is the break-even rent?a)$16,770.00b)$16,947.50c)$21,102.46d)$24,927.54Answer: (b)Short Problems1.You are currently renting a house for $17,000 a year and you also have an option to buy it for$300,000. Maintenance and property taxes are $5,040 per year and these costs are included in your rent. Property taxes ($3,360 of the $5,040) are deductible for income tax purposes.Your tax rate is 40%. You wish to provide yourself with housing at the lowest present value of cost. The real after-tax rate is 3.1% per year. Should you rent or buy? What is the break-even rent?Answer:After-tax outflow for property taxes each year is 0.6 x $3,360 = $2,016Cash outflow in year t = $1,680 + $2,016= $3,696PV cost of owning = $300,000 + $3,696/i= $300,000 + $3696/0.031= $419,226PV cost of renting = $17,000/i= $17,000/0.031= $548,387You would be better off buying the house.Break-even rent: X/0.031 = $300,000 +$3,696/0.031X = $12,996The break-even rent is $12,996.So if the rent is less than $12,996 per year, you would prefer to keep renting.2.You are currently renting a house for $16,000 a year and you also have an option to buy it for$250,000. Property taxes and maintenance care is $5,000 per year, and these costs areincluded in your rent. Property taxes ($3,200 of the $5,000) are deductible for income tax purposes. Your tax rate is 40%. You wish to provide yourself with housing at the lowest present value of cost. The real before-tax discount rate is 3.5% per year. Should you rent or buy? What is the break-even rate?Answer:Real after-tax rate = 0.6 x 0.035= 0.021After-tax cash outflow for property taxes each year is 0.6 x $3,200 = $1,920Cash outflow for year t = $1,800 + $1,920= $3,720PV cost of owning = $250,000 + $3,720/i= $250,000 + $3,720/0.021= $427,143PV cost of renting = $16,000/i= $16,000/0.021= $761,905You would be better off buying the house.To find the break-even rent:X/0.021 = $250,000 + $3,720/0.021X = $8,970So if the rent is less than $8,970 per year, you would be better off renting.3.Kieran is currently twenty-five years old, plans to retire at age sixty, and to live to age eighty.His labor income is $45,000 per year, and he intends to maintain a constant level of real consumption spending over the next fifty-five years. Assuming a real interest rate of 3%, no taxes, and no growth in real labor income, what is the val ue of Kieran’s human capital? What is the value of Kieran’s permanent income?Answer:n i PV FV PMT Result35 3 ? 0 45,000 PV = $966,925n i PV FV PMT Result55 3 $966,925 0 ? PMT = $36,114The value of Kieran’s human capital is $966,925.The value of Kieran’s permanent income is $36,114.4.Mariana is currently thirty years old, plans to retire at age seventy and to live to age ninety.Her labor income is $60,000 per year, and she intends to maintain a constant level of real consumption spending over the next sixty years. Assuming a real interest rate of 4% per year, no taxes and no growth in real labor income, what is the value of Mariana’s human capital?What is the value of Mariana’s permanent income?Answer:n i PV FV PMT Result40 4 ? 0 60,000 PV = $1,187,566n I PV FV PMT Result60 4 $1,187,566 0 ? PMT = $52,493The value of Mariana’s human capital is $1,187,566.The value of Mariana’s permanent income is $52,493.5.Your employer, Novocastrian Films, has agreed to make 60 quarterly payments of $1,000each into a trust account to fund your early retirement. The first payment will be made 3months from now. At the end of 15 years (60 payments), you will be paid 15 equal annual payments, with the first receipt to be made at the beginning of Year 16 (or the end of Year15). The funds will be invested at a nominal rate of 10.0%, quarterly compounding, duringboth the accumulation and the distribution periods. How large will each of your 15 receipts be?Answer:First determine the effective annual rate:EFF = (1 + 0.10/4)4–1= 10.38%Next, determine amount at end of year 15N I PMT Result_____________15 10.38 $4000 FV = $130,983.39At the end of year 15, there will be $130,983.39 in your retirement account.Since you will be making withdrawals at the beginning of each year, PV = $130,983/(1 +i), or $118,625.10.N I PV Result___________15 10.38 -$118,625.10 PMT = $15,935.89Each of the receipts will be $15,935.896.Mr. Palin has received a job offer from a large investment bank as an assistant to the vicepresident and Mr. Palin’s base salary will be $90,000. In addition, he will receive his first annual salary payment one year from the day he begins work. He will also get an immediate $45,000 bonus for joining the company and his salary will grow at 8 percent each year. Mr.Palin is expected to work for 20 years. What is the present value of the offer if the appropriate discount rate is 11 percent?Answer:Simplest approach is to set up a spreadsheet like:Year PMT PV@11%0 45,000 45,0001 90,000 81,081.082 97,200 78,889.70. . .. . .. . .19 359,641.75 49,514.6320 388,413.10 $48,176.39Total: $1,310,649.82The present value of the offer is $1,310,649.827.Natalia will face a tax rate of 25% before and after retirement. The interest rate is 9%. She is35 years from her retirement date and invests $5,000 to a tax deferred retirement plan. If shechooses to withdraw the total accumulated amount at retirement, what will she be left with after paying taxes?Answer:$5,000 x 1.0935 = $102,069After taxes this leaves $102,069 x 0.75 = $76,5528.Damian is currently twenty-five years old and plans to live to age eighty. His labor income is$80,000 per year, and he plans to maintain a constant level of real consumption spending over the next fifty-five years. Damian plans to retire at age 60. Assume the real interest rate is 5% per year and there are no taxes and no growth in real labor income. What is the value ofDamian’s human capital? What is the value of Damian’s permanent income?Answer:N I PV FV PMTResult_________35 5 ? 0 $80,000 PV =$1,309,936N I PV FV PMT Result________55 5 $1,309,936 0 ? PMT = $70,300Damian’s human capital is $1,309,936.Damian’s permanent income is $70,300.9.You are currently renting a house for $25,800 a year and you have an option to buy it for$350,000. Maintenance and property taxes are $6,150 per year, and these costs are included in your rent. Property taxes ($4,150 of the $6,150) are deductible for tax purposes. Your tax rate is 35%. The real after tax rate is 3.5%. What is the NPV of the investment in the house?Answer:After-tax outflow for property taxes each year is 0.65 x $4,150 = $2,697.50Cash outflow in year t = $2,697.50 + $2,000= $4,697.50PV cost of owning = $350,000 + $4,697/0.035= $350,000 + $134,214= $484,214PV cost of renting = $25,800/0.035= $737,143So the NPV of investing in the house instead of renting is $737,143 – $484,214 = $252,929.10.Carson will face a tax rate of 30% before and after retirement. The interest rate is 6%. He is32 years from his retirement date and invests $3,000 to a tax deferred retirement plan. If hechooses to withdraw the total accumulated amount at retirement, what will he be left with after paying taxes? Show how to find the answer using the rule, “Deferral earns you the pretax rate of return after tax.”Answer:If Carson paid the initial tax he would have $3,000 x 0.7 = $2,100 to invest.Investing $2,100 at the pretax rate of 6% would result in $2,100 x 1.0632 = $13,552Longer Problems1.Tamara is currently twenty-eight years old, plans to retire at age seventy and to live to ageninety. Her labor income is $50,000 per year, and she intends to maintain a constant level of real consumption spending over the next sixty-two years. Assume no taxes, no growth in real labor income and a real interest rate of 4% per year.(a)What is the value of Tamara’s human capital?(b)What is the value of Tamara’s permanent income?Answer:(a) N I PV FV PMT Result42 4 ? 0 $50,000 PV =$1,009,281(b) N I PV FV PMT Result62 4 $1,009,281 0 ? PMT =$44,261The value of Tamara’s human capital is $1,009,281The value of Tamara’s permanent income is $44,2612.You have just turned twenty-eight years of age and feel it is necessary to upgrade yourqualifications. After some consideration, you feel that undertaking full-time study for an MBA degree is one alternative. For the two years of full-time study, tuition and livingexpenses will be $25,000 per year. In addition, you will have to give up your current job witha salary of $35,000 per year. Assume all cash flows occur at the end of the year. Assume areal interest rate of 4% per year, ignoring taxes. Also assume that the salary increase is at a constant real amount that starts after you complete your degree (at the end of the yearfollowing graduation) and lasts until retirement at age sixty-five. In order to justify theinvestment, by how much does your salary have to increase as a result of getting the MBA degree?Answer:Find the FV of tuition and foregone salary at the end of two years:N i PV FV PMT Result________2 4 0 ? 60,000 FV = $122,400Find the increase in salary that has this amount as its PV:n i PV FV PMT Result_______35 4 $122,400 0 ? PMT = $6,5583.At the age of thirty Terry was earning $30,000 and decided to undertake an MBA to increasehis earning potential. Two years later Terry has his degree and has achieved a constant real increase of $5,898 in his annual salary that will last until he retires at age sixty. If Terry lives to the age of ninety, what will be the value of his human capital and permanent income?Assume a real interest rate of 2.52% per year, no taxes, and no growth in real labor income.Answer:New base salary = $30,000 + $5,898 = $35,898n i PV FV PMT Result________28 2.52 ? 0 $35,898 PV = $714,899n i PV FV PMT Result________58 2.52 $714,899 0 ? PMT = $23,584The value of Terry’s human capital is $714,899.The value of Terry’s permanent income is $23,584.4.Juliet currently rents an apartment but has the option to buy it for $185,000. Property taxesare $2,000 per year and are deductible for income tax purposes. Annual maintenance costs are $1,800 per year, but are not tax deductible. Juliet expects that the above taxes willincrease at the rate of inflation. Her income tax rate is 35%, and she can earn a before-tax real interest rate of 5% per year. If Juliet buys the apartment she plans to keep it forever. What is the “break-even” annual rent such that Juliet would buy the apartment if the rent exceeded this amount?Answer:Real after-tax rate = 0.65 x 0.05= 0.0325 (or 3.25%)After-tax annual outflow for property taxes each year is 0.65 x $2,000 = $1,300Break-even rent: X/0.035 = $185,000 + $3,100/0.0325X = 0.035($185,000) + $3,100X = $6,012.50 + $3,100X = $9,112.50So the break-even rent is $9,112.50.5.Anton’s retirement goal is to set aside an amount of money each year into a savings accountuntil he retires so that he can withdraw $80,000 each year during his retirement. He expects to retire in thirty years and expects to live for twenty years following his retirement. Anton expects to be able to earn 9 percent per year on his account balance. Calculate the deposit Anton must make for Plan 1 and the amount of the deposit Anton must make for Plan 2.Plan 1: Anton's first deposit will be one year from today and his last deposit will betwenty-nine years from today. He intends to make his first withdrawal thirty years from today.Plan 2: Anton's first deposit will be today and his last deposit will be thirty years fromtoday. He intends to make his first withdrawal thirty one years from today.Answer:Plan 1N I PMT Result__________20 9 $80,000 PV = $730,283.65N I FV Result__________29 9 $730,283.65 PMT = $5,882.96Under Plan 1, Anton must deposit $5, 882.96Plan 2N I PMT Result__________20 9 $80,000 PV = $730,283.65(set to Begin mode)N I FV Result_______31 9 $730,283.65 PMT = $4,479Under Plan 2, Anton must deposit $4,479.6.Your 68 year old mother plans to retire in 2 years, and she expects to live independently for 3years. She wants a retirement income that has, in the first year, the same purchasing power as $60,000 has today. However, her retirement income will be of a fixed amount, so her real income will decline over time. Her retirement income will start the day she retires (2 years from today), and she will receive a total of 3 retirement payments. Inflation is expected to be constant at 6%. Your mother has $100,000 in savings now, and she can earn 9% on savings now and in the future. How much must she save each year, starting today, to meet herretirement goals?Answer:First of all, your mother needs the following payments at age 70-72:Age 70: $67,416Age 71: $71,460.96Age 72: $75,748.62At age 68, the PV of these cash flows = $165,585.90Your mother has already set aside $100,000So to calculate what she has to save:Set calculator to Begin modePV N I/Y Result$65,585.90 2 9 PMT = $34,205.097. A relative of yours has just turned 45 years old and plans on retiring in 15 years on her 60thbirthday. She is saving money today for her retirement and is establishing a retirementaccount with your office. She would like to withdraw money from her retirement account on her birthday each year until she dies. She would ideally like to withdraw $60,000 on her 60th birthday, and increase her withdrawals 10% a year through her 69th birthday (i.e., she would like to withdraw $141,476.86 on her 69th birthday). She plans to die on her 70th birthday, at which time she would like to leave $400,000 to her descendants. Your relative currently has $100,000. You estimate that the money in the retirement account will earn 11% a year over the next 25 years. Calculate how much your relative should deposit each year (at the end of each year).Answer:Between ages 60-70, cash flows look like:Year CF Get the PV of these withdrawals.6060,0006166,006272,600. .. .. .69141,476.9070400,000At age 60, PV = $717,124.72At age 45, PV = $149,882.18Relative already has $100,000Solve:N I PV Result_________15 11 $49,882.18 PMT = $6,936.888.Consider the following retirement plan. Today is January 1 and your employer will make a$100 contribution to your retirement plan at the end of January and this amount will increase by $100 each month through December 31. Thus in February you get $200 and then up to a $1,200 contribution on December 31. Thus at the end of each January, you will alwaysreceive $100 and the end of each December you will always receive $1,200. The employer will continue this contribution pattern for the next 25 years. You expect to receive a 12% quoted yield, compounded monthly, on your investments. How much money will be in your account when you retire?Answer:Determine what the monthly deposits are worth on annual basis:CF0 = 0, CF1= 100, …, CF12 = $1,200NPV = $7,182.38 at start of each year.Determine EFF = 12.68%Set calculator to Begin mode:N I PMT Result_____________25 12.68 $7,182.38 F = $1,198,4879.Assume that you are planning for your financial future and you would like to fund all of yourfinancial needs by making monthly payments into an account that will pay 10 percent,compounded monthly. You plan to make these monthly payments for a total of 30 years with the first payment to be made one month from today. How much should your monthlypayments be?You need to use the following information:You have promised your partner that you will take a trip to Europe 3 years from today.a)You estimate that the trip will cost $10,000.b)You will retire in 30 years. If you could retire today you estimate that you wouldneed sufficient funds to purchase a 15 year fixed payment annuity that would pay$50,000 per year with the first payment to be received one year after you retire. Youassume that the price you will have to pay for the annuity will be based on an interestrate of 8.5 percent.Due to inflation, you estimate that the amount of the required annual annuitypayment will increase by 4 percent per year until the date you receive the firstpayment, but the annuity payment will remain fixed once you purchase the annuity.c)Your parents have promised to give you a piece of real estate in 5 years and today thereal estate is worth $12,000. You expect that the real estate will increase in value by9 percent per year. You plan to sell the real estate as soon as you receive it and toplace the proceeds in your account.d)You have already saved $15,000, which you will place in your account today.Answer:General strategy: get PV of each of the steps and then determine the monthly payment.Step a: N = 36I = 10/12 = 0.833FV = $10,000PV = $7,417.70Step b: Find FV of payment expected to increase:PV = $50,000, I/y = 4, N = 30, FV = $162,169.88PV at t = 30 of payments (annual compounding)PMT = $162,169.88, N = 15, I = 8.5PV = $1,346,697.05This is the lump sum need at t = 30 to buy the annuity.PV at t = 0 of the retirement annuity cost (monthly compounding)FV = $1,346,697.05, N = 360, I = 0.833PV = $67,886.77Step c: Value of land: FV = $18,463.49PV of land = ?FV = 18,463.49, N = 60, I = 0.833PV = ($11,222)Negative since it reduces the value neededFinally, SUM of all t = 0 present values:$7,417.40 + $67,886.77 + (11,222) + (15,000) = $49,082.17PV = $49,082.17n = 360I = 0.833CPT PMT = $430.73Monthly payment = $430.73。