al versus Nominal Cash Flows a It is 2016 youve just graduat

al versus Nominal Cash Flows. a. It is 2016, you\'ve just graduated college, and you are contemplating your lifetime budget. You think your general living expenses will average around $50,000 a year. For the next 8 years, you will rent an apartment for $16,000 a year. After that, you will want to buy a house that should cost around $250,000. In addition, you will need to buy a new car roughly once every 10 years, costing around $30,000 each. In 25 years, you will have to put aside around $150,000 to put a child through college, and in 30 years you\'ll need to do the same for another child. In 50 years, you will retire and will need to have accumulated enough savings to support roughly 20 years of retirement spending of around $35,000 a year on top of your Social Security benefits. The interest rate is 5% per year. What average salary will you need to earn to support this lifetime consumption plan? b. Whoops! You just realized that the inflation rate over your lifetime is likely to average about 3% per year, and you need to redo your calculations. As a rough cut, it seems reasonable to assume that all relevant prices and wages will increase at around the rate of inflation. What is your new estimate of the required salary (in today\'s dollars)?

Solution

A) First we would calculate the present value of lifetime expenditures General living expenses for 50 years 50000*(1/0.05-1/(0.05*(1.05^50)) This would give us $912796 Apartment rent of $16000 for 8 years 8000*(1/0.05-1/(0.05*(1.05^8)) This would give us $103411 Home Purchase of $250000 in 9 years PV=250000(1/(1.05^9) $161,152 Car purchase at every 10th year 30000*(1/1.05^0) 30000 30000*(1/1.05^10) 18417 30000*(1/1.05^20) 11307 30000*(1/1.05^30) 6941 30000*(1/1.05^40) 4261 30000*(1/1.05^50) 2616 73542 College education in 25 years 150000*(1/1.05^25) 44295 College education in 30 years 150000*(1/1.05^30) 34707 Retirement spending for 20 years 35000*(1/0.05-(1/0.05*(1.05^20)) $436,177 Present value of $436177 = 436177/(1.05^50) $38,036 Adding all the expenditure we get $1367939 To find the average salary necessary to support the lifetime consumption plan C*(1/0.05-(1/0.05*(1.05^50))) = $1367939 Solving above we would get $74931 B In part a we have discounted real cash flows using a nominal interest rate. Here we would repeat the same process with real interest rate (1.05/1.03)-1 0.019417 General living expenses for 50 years 50000*(1/0.0194-1/(0.0194*(1.0194^50)) This would give us $ 1591184 Apartment rent of $16000 for 8 years 8000*(1/0.0194-1/(0.0194*(1.0194^8)) This would give us $ 117511 Home Purchase of $250000 in 9 years PV=250000(1/(1.0194^9) $210,300 Car purchase at every 10th year 30000*(1/1.0194^0) 30000 30000*(1/1.0194^10) 24756 30000*(1/1.0194^20) 20428 30000*(1/1.0194^30) 16857 30000*(1/1.0194^40) 13910 30000*(1/1.0194^50) 11479 117430 College education in 25 years 150000*(1/1.0194^25) 92785 College education in 30 years 150000*(1/1.0194^30) 84285 Retirement spending for 20 years 35000*(1/0.0194-(1/0.0194*(1.0194^20)) $575,530 Present value of $ 575530 = 575530/(1.0194^50) $220,210 Adding all the expenditure we get $ 2433705 To find the average salary necessary to support the lifetime consumption plan C*(1/0.0194-(1/0.0194*(1.0194^50))) = $ 2433705 $76,475 One should save on an average $ 76475 each year