Question

a. It is 2016, you've just graduated college, and you are contemplating your lifetime budget. You think your general pre-retirement living expenses will average around $50,000 a year. For the next 8 years, you will rent an apartment for $16,000 a year (assume end-of-period payments). At the end of Year 8, 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, starting now and continuing for the next 50 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? (Do not round intermediate calculations. Round your answer to the nearest whole dollar. All spending amounts are in real dollars.) Average salary needed 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)? (Do not round intermediate calculations. Round your answer to the nearest whole dollar. All spending amounts are in real dollars.) New estimate of the required salary

Answer 1

a. Calculation of present value of all expenditures:

PV of general living expenses of $50,000 per year for 50 years = Expenses * PVIFA (5%, 50 years)

= $50,000 * 18.2559

= $912,796

PV of rent of $16,000 for 8 years = Expenses * PVIFA (5%, 8 years)

= $16,000 * 6.4632

= $103,411

PV of home purchased for $250,000 in 9 years = Cost * PVIF (5%, 9 years)

= $250,000 * 0.6446

= $161,152

PV of automobiles purchased in year 0 = $30,000

PV of automobiles purchased in year 10 = $30,000 * PVIF (5%, 10 years) = $18,417

PV of automobiles purchased in year 20 = $30,000 * PVIF (5%, 20 years) = $11,307

PV of automobiles purchased in year 30 = $30,000 * PVIF (5%, 30 years) = $6,941

PV of automobiles purchased in year 40 = $30,000 * PVIF (5%, 40 years) = $4,261

PV of automobiles purchased in year 50 = $30,000 * PVIF (5%, 50 years) = $2,616

PV of college education in year 25 = Expenses * PVIF (5%, 25 years)

= $150,000 * 0.2953

= $44,295

PV of college education in year 30 = Expenses * PVIF (5%, 30 years)

= $150,000 * 0.2314

= $34,707

Calculation of value of retirement portfolio:

Annual saving = $35,000

Number of years amount saved = 20 years

Value of retirement portfolio = Annual saving * PVIFA (5%, 20 years)

= $35,000 * 12.4622

= $436,177

PV of retirement portfolio = Value retirement portfolio * PVIF (5%, 50 years)

= $436,177 * 0.0872

= $38,036

Sum of present values of all expenditures = $912,796 + $103,411 + $161,152 + $30,000 + $18,417 + $11,307 + $6,941 + $4,261 + $2,616 + $44,295 + $34,707 + $38,036

= $1,367,939

The present value of salary should be equal to sum of present values of all expenditures.

Salary * PVIFA (5%, 50 years) = $1,367,939

Salary * 18.2559 = $1,367,939

Salary = $74,931

b. Calculation of real interest rate giving effect to inflation:

Real interest rate = (1.05 / 1.03) - 1 = 0.0194 or 1.94%

All the calculations made in part (a) will be now recalculated using the real interest rate of 1.94%.

PV of general living expenses of $50,000 per year for 50 years = Expenses * PVIFA (1.94%, 50 years)

= $50,000 * 31.8237

= $1,591,184

PV of rent of $16,000 for 8 years = Expenses * PVIFA (1.94%, 8 years)

= $16,000 * 7.3445

= $117,511

PV of home purchased for $250,000 in 9 years = Cost * PVIF (1.94%, 9 years)

= $250,000 * 0.8412

= $210,300

PV of automobiles purchased in year 0 = $30,000

PV of automobiles purchased in year 10 = $30,000 * PVIF (1.94%, 10 years) = $24,756

PV of automobiles purchased in year 20 = $30,000 * PVIF (1.94%, 20 years) = $20,428

PV of automobiles purchased in year 30 = $30,000 * PVIF (1.94%, 30 years) = $16,857

PV of automobiles purchased in year 40 = $30,000 * PVIF (1.94%, 40 years) = $13,910

PV of automobiles purchased in year 50 = $30,000 * PVIF (1.94%, 50 years) = $11,479

PV of college education in year 25 = Expenses * PVIF (1.94%, 25 years)

= $150,000 * 0.6186

= $92,785

PV of college education in year 30 = Expenses * PVIF (1.94%, 30 years)

= $150,000 * 0.5619

= $84,285

Calculation of value of retirement portfolio:

Annual saving = $35,000

Number of years amount saved = 20 years

Value of retirement portfolio = Annual saving * PVIFA (1.94%, 20 years)

= $35,000 * 16.4465

= $575,530

PV of retirement portfolio = Value retirement portfolio * PVIF (1.94%, 50 years)

= $575,530 * 0.3826

= $220,210

Sum of present values of all expenditures = $1,591,184 + $117,511 + $210,300 + $30,000 + $24,756 + $20,428 + $16,857 + $13,910 + $11,479 + $92,785 + $84,285 + $220,210

= $2,433,705

The present value of salary should be equal to sum of present values of all expenditures.

Salary * PVIFA (1.94%, 50 years) = $2,433,705

Salary * 31.8237 = $2,433,705

Salary = $76,475