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
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