Question

.    Elliot makes $250,000 a year and pays 30% taxes on $150,000 and 35% on his remaining salary. His expenses are $110,000 (per year). He wants to invest a fixed amount EVERY day into an investment fund for 5 years and he hopes to get a 12% return. (20 PTS)

a.    What is the maximum amount he can invest every day? (5 PTS) (Find the annual investment amount and divide by 365).

b.    What will be the worth of his portfolio after 5 years? (5 PTS)

c.     After 5 years, Kassidy's income increases to $300,000. He wants to reinvest for another 5 year, but this time, his return will be 10% and his expenses have increased by 15%. What will be the worth of his portfolio after 5 years (total of 10 years)? (5 PTS)

d.    What will the Present Value of his portfolio, assuming a 6% discount rate and NPER is 10 years? (5 PTS)

Answer 1

a. Salary = $250000; Taxes = (150000* 30%) + (100000*35%) = 80000. Net of Tax salary = 170000

Expenses = 110000; hence savings available for investments = (170000-110000) = $ 60,000

Thus maximum per day investment = 60000/365 = $ 164.38

b. We assume that 12% return in evenly distributed and every day investments start earning 12% right away till the end of 5 years. Then this is like an annuity, where the number of periods will be (365 * 5) = 1825; the interest rate will be (12%/365) = 0.033%

FV annuity formula = Periodic Cash flow * [(1+r)^t - 1]/r ; where r is the appicable interest rate and t is the number of periods.

FV = 164.38 * [(1+0.033%)¹⁸²⁵ - 1]/0.033% = $ 410,969.57

c. Salary income = $ 300,000; Taxes = (150000 * 30%) + (150000 * 35%) = 97500; Net of tax salary = 202500; Expenses = 110000 * (1+15%) = 126500; Savings available for investments = 76000 or daily investment of $208.22

Value in 5 years (1825 days) at 10% or (10%/365) = 0.027%

FV = 208.22 * [(1+0.027%)¹⁸²⁵ - 1]/0.027% = $ 492,942.36

Total Value at the end of 10 years = 492942.36 + 410969.57 * (1+10%)⁵ = $ 1,154,812.96

d. PV = 1154812.96 / (1+6%)¹⁰ = $ 644,841.52