Question

Dom has $90,000 that he wishes to invest now in order to use the accumulation for purchasing a retirement annuity in five years. After consulting with his financial advisor, he has been offered four types of fixed-income investments, labeled as investments A, B, C, and D.

Investments A and B are available at the beginning of each of the next five years (call them years 1–5). Each dollar invested in A at the beginning of a year returns $1.20 (a profit of $0.20) two years later, in time for immediate reinvestment. Each dollar invested in B at the beginning of a year returns $1.36 three years later.
Investments C and D will each be available just once in the future. Each dollar invested in C at the beginning of year 2 returns $1.66 at the end of year 5. Each dollar invested in D at the beginning of year 5 returns $1.12 at the end of year 5.
Your uncle is obligated to make a balloon payment on an existing loan in the amount of $24,000 at the end of year 3. He wants to make that payment out of the investment account.
1) Devise an investment plan for your uncle that maximizes the value of the investment account at the end of five years. How much money will be available for the annuity in five years?
2) Show the network diagram corresponding to the solution in (1). That is, label each of the arcs in the solution and verify that the flows are consistent with the given information.

Answer 1

First of all, you must invest enough money in B in order to pay your debt.

present value = future value / expected return

present value = $24,000 / $1.36 = $17,647.06

you have $90,000 - $17,647.06 = $72,352.94 to invest in A.

at the end of year 2, you will have:

future value = present value x expected return = $72,352.94 x $1.20 = $86,823.53

then you should invest that money ($86,823.53) in invested D and at the end of year 4 you will have:

future value = $86,823.53 x $1.66 = $144,127.06

finally, you should invest $144,127.06 in investment E and at the end of ear 5 you will have:

future value = $144,127.06 x $1.12 = $161,422.31

2) it is really hard to draw a diagram without drawing tools, but i will try

⇒ invest $17,647.06 in B ⇒ year 3, collect $24,000

from B and pay off debt

today

$90,000

⇒ invest $72,352.94 ⇒ year 2, invest ⇒ year 4, invest

in A $86,823.53 in D $144,127.06 in E

continues ... ⇒ year 5, collect $161,422.31 from E