Question

XYZ has an investment worth $56,000. The investment will make a special, extra payment of X to XYZ in 3 years from today. The investment also will make regular, fixed annual payments of $12,000 to XYZ with the first of these payments made to XYZ in 1 year from today and the last of these annual payments made to XYZ in 5 years from today. The expected return for the investment is 12.3 percent per year. What is X, the amount of the special payment that will be made to XYZ in 3 years

Answer 1

The special return will be for 23,330.11 at year 3

Step-by-step explanation:

we know that the expected return AKA internal rate of return is 12.30 per year

we set up the time-line for the investment:

F0 -56,000 investment

constant return of 12,000 for 5 years.

additional return at F3

F0 + PV of the F3 return + PV of the 12,000 annuity = 0

present value of the annuity:

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 12,000.00

time 5

rate 0.123

`12000 * (1-(1+0.123)^(-5) )/(0.123) = PV\\`

PV $42,937.7486

Present value of the additional return:

56,000 - 42,937.75 = 13,062.25

Now, we know that this is the discounted amount of the nominal return at 12.30% during 3 years:

`(Nominal)/((1 + rate)^(time) ) = PV`

`(Nominal)/((1 + 0.1230)^(5) ) = 13,062.25`

Nominal = 23,330.11