Question

XYZ has an investment worth $56,000. The investment will make a special, extra payment of X to XYZ in 2 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 2 years?

Answer 1

Value of Investment = PV of CFs from it.

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

PV of Regular CFs:

Particulars	Amount
Cash Flow	$          12,000.00
Int Rate	12.3000%
Periods	5

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 12000 * [ 1 - [(1+0.123)^-5]] /0.123
= $ 12000 * [ 1 - [(1.123)^-5]] /0.123
= $ 12000 * [ 1 - [0.5599]] /0.123
= $ 12000 * [0.4401]] /0.123
= $ 42937.75

PV of Special CF = CF * PVF(r%, n)

= X * PVF ( 12.3% , 2 )

= X * 0.8905

Thus 0.8905 X + 42937.75 = 56000

0.8905X = 56000 -42937.75

X = 13062.25 / 0.8905

= $ 14668.91

SPecial payment in 2 Years is $ 14668.91