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 amount is computed as follows:

Amount of investment = Present value of future cash flows + Special payment / 1.123³

$ 56,000 = Annual amount x [ (1 – 1 / (1 + r)ⁿ) / r ] + Special payment / 1.123³

$ 56,000 = $ 12,000 x [ (1 - 1 / (1 + 0.123)⁵ ) / 0.123 ] + Special payment / 1.123³

$ 56,000 = $ 42,937.74864 + Special payment / 1.123³

$ 13,062.25136 x 1.123³ = Special payment

Special payment = $ 18,499.39 Approximately

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