Zach has an investment worth 113,912 dollars. The investment will make a special

Question

Zach has an investment worth 113,912 dollars. The investment will make a special payment of X to Zach in 4 quarters in addition to making regular quarterly payments to Zach forever. The first regular quarterly payment to Zach is expected to be 3,830 dollars and will be made in 3 months. All subsequent regular quarterly payments are expected to increase by 0.35 percent per quarter forever. The expected return for the investment is 3.79 percent per quarter. What is X, the amount of the special payment that will be made to Zach in 4 quarters?

Explanation / Answer

First regular quarterly payment = $3830

Subsequent regular quarterly payment wil be increased by = 0.35%

Expected return for the investment is 3.79%

X will be = payment of 4 quarters + perpetual payment

the formula to calculate the perpetual payment = 4th quarter payment / (Expected return - growth rate)

X = 4 quarter payments + perpetual payments

= 3830 + 3843.41 + 3856.86 + 3870.36 + 112510.35 = $127910.96

Period 1 2 3 4 Perpetual Growth rate 0.35% 0.35% 0.35% 0.35% (3.79% - 0.35%) = 3.44% Invetment amount 3830 (3830*1.0035) = 3843.41 (3843.41*1.0035) = 3856.86 (3856.86*1.0035)= 3870.36 (3870.36/3.44%) = 112510.35

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