Question

Jack has just retired and has received a lump sum pay-out of $1,300,000. He invests part of this pay-out on an investment property which earns 6 percent per annum and provides a perpetual income to him of $60,000 per year (assuming end-of-year withdrawals). He puts the rest of the pay out in another investment in the form of an annuity which earns 4 percent per annum. He wants to make equal annual withdrawals over the next 10 years from this investment annuity, leaving a balance of zero, to fund some overseas trips and a few other extravagances. Required (i) Calculate how much Jack has invested in the investment property. (ii) Show how much extra Jack can expect to spend each year (assuming end-of-year withdrawals), over and above the $60,000 from the property investment, for the next ten years from the investment annuity. Note: ignore tax in your calculations.

Answer 1

Investment value = annual cash flow/required return

(1)Hence,amount invested in investment property = 60,000/6%

= $1,000,000

(2)Amount in annuity investment = 1,300,000-1,000,000 = $300,000

Let amount if withdrawals each year be x

300,000 = x*PVAF(4%, 10 years)

300,000 = x*8.11089577

X = $36,987.28

Hence, amount that Jack can spend each year (assuming end-of-year withdrawals), over and above the $60,000 from the property investment, for the next ten years from the investment annuity = $36,987.28