Question

Jonathan and his wife, Ivy, are empty nesters with annual salaries of $500,000 and $300,000, respectively. Both expected their salaries to increase by 5% per year. Although Jonathan, aged 55, he expects to work for another ten years before retiring. Ivy, aged 52, is not in good health and plans to retire in five years’ time. After she retires, she expects to incur about $150,000 in medical bills from the sixth year onwards, increasing at 2% per year thereafter due to the rising cost of healthcare. For the coming year, the couple expects to incur a combined $220,000 in living expenses, which are also expected to grow annually at 2% due to inflation. Your team has been tasked by Jonathan and Ivy to grow their portfolio, which currently has investable assets of $1.5 million to $10 million over a ten-year horizon. In any given year, net cash flow surpluses are expected to contribute to the portfolio and net cash flow needs are expected to be met from the portfolio. Jonathan and Ivy would like the portfolio to be diversified and take only long positions in Singaporean equities. Your risk assessment indicates that they can tolerate a 1% chance of losses exceeding $300,000 in any given year. The effective income tax rate is 15% for both Jonathan and Ivy. Neither capital gains nor dividends are taxed. Assume all cash flows occur at the end of the year.

Question: Prepare an estimate of the return requirement for Jonathan’s portfolio.

Answer 1

Jonathan salary growth rate	5%
Ivy salary growth rate	5%
Medical expense inflation	2%
General inflation	2%
Tax rate	15%

Year	1	2	3	4	5	6	7	8	9	10
Jonathan salary	500,000	525,000	551,250	578,813	607,753	638,141	670,048	703,550	738,728	775,664
Ivy salary	300,000	315,000	330,750	347,288	364,652	-	-	-	-	-
Total income	800,000	840,000	882,000	926,100	972,405	638,141	670,048	703,550	738,728	775,664
Expenses
Ivy medical						150,000	153,000	156,060	159,181	162,365
Living expense	220,000	224,400	228,888	233,466	238,135	242,898	247,756	252,711	257,765	262,920
Tax payment	120,000	126,000	132,300	138,915	145,861	95,721	100,507	105,533	110,809	116,350
Total expense	340,000	350,400	361,188	372,381	383,996	488,619	501,263	514,303	527,755	541,635
Net investable savings	460,000	489,600	520,812	553,719	588,409	149,522	168,785	189,247	210,972	234,029

Current value of portfolio	1,500,000
Target future value of portfolio	10,000,000
Time to grow (years)	10

The effective cash flows are -
Year	0	1	2	3	4	5	6	7	8	9	10
	1,500,000	460,000	489,600	520,812	553,719	588,409	149,522	168,785	189,247	210,972	(9,765,971)
IRR	9.847%

Cross-check
Calculating FV of cash flows at the calculated IRR

FV	3,836,663	1,071,110	1,037,842	1,005,043	972,763	941,045	217,696	223,714	228,350	231,746	234,029
	=FV(IRR,(10-YEAR),0,-CASHFLOW)										(IGNORE LIQUIDATION)
Total FV	10,000,000

Hence, we can see that by compounding the portfolio at the calculated IRR of 9.847%, the portfolio reaches a total value of $10 M at the end of 10th year