Question

Tom and Debbie are starting to take their retirement planning seriously. They are both 46 and plan to retire in 20 years at the age of 66. They expect to live 15 years in retirement (a life expectancy of 81). Between their 401k and IRA accounts, they currently have $67,966 in retirement savings.

They currently have a combined income of $88,000 per year and expect to be able to live comfortably in retirement with 80% of their current purchasing power. They expect inflation to be 2% per year for the rest of their lives. They also expect to earn 11.0% per year (the average return on Blue Chip stocks) on their investments, both now and in retirement.

Conduct an analysis of their retirement planning needs and provide them with a professionally written letter. In the letter and attached schedules provide information that answers the following questions. Please include a description of the relevant assumptions and any explanatory comments that make the results easier to understand.

1. What amount of annual income will they need (after adjusting for inflation) in each of the fifteen years of retirement to have the purchasing power of 80% of their current income?

2. Assuming they will continue to earn 11.0% on their investments, how much money will they need to have in their retirement accounts when they retire so that it will provide the fifteen years of income? (note: at the end of the 15 years the account balance should be zero.)

3. Taking into account what they currently have in savings, how much will they have to save each month to meet their retirement needs?

4. Sensitivity analysis: Redo the analysis assuming that they only earn 9% on their investments, instead of 11.0%. Determine the needed amounts so they have the money they need in retirement.

Note: Assume that all payments will be made at the end of the period (ordinary annuity).

Answer 1

	1	Annual Income Needed
		Current combined income	$88,000
		Income needed at current prices	$70,400	(80%*88000)
		Inflation rate	20%
		Number of years to retirement	20
		Amount required at retirement	$104,611	(70400*((1+0.02)^20)
		Amount required in year 2 of retirement	$106,703	(104611*1.02)
		Years from Retirement	Income Needed
		1	$104,611
		2	$106,703
		3	$108,837
		4	$111,014
		5	$113,234
		6	$115,499
		7	$117,809
		8	$120,165
		9	$122,568
		10	$125,019
		11	$127,520
		12	$130,070
		13	$132,672
		14	$135,325
		15	$138,032
	2	Amount needed in retirement account
		Amount needed =Present value of Cash flows at retirement
		Present Value(PV) of Cash Flow:
		(Cash flow)/((1+i)^N)
		i=discount rate =interest =11%=0.11
		N=Year of Cash Flow
		N	CF	PV=CF/(1.11^N)
		Year	Cash Flow	Present value
		1	$104,611	$94,244
		2	$106,703	$86,602
		3	$108,837	$79,581
		4	$111,014	$73,128
		5	$113,234	$67,199
		6	$115,499	$61,750
		7	$117,809	$56,744
		8	$120,165	$52,143
		9	$122,568	$47,915
		10	$125,019	$44,030
		11	$127,520	$40,460
		12	$130,070	$37,179
		13	$132,672	$34,165
		14	$135,325	$31,395
		15	$138,032	$28,849
			SUM	$835,383
	A	Amount needed in retirement account at the time of retirement	$835,383
	4	Monthly Savings required:
	B	Future Value of current Savings at retirement	$547,963	(67966*(1.11^20)
	FV=A-B	Amount of additional savings required	$287,420
	Nper	Number of months of savings=20*12	240
		Monthly interest rate=r
		(1+r)^12=1.11
		1+r=1.11^(1/12)=	1.00873459
	Rate	Monthly interest rate=r	0.00873459
	PMT	Monthly Savings required:	$355.48	(using PMT function of excel with Rate =0.00873459,Nper=240, Fv=-287420)
		Excel command: PMT(0.00873459,240,,-287420)