Question

Problem: Jonathan and Beth plan on retiring in 15 years. They have made progress on their retirement portfolio (they currently have $100,000 in their 401ks + IRAs), but need to do more. Recognizing their lack of planning they have come to you for help in determining how much they need to save annually to produce an inflation-adjusted equivalent of $50,000 per year paid at the beginning of each your over 20 years of retirement. Moreover, they would like to leave a flat $1 million (not increased for any inflation) to their children. Upon further discussion, you and your clients assume that inflation will average 3% prior to retirement and 4% thereafter. Further, your clients estimate that they will earn 12% per year prior to retirement and 7% per year during retirement. Based on the above data assumptions provide your clients with answers to the following questions. The Havertons are quite concerned that they will be unable to contribute that much to their retirement accounts, especially for the first 10 or 15 years. Reacting to their concern you suggest a serial payment strategy. You explain to them that the contributions can be calculated so that each year increases by the amount of inflation. That will eliminate some of the early-year budgeting stresses associated with level payments. The Havertons are impressed by your suggestion and expertise and anxiously await your analysis. Answer the following questions based on the lump sum need you calculated for part one of this case study. • Question 2.1 – What is the amount of the first serial payment the Havertons will make at the end of year one? • Question 2.2 – What is the amount of the second serial payment the Havertons will make at the end of year two?

Answer 1

	ears to retirement	15
	Amount of annualwithdrawal (inflation adjusted)	$50,000
	Current inflation rate=3%
	First instalment of inflation adjusted withdrawal	$77,898	(50000*(1.03^15)
	Inflation rateafter retirement=4%	0.04
	Amount in year 0 (at the time of retirement)=Beginning of year	$77,898
	Amount in year 1	$81,014	(50000*(1+0.04)
	Amount Required in Year (N+1)=Amount required in year(N)*1.04
	Present Value (PV) of Cash Flow:
	(Cash Flow)/((1+i)^N)
	i=Discount Rate=interest rate=7%(during retirement)	0.07
	N=Year of Cash Flow
	Amount Left at the end of 20years	$1,000,000
	PRESENT VALUE OF WITHDRAWAL AFTER RETIREMENT
	N	A	PV=A/(1.07^N)
	Years after retirement	Amount Required	Present value of withdrawal
	0	$77,898	$                    77,898
	1	$81,014	$                    75,714
	2	$84,255	$                    73,591
	3	$87,625	$                    71,528
	4	$91,130	$                    69,523
	5	$94,775	$                    67,573
	6	$98,566	$                    65,679
	7	$102,509	$                    63,837
	8	$106,609	$                    62,048
	9	$110,874	$                    60,308
	10	$115,309	$                    58,617
	11	$119,921	$                    56,974
	12	$124,718	$                    55,376
	13	$129,707	$                    53,824
	14	$134,895	$                    52,315
	15	$140,291	$                    50,848
	16	$145,902	$                    49,422
	17	$151,738	$                    48,036
	18	$157,808	$                    46,690
	19	$164,120	$                    45,381
	20	$1,000,000	$                  258,419
		SUM	$               1,463,601
	Amount required on the date of retirement	$               1,463,601
	Amount available in current savings	$100,000
	Future Value of current savings at the time of retirement	$547,357	(100000*(1.12^15)
	Balance Savings Required	$                  916,244	(1463601-547357)
	Assume, saving in thencurrent year end (year1)	$1
	Saving in year 2=1*1.03=	$1.03	(Inflation adjusted)Inflation rate=3%
	Saving in year (N+1)=Saving in year (N)*1.03
	Interest rate on savings before retirement=12%=0.12
Future Value (FV) of savings at retirement(after 15 years)=(Savings)*(1.12^(15-N))
	N	A	FV=A*(1.12^(15-N))
	Year	Savings	Future Value of Savings at retirement
	1	$1	4.887112285
	2	$1.03	4.494397905
	3	$1.06	4.13324093
	4	$1.09	3.801105499
	5	$1.13	3.495659521
	6	$1.16	3.21475831
	7	$1.19	2.956429517
	8	$1.23	2.718859288
	9	$1.27	2.500379524
	10	$1.30	2.299456169
	11	$1.34	2.114678441
	12	$1.38	1.944748924
	13	$1.43	1.788474456
	14	$1.47	1.644757759
	15	$1.51	1.512589725
		SUM	43.50664825
X	If initial Saving is $1 amount accumulated at retirement	43.50664825
Y	Amount required at retirement	$                  916,244
X=Y/X	Initial Saving required	$               21,059.87
	Amount of first serial payment at the end of year1	$               21,059.87
	Amount of Second serial payment at the end of year2	$               21,691.66	(21059.87*1.03)