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Question

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Brothers, Mark and Mike Lalla want to plan for their retirement and need your advice.

Mark plans to travel extensively in the first 5 years of his retirement and will need $450,000 each year to do so. After that he will be able to live on $100,000 per year. Mark does not know how long he will live so once started, he needs to be able to withdraw the $100,000 each year forever.

Mike plans on having some income from a part time job in the first 5 years of his retirement so will only need $50,000 per year. He then plans on travelling lavishly for the next 6 years and will need $750,000 per year. He figures he will not live past that point so will not need any more funds.

Both men will retire next year and thus will need the first cash flow from his retirement fund at that time. If both can earn an 8% rate of return, calculate how much each brother will need today to realize his retirement dream.

Explanation / Answer

Solution:- Mark fund requirement

4,50,000 for 5 years then 100,000 continously

Pv of Annuity =Annuity amount*PVAF(r,n)

PV= 450,000*PVAF(8%,5 years) = 450,000*3.993 = 1,796,850

Pv of perpetuity 6 years cash flow/r = 100,000/0.08 = 1250,000

Pv of perpetuity today =FV*PVF(r,n) =1250,000*PVF(8%,5 years) =1250,000*0.681 = $851,250

So Mark total fund requirement is $ (1796,850+851,250) = $2,648,100

Mike fund requirement

50,000 for first 5 years then 750,000 for next 6 years

Pv of Annuity =Annuity amount*PVAF(r,n)

=50,000*PVAF(8%,5 years) = 50,000*3.993 = $199,650

similarly PV of 750,000 for next 6 years is

=750,000*PVAF(8%,6 years) =750,000*4.623 = $3467,250

PV of the fund today=FV*PVF(r,n)

=3467,250*PVF(8%6 years) =3467,250*0.630 =$ 2184,368

So Mike total fund requirement is $(199,650 + 2184,368 ) =$2,384,018

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