The New England Patriots plan to provide a retirement annuity for their coach, B
ID: 2810407 • Letter: T
Question
The New England Patriots plan to provide a retirement annuity for their coach, Bill Belichick, who will retire in 10 years. When he retires, he will receive an end-of-year annuity of $150,000 for 20 years. In order to fund Bill’s annuity, the Patriots plan to make equal annual end-of-year deposits into an account that will earn 7% per year. When the 20-year distribution period begins, they will move the money into a different account that will earn 10% per year. There will be no money left in the account at the end of 20 years. Note that the first deposit will be at the end of year 1 and the first distribution payment will be at the end of year 11.
Draw a time line showing all of the cash flows associated with the Patriots plan for Bill’s retirement annuity.
How much do the Patriots need to accumulate in order to fund Bill’s annuity?
How much must the Patriots’ equal annual end-of-year deposits be in order to fully fund Bill’s retirement?
How much would the Patriots have to deposit annually if they could earn 8% instead of 7% during the accumulation period?
What would they have to deposit annually if Bill’s retirement were perpetuity instead of a 20-year annuity.
Explanation / Answer
Time line:
Accumulation required:
rate =0.10
n=20
pmt=150,000
Using excel PV function:
=PV(0.1,20,-150000,0)
=$1,277,034.56
Annual end of payments:
n=10
rate =0.07
FV=1277034.56
Using excel pmt function:
=PMT(0.07,10,-1277034.558)
=$181,820.99
For 8% the calculations shall be:
n=10
rate =0.08
FV=1277034.56
Using excel pmt function:
=PMT(0.08,10,-1277034.558)
=$190,315.81
If Bills retirement was perpetuity the,
Required value of funds=150,000/0.1=$1,500,000
n=10
rate =0.07
FV=1500000
Using excel pmt function:
=PMT(0.07,10,-1500000)
=$213,566.25
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