FIN 254 Case 1 1.
Assume that your father is now 50 years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retires, that is, until he is 85. He wants a fixed re- tirement income that has the same purchasing power at the time he retires as $40,000 has today (he realizes that the real value of his retirement income will decline year by year after he retires). His retirement income will begin the day he retires, 10 years from today, and he will then get 24 additional annual payments. Inflation is expected to be 5 percent per year from today forward; he currently has $100,000 saved up; and he expects to earn a return on his savings of 8 percent per year, annual compounding. To the nearest dollar, how much must he save during each of the next 10 years (with deposits being made at the end of each year) to meet his retirement goal? 2. You are serving on a jury. A plaintiff is suing the city for injuries sustained after falling down an uncovered manhole. In the trial, doctors testified that it will be 5 years before the plaintiff is able to return to work. The jury has already decided in favor of the plain- tiff, and has decided to grant the plaintiff an award to cover the following items: (1) Recovery of 2 years of back-pay ($34,000 in 2000, and $36,000 in 2001). Assume that it is December 31, 2001, and that all salary is received at year end. This recov- ery should include the time value of money. (2) The present value of 5 years of future salary (2002–2006). Assume that the plaintiff’s salary would increase at a rate of 3 percent a year. (3) $100,000 for pain and suffering. (4) $20,000 for court costs. Assume an interest rate of 7 percent. What should be the size of the settlement?
3. a.
Set up an amortization schedule for a $25,000 loan to be repaid in equal installments at the end of each of the next 5 years. The interest rate is 10 percent, compounded annually. b. How large must each annual payment be if the loan is for $50,000? Assume that the interest rate remains at 10 percent, compounded annually, and that the loan is paid off over 5 years. c. How large must each payment be if the loan is for $50,000, the interest rate is 10 percent, compounded annually, and the loan is paid off in equal installments at the end of each of the next 10 years? This loan is for the same amount as the loan in part b, but the payments are spread out over twice as many periods. Why are these payments not half as large as the payments on the loan in part b? 4. Case from Gitman (Chapter 4 p-22) : Funding Jill Morgan’s Retirement Annuity
Good Luck!!!
1) As the inflation rate is 5% per year after 10 years if I want to buy the same thing that I can buy with $40000 then I need to have the following amount of money: FV = PV(1+k)n , Here, FV = money I need after 10 years to have the same purchasing power that has today’s $40000 k= inflation rate, n= years so, FV = 40000(1+.05)10 = $65155.79 To have this amount after 10 years I need to save the following amount each year:
(
FVAn = PMT[∑
)
(
] = PMT[
)
]
FVA= 65155.79 n=10, k=8% (as the savings interest rate is 8%)
so, PMT = [ (
)
] =[
(
)
]
PMT= PMT = $4497.671 So, My father needs to save $4498 each year to have the same purchasing power that has today’s $40000
2.) Future value of year 2000 salary = 34000(1+.07) = $36380 value of year 2001 salary (current time) = $36000 Future Salary of year 2002-2006 (salary increase 3% per year) 2002 2003 2004 2005 2006
36000 (1+.03) 37080(1+.03)
37080 38192.4 39338.172 40518.31716 41733.86667
38192.4(1+.03) 39338.172(1+.03) 40518.31716(1+.03)
Present value of year 2002-2006 salary= 2002 2003 2004 2005 2006
Total =
34654.21 33358.72 32111.67 30911.23 29755.67
$160791.5
(we need to use the unequal stream PV formula to find out the PV of this annuity)
PV = PMT
(
)
+ PMT
(
)
+PMT
(
)
+ PMT
(
)
+ PMT
(
)
PMT=each year’s salary k= interest rate so, PV = 160791.4935 So the total settlement amount =36800+36000+160791.5+100000(suffering cost)+20000(court fee) = $353171.5
3-a) Beginning Amount
Year
2012 2013 2014 2015 2016
Column 1 25000 20905.063 16400.6323 11445.75853 5995.397383
Payment Column 2 6594.937 6594.937 6594.937 6594.937 6594.937
Interest Repayment of Principal Remaining Balance Column 3 Column 4 (column2-column3) Column 5 (column1-column4) 2500 4094.937 20905.063 2090.506 4504.4307 16400.6323 1640.063 4954.87377 11445.75853 1144.576 5450.361147 5995.397383 599.5397 5995.397262 0.0001213
Interest = 25000*0.1=2500, 20905.063*0.1=2090.506, 16400.6323*0.1=1640.063, 11445.75853*0.1=1144.576, 5995.397383*0.1=599.5397
PV of Annuity = PMT
[
(
)
]
PV of annuity = 25000, k = 10%=0.1, n= 5, PMT=payment=? So, payment =
$6594.937
= (
)
(
)
3-b) Payment = payment =
$13189.87404
= (
)
(
)
PV of annuity = 50000, k = 10%=0.1, n= 5, PMT=payment=?
3-c) Payment = payment =
= (
$8137.269744
)
(
)
Here, PV of annuity = 50000 and n=10 The amount is not as half as part “b” because of the present value interest factor
4) To answer this question I must find the present value of the annuity for next 25 years. So,
PVAn = PMT[∑
] = PMT )
(
[
(
)
]
= PMT
[
(
)
]
Here, PVAn= present value of the annuity = amount I am willing to pay for this retirement plan k= interest rate = 9%, n=25 years, PMT=$12000
so, PVAn= 12000
[
(
)
]
= 12000* 9.82258 = $117870.9553 So, I would like to pay $117870.9553 for this retirement plan.
