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1. It takes $25,000 every year to put on the Octagon Arts Festival here in Ames

ID: 2507311 • Letter: 1

Question

1. It takes $25,000 every year to put on the Octagon Arts Festival here in Ames each September. At the

beginning of September this year, an anonymous donor contributed $100,000 to be used for the annual arts

festival. If the committee uses the donation to pay for this years event and invests the rest in an account

paying 4% interest, how many more festivals (after this years) can be sponsored without raising more

money?

2. On Friday, February 21 a retired electronics technician from Cedar Rapids, Iowa won $200,000 in Thursday

evening drawing of the Iowa Lotterys Pick 4 game. (Source: www.usamega.com/lottery-news.asp) Lets say

the winner is offered a choice of a one-time payment of $200,000 or a guaranteed $22,000 per year for 10

years. If the value of money is 5%, which option should he choose?

3. George wants to buy a new snowmobile. Three purchase plans are available:

Plan A: $5000 cash immediately

Plan B: $1500 down and 36 monthly payments of $97.75

Plan C: $1000 down and 48 monthly payments of $96.50

If George expects to keep the snowmobile for 5 years, and his cost of money is 6% (compounded monthly),

which payment plan should he choose?

4. A bridge is being considered at a cost of $220M. The annual maintenance costs are estimated to be $150k. A

major renovation costing $50M is required every 25 years. What is the capitalized cost (analysis period =

infinite) of the bridge at 5% interest

5. The city council wants the municipal engineer to evaluate three alternatives for supplementing the city water

supply.

1. The first alternative is to continue deep-well pumping at an annual cost of $10,500.

2. The second alternative is to install an 18 pipeline from a surface reservoir. First cost is $25,000 and

annual pumping cost is $7000.

3. The third alternative is install a 24 pipeline from the reservoir at a first cost of $34,000 and annual

pumping cost of $5000.

The life of each alternative is 20 years. For the second and third alternatives, salvage value is 10% of first cost.

With interest at 8%, which alternative should be engineer recommend? Use present worth analysis.

6. An engineer is considering buying a life insurance policy for his family. He currently owes $77,500 in various

debts, and he would like his family to have an annual available income of $35,000 indefinitely (that is, to

ensure that the original capital does not decrease, the annual interest should amount to $35,000).

a. If the engineer assumes that any money from the insurance policy can be invested in an account paying a

guaranteed 4% annual interest, how much life insurance should be buy (to cover current debt and ensure

the annual income)?

b. If he now assumes that they money can be invested at 7% annual interest, how much life insurance

should be buy?

Explanation / Answer




1.)

remaing amount this year =$75000

the above amount will generate a cash flow of $25000 every year


75000 = 25000*PVIFA(4,n)

75000=25000*[1-(1.04^-n]/.04

1-3*.04 = 1.04^-n


1.13636 = 1.04^n


n = 3.25 year

so, 3 more years can be fully sponsored


2).


PV of future cash flow = 22000*PVIFA(5,10) = 22000*7.7217 = $169877.4


it should choose ist option i.e single payment of $200000


3).


interest rate per month = 6/12 = .5%


PV of cash flow of PLan B


PV = 97.75*PVIFA(.5,36) = 97.75*32.8710 = $3213.14


totala amount paid = 1500+3213.14 = $4713.14


PV of cash flow for paln C


PV = 96.5*PVIFA(.5,48) = 96.5*42.5803 = $4108.99

amount paid total = $4108.99+1000 = $5108.99


so, Plan be should be chosen by george

4).


let effective interest rate for 25 year = 1.05^25-1 = 2.3863 = 238.63%

tot calculate NPV of all future cash flow = 220000000+(150000/.05)+(50000000/2.3863) = 243952939.697


5).


for 1st alternative


total effective cost = 10500*PVIFA(8,20) = 10500*9.8181 = $103090.05


for 2nd alternativve = 25000+7000*PVIFA(8,20)-(2500/1.08^20) = 25000+7000*9.8181-(2500/1.08^20) = $93190.32


for 3rd alternative = 34000+5000*PVIFA(8,20)-(3400/1.08^20) = 34000+5000*9.8181-(3400/1.08^20) = $82361.036


alternative 3rd is best


6).


a) amount that he should buy @4%= 77500+(35000/.04) = $952500


b) amount that he should buy @7% = 77500+(35000/.07) = $577500