A local youth baseball league has acquired through a gift significant land to bu
ID: 2647861 • Letter: A
Question
A local youth baseball league has acquired through a gift significant land to build new ball fields. They are planning ahead and would like to eventually install lights at these fields. They plan on installing these new lights over a 3 year period starting 3 years from now and would like to do 3 fundraisers to fully fund it before the new fields and lights can be installed. Additional fund raisers for the lighting project are not expected to be required.
New lights would cost $25,000 for each ball field today but prices are expected to increase 2% per year. They currently have $10,000 saved and allocated to this project. They are planning to have fundraisers now and at the beginning of each year for the next 2 years and would like to fully fund the project before installation of the lights for the first ball field.
Assumptions: Project is fully funded 3 years from today at the time of the first payment for the first set of lights for the first ball field. The second and third installation of lights will happen at the beginning of each of the years subsequent to the first year the lights are installed. Deposits from fund raisers are made today and at the beginning of year 2 and year 3. Assume that each fund raiser will raise an equal amount of money that can be allocated to the lighting project. Assume that money invested will earn 6% interest.
How much must each of the fund raising events raise to fully fund the project?
How would your answer be different if the fund raisers happened at the end of each of the 3 years and not at the beginning?
Explanation / Answer
Hi,
Cost of light in the year 3 = 10000*(1+2%)^3
=$10612.08
Cost of light in the year 4 = 10000*(1+2%)^4
=$10824.32
Cost of the light in year 5 = 10000*(1+2%)^5
=$11040.81
Total Amount required = $(10612.08+10824.32+11040.81)
=$32477.21
amount of fund raiser required:
=>32477.21 = annual payment*(1-(1+6%)^(-3))/6%
=> annual payment = $12150.04
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annual payment required if fund raisers happened at the end of each of the 3 years and not at the beginning:
32477.21 = annual payment +annual payment*((1-(1+6%)^(-2)/6%)
=> annual payment = $11462.30
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