Maintenance money for an athletic complex has been sought. Mr. Kendall, Athletic
ID: 2811940 • Letter: M
Question
Maintenance money for an athletic complex has been sought. Mr. Kendall, Athletic Director, would like to solicit a donation to cover all future expected maintenance costs for the building. These maintenance costs are expected to be S1.5 million each year for the first five years, $1.8 million each year for years 6 through 10, and $2 million each year after that. (The building has an indefinite service life.) If the money is placed in an account that will pay 5% interest compounded annually, how large should the gift be? Click the icon to view the interest factors for discrete com pounding when i-5% per yea The gift should be million. (Rlound to two decimal places)Explanation / Answer
Gift = Present value today = $37.16 million
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WORKING
Present value of perpetuity i.e. payment required forever after 10th year should be known before calculating other payment present values.
Present value of perpetuity at year 10 end = 2 / 5% = $40 millions
We will discount the perpetuity at end of 10th year to present in below equation along with other cash flows:
Years
Cash flows = C
Discount factor = df
PV = C x df
1
1.5
0.952380952
1.43
2
1.5
0.907029478
1.36
3
1.5
0.863837599
1.30
4
1.5
0.822702475
1.23
5
1.5
0.783526166
1.18
6
1.8
0.746215397
1.34
7
1.8
0.71068133
1.28
8
1.8
0.676839362
1.22
9
1.8
0.644608916
1.16
10
1.8 + 40 = 41.8
0.613913254
25.66
Total of PV =
$37.16 million
OR
Present value today = 1.5/(1+5%)^1 + 1.5/(1+5%)^2 + 1.5/(1+5%)^3 + 1.5/(1+5%)^4 + 1.5/(1+5%)^5 + 1.8/(1+5%)^6 + 1.8/(1+5%)^7 + 1.8/(1+5%)^8 + 1.8/(1+5%)^9 + 1.8/(1+5%)^10 + 40/(1+5%)^10
Present value today = $37.16 million
Years
Cash flows = C
Discount factor = df
PV = C x df
1
1.5
0.952380952
1.43
2
1.5
0.907029478
1.36
3
1.5
0.863837599
1.30
4
1.5
0.822702475
1.23
5
1.5
0.783526166
1.18
6
1.8
0.746215397
1.34
7
1.8
0.71068133
1.28
8
1.8
0.676839362
1.22
9
1.8
0.644608916
1.16
10
1.8 + 40 = 41.8
0.613913254
25.66
Total of PV =
$37.16 million
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