A privately run, for-profit, prison is considering ways in which it can cut its monthly costs and therefore increase profit. One idea it is considering is to pay a judge to guarantee convicted prisoners in poor health win their appeals and are set free. The prison believes it can realize the monthly cost savings below over the initial year of the plan. What is the present value of the first year's monthly cost savings?MonthSavings ($)13,50026,00036,50049,00059,00069,00079,40089,80094,800105,000112,000123,500Total77,500Assume a discount rate of 8%. Show both written and excel solutions.

Question
Asked Sep 15, 2019

A privately run, for-profit, prison is considering ways in which it can cut its monthly costs and therefore increase profit. One idea it is considering is to pay a judge to guarantee convicted prisoners in poor health win their appeals and are set free. The prison believes it can realize the monthly cost savings below over the initial year of the plan. What is the present value of the first year's monthly cost savings?

Month Savings ($)
1 3,500
2 6,000
3 6,500
4 9,000
5 9,000
6 9,000
7 9,400
8 9,800
9 4,800
10 5,000
11 2,000
12 3,500
Total 77,500

Assume a discount rate of 8%. Show both written and excel solutions.

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Expert Answer

Step 1

Calculate the present value as follows:

A
C
D
1 Month Monthly savings PV factors@ 8% |Present values
3,500.00 0.925925925925926
6,000.00 0.857338820301783
6,500.00 0.793832241020170
9,000.00 0.735029852796453
9,000.00 0.680583 197033753
9,000.00 0.630169626883105
9,400.00 0.583490395262 134
9,800.00 0.540268884501976
4,800.00 0.500248967 131459
5,000.00 0.463193488084684
2,000.00 0.428882859337671
3,500.00 0.397113758645991
3,240.74
5,144.03
1
2
2
3
5,159.91
4
6,615.27
4
5
5
6,125.25
6
5,671.53
7
7
5,484.81
5,294.64
9
2,401.20
2,315.97
9
10
10
11
11
857.77
12
12
1,389.90
13
Present Value
49,701.00
14
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A C D 1 Month Monthly savings PV factors@ 8% |Present values 3,500.00 0.925925925925926 6,000.00 0.857338820301783 6,500.00 0.793832241020170 9,000.00 0.735029852796453 9,000.00 0.680583 197033753 9,000.00 0.630169626883105 9,400.00 0.583490395262 134 9,800.00 0.540268884501976 4,800.00 0.500248967 131459 5,000.00 0.463193488084684 2,000.00 0.428882859337671 3,500.00 0.397113758645991 3,240.74 5,144.03 1 2 2 3 5,159.91 4 6,615.27 4 5 5 6,125.25 6 5,671.53 7 7 5,484.81 5,294.64 9 2,401.20 2,315.97 9 10 10 11 11 857.77 12 12 1,389.90 13 Present Value 49,701.00 14

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Step 2

Working not...

A
D
1 Month Monthly savings PV factors@ 8% Present values
|=1/((1+8%)^A2)
|=1/(1+8%)^A3)
|=1/((1+8%)^A4) =B4*C4
|-1/(1+8%)^A5)
|-1/(1+8%)^A6)
|=1/((1+8%)^A7)
|=1/(1+8%)^A8)
|=1/ (( 1 + 8%)^A9)
|=1/((1+8%)^A10)B10*C10
= 1/ (( 1+8%)^A1 1) B11*C11
= 1 / (( 1+8% )^A12)B12*C12
= 1 / (( 1+8% )^A13) B13 C13
3500
6000
6500
9000
9000
9000
=B2*C2
ЕВ3*СЗ
2 1
3 2
4 3
5 4
-B5 C5
-B6*C6
=B7 C7
=B8*C8
=B9*C9
6 5
7 6
9400
9800
4800
5000
2000
3500
8 7
9 8
10 9
11 10
12 11
13 12
|=SUM(D2:D13)
Present Value
14
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A D 1 Month Monthly savings PV factors@ 8% Present values |=1/((1+8%)^A2) |=1/(1+8%)^A3) |=1/((1+8%)^A4) =B4*C4 |-1/(1+8%)^A5) |-1/(1+8%)^A6) |=1/((1+8%)^A7) |=1/(1+8%)^A8) |=1/ (( 1 + 8%)^A9) |=1/((1+8%)^A10)B10*C10 = 1/ (( 1+8%)^A1 1) B11*C11 = 1 / (( 1+8% )^A12)B12*C12 = 1 / (( 1+8% )^A13) B13 C13 3500 6000 6500 9000 9000 9000 =B2*C2 ЕВ3*СЗ 2 1 3 2 4 3 5 4 -B5 C5 -B6*C6 =B7 C7 =B8*C8 =B9*C9 6 5 7 6 9400 9800 4800 5000 2000 3500 8 7 9 8 10 9 11 10 12 11 13 12 |=SUM(D2:D13) Present Value 14 co.

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