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

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Asked Sep 15, 2019
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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? 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:

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A B C D 1 Month Monthly savings PV factors@ 8% |Present values 3,500.00 0.925925925925926 6,000.00 0.857338820301783 6,500.00 0.79383224 1020 1 70 9,000.00 0.735029852796453 9,000.00 0.680583 197033753 9,000.00 0.630169626883 105 9,400.00 0.583490395262134 9,800.00 0.54026888450 1976 1 3,240.74 2 5,144.03 2 3 5,159.91 4 4 6,615.27 5 5 6,125.25 6 5,671.53 7 7 5,484.81 8 5,294.64 2,401.20 9 4,800.00 0.500248967 13 1459 5,000.00 0.463193488084684 2,000.00 0.428882859337671 3,500.00 0.397113758645991 9 10 10 2,315.97 11 11 857.77 12 1,389.90 12 13 Present Value 49,701.00 14 LC

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Step 2

Working not...

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A B C 1 Month Monthly savings PV factors 8% Present values =B2*C2 B3*C3 -B4*C4 = B5*C5 ЕВ6*С6 =B7*C7 =B8*C8 =B9*C9 3500 6000 6500 9000 9000 9000 9400 9800 4800 5000 2000 3500 |=1/ (( 1 + 8%)^A2) |=1/ ((1 + 8%)^A3) |=1/(1+8%^A4) |=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%)^A11) |=B11*C11 1/ (( 1+8%)^A12) B12 C12 |=1/((1+8%)^A13)B13*C13 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 |-SUM(D2:D13) Present Value 14

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