Calculate the payback period.

Question

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Answer 1

Question

Chapter 13, Problem 32P

(a):

To determine

Calculate the payback period.

(a):

Expert Solution

Explanation of Solution

Investment (C) is $245,000. Expense (AE) is $38,000 per year. Income (AI) is $92,000. MARR (i) is 15%. Salvage value (SV) is 15% of the first cost.

Payback period (n) can be calculated as follows:

(AI−AE)((1+i)n−1i(1+i)n)+SV(1+i)n=C(92,000−38,000)((1+0.15)n−10.15(1+0.15)n)+0.15×245,000(1+0.15)n=245,00054,000((1+0.15)n−10.15(1+0.15)n)+36,750(1+i)n=245,00054,000((1+0.15)n−10.15(1+0.15)n)+36,750(1+i)n=245,000

Substitute n as 7 by trial and error method to verify the time period in the above calculation.

−54,000((1+0.15)7−10.15(1+0.15)7)+36,750(1+0.15)7=−245,000−54,000(2.6600−10.15(2.6600))+36,7502.6600=−245,000−54,000(1.66000.399)+36,7502.6600=−245,000−54,000(4.1604)+13,815.79=−245,000−224,661.6+13,815.79=−245,000−210,845.81<−245,000

Since the calculated present value of the cost is less than the initial cost, increase the payback period to 8.

−54,000((1+0.15)8−10.15(1+0.15)8)+36,750(1+0.15)8=−245,000−54,000(3.05902−10.15(3.05902))+36,7503.05902=−245,000−54,000(2.059020.45885)+12,013.65=−245,000−54,000×4.4873+12,013.65=−245,000−242,314.2+12,013.65=−245,000−230,300.55≈−245,000

Since the calculated value is nearly equal to the initial cost, it is verified that the payback period is 8 years.

(b):

To determine

Calculate the payback period using spreadsheet.

(b):

Expert Solution

Explanation of Solution

The spreadsheet function for payback period is given below:

= NPER(15%,54000,-245000,0.15*245000)

The above function gives the value of 7.4 years.

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Answer 2

Question

Chapter 13, Problem 32P

(a):

To determine

Calculate the payback period.

(a):

Expert Solution

Explanation of Solution

Investment (C) is $245,000. Expense (AE) is $38,000 per year. Income (AI) is $92,000. MARR (i) is 15%. Salvage value (SV) is 15% of the first cost.

Payback period (n) can be calculated as follows:

(AI−AE)((1+i)n−1i(1+i)n)+SV(1+i)n=C(92,000−38,000)((1+0.15)n−10.15(1+0.15)n)+0.15×245,000(1+0.15)n=245,00054,000((1+0.15)n−10.15(1+0.15)n)+36,750(1+i)n=245,00054,000((1+0.15)n−10.15(1+0.15)n)+36,750(1+i)n=245,000

Substitute n as 7 by trial and error method to verify the time period in the above calculation.

−54,000((1+0.15)7−10.15(1+0.15)7)+36,750(1+0.15)7=−245,000−54,000(2.6600−10.15(2.6600))+36,7502.6600=−245,000−54,000(1.66000.399)+36,7502.6600=−245,000−54,000(4.1604)+13,815.79=−245,000−224,661.6+13,815.79=−245,000−210,845.81<−245,000

Since the calculated present value of the cost is less than the initial cost, increase the payback period to 8.

−54,000((1+0.15)8−10.15(1+0.15)8)+36,750(1+0.15)8=−245,000−54,000(3.05902−10.15(3.05902))+36,7503.05902=−245,000−54,000(2.059020.45885)+12,013.65=−245,000−54,000×4.4873+12,013.65=−245,000−242,314.2+12,013.65=−245,000−230,300.55≈−245,000

Since the calculated value is nearly equal to the initial cost, it is verified that the payback period is 8 years.

(b):

To determine

Calculate the payback period using spreadsheet.

(b):

Expert Solution

Explanation of Solution

The spreadsheet function for payback period is given below:

= NPER(15%,54000,-245000,0.15*245000)

The above function gives the value of 7.4 years.

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Answer 3

Question

Chapter 13, Problem 32P

(a):

To determine

Calculate the payback period.

(a):

Expert Solution

Explanation of Solution

Investment (C) is $245,000. Expense (AE) is $38,000 per year. Income (AI) is $92,000. MARR (i) is 15%. Salvage value (SV) is 15% of the first cost.

Payback period (n) can be calculated as follows:

(AI−AE)((1+i)n−1i(1+i)n)+SV(1+i)n=C(92,000−38,000)((1+0.15)n−10.15(1+0.15)n)+0.15×245,000(1+0.15)n=245,00054,000((1+0.15)n−10.15(1+0.15)n)+36,750(1+i)n=245,00054,000((1+0.15)n−10.15(1+0.15)n)+36,750(1+i)n=245,000

Substitute n as 7 by trial and error method to verify the time period in the above calculation.

−54,000((1+0.15)7−10.15(1+0.15)7)+36,750(1+0.15)7=−245,000−54,000(2.6600−10.15(2.6600))+36,7502.6600=−245,000−54,000(1.66000.399)+36,7502.6600=−245,000−54,000(4.1604)+13,815.79=−245,000−224,661.6+13,815.79=−245,000−210,845.81<−245,000

Since the calculated present value of the cost is less than the initial cost, increase the payback period to 8.

−54,000((1+0.15)8−10.15(1+0.15)8)+36,750(1+0.15)8=−245,000−54,000(3.05902−10.15(3.05902))+36,7503.05902=−245,000−54,000(2.059020.45885)+12,013.65=−245,000−54,000×4.4873+12,013.65=−245,000−242,314.2+12,013.65=−245,000−230,300.55≈−245,000

Since the calculated value is nearly equal to the initial cost, it is verified that the payback period is 8 years.

(b):

To determine

Calculate the payback period using spreadsheet.

(b):

Expert Solution

Explanation of Solution

The spreadsheet function for payback period is given below:

= NPER(15%,54000,-245000,0.15*245000)

The above function gives the value of 7.4 years.

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Answer 4

Question

Chapter 13, Problem 32P

(a):

To determine

Calculate the payback period.

(a):

Expert Solution

Explanation of Solution

Investment (C) is $245,000. Expense (AE) is $38,000 per year. Income (AI) is $92,000. MARR (i) is 15%. Salvage value (SV) is 15% of the first cost.

Payback period (n) can be calculated as follows:

(AI−AE)((1+i)n−1i(1+i)n)+SV(1+i)n=C(92,000−38,000)((1+0.15)n−10.15(1+0.15)n)+0.15×245,000(1+0.15)n=245,00054,000((1+0.15)n−10.15(1+0.15)n)+36,750(1+i)n=245,00054,000((1+0.15)n−10.15(1+0.15)n)+36,750(1+i)n=245,000

Substitute n as 7 by trial and error method to verify the time period in the above calculation.

−54,000((1+0.15)7−10.15(1+0.15)7)+36,750(1+0.15)7=−245,000−54,000(2.6600−10.15(2.6600))+36,7502.6600=−245,000−54,000(1.66000.399)+36,7502.6600=−245,000−54,000(4.1604)+13,815.79=−245,000−224,661.6+13,815.79=−245,000−210,845.81<−245,000

Since the calculated present value of the cost is less than the initial cost, increase the payback period to 8.

−54,000((1+0.15)8−10.15(1+0.15)8)+36,750(1+0.15)8=−245,000−54,000(3.05902−10.15(3.05902))+36,7503.05902=−245,000−54,000(2.059020.45885)+12,013.65=−245,000−54,000×4.4873+12,013.65=−245,000−242,314.2+12,013.65=−245,000−230,300.55≈−245,000

Since the calculated value is nearly equal to the initial cost, it is verified that the payback period is 8 years.

(b):

To determine

Calculate the payback period using spreadsheet.

(b):

Expert Solution

Explanation of Solution

The spreadsheet function for payback period is given below:

= NPER(15%,54000,-245000,0.15*245000)

The above function gives the value of 7.4 years.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 13, Problem 32P

(a):

To determine

Calculate the payback period.

(a):

Expert Solution

Explanation of Solution

Investment (C) is $245,000. Expense (AE) is $38,000 per year. Income (AI) is $92,000. MARR (i) is 15%. Salvage value (SV) is 15% of the first cost.

Payback period (n) can be calculated as follows:

(AI−AE)((1+i)n−1i(1+i)n)+SV(1+i)n=C(92,000−38,000)((1+0.15)n−10.15(1+0.15)n)+0.15×245,000(1+0.15)n=245,00054,000((1+0.15)n−10.15(1+0.15)n)+36,750(1+i)n=245,00054,000((1+0.15)n−10.15(1+0.15)n)+36,750(1+i)n=245,000

Substitute n as 7 by trial and error method to verify the time period in the above calculation.

−54,000((1+0.15)7−10.15(1+0.15)7)+36,750(1+0.15)7=−245,000−54,000(2.6600−10.15(2.6600))+36,7502.6600=−245,000−54,000(1.66000.399)+36,7502.6600=−245,000−54,000(4.1604)+13,815.79=−245,000−224,661.6+13,815.79=−245,000−210,845.81<−245,000

Since the calculated present value of the cost is less than the initial cost, increase the payback period to 8.

−54,000((1+0.15)8−10.15(1+0.15)8)+36,750(1+0.15)8=−245,000−54,000(3.05902−10.15(3.05902))+36,7503.05902=−245,000−54,000(2.059020.45885)+12,013.65=−245,000−54,000×4.4873+12,013.65=−245,000−242,314.2+12,013.65=−245,000−230,300.55≈−245,000

Since the calculated value is nearly equal to the initial cost, it is verified that the payback period is 8 years.

(b):

To determine

Calculate the payback period using spreadsheet.

(b):

Expert Solution

Explanation of Solution

The spreadsheet function for payback period is given below:

= NPER(15%,54000,-245000,0.15*245000)

The above function gives the value of 7.4 years.

Answer 6

Chapter 13, Problem 32P

(a):

To determine

Calculate the payback period.

(a):

Expert Solution

Explanation of Solution

Investment (C) is $245,000. Expense (AE) is $38,000 per year. Income (AI) is $92,000. MARR (i) is 15%. Salvage value (SV) is 15% of the first cost.

Payback period (n) can be calculated as follows:

(AI−AE)((1+i)n−1i(1+i)n)+SV(1+i)n=C(92,000−38,000)((1+0.15)n−10.15(1+0.15)n)+0.15×245,000(1+0.15)n=245,00054,000((1+0.15)n−10.15(1+0.15)n)+36,750(1+i)n=245,00054,000((1+0.15)n−10.15(1+0.15)n)+36,750(1+i)n=245,000

Substitute n as 7 by trial and error method to verify the time period in the above calculation.

−54,000((1+0.15)7−10.15(1+0.15)7)+36,750(1+0.15)7=−245,000−54,000(2.6600−10.15(2.6600))+36,7502.6600=−245,000−54,000(1.66000.399)+36,7502.6600=−245,000−54,000(4.1604)+13,815.79=−245,000−224,661.6+13,815.79=−245,000−210,845.81<−245,000

Since the calculated present value of the cost is less than the initial cost, increase the payback period to 8.

−54,000((1+0.15)8−10.15(1+0.15)8)+36,750(1+0.15)8=−245,000−54,000(3.05902−10.15(3.05902))+36,7503.05902=−245,000−54,000(2.059020.45885)+12,013.65=−245,000−54,000×4.4873+12,013.65=−245,000−242,314.2+12,013.65=−245,000−230,300.55≈−245,000

Since the calculated value is nearly equal to the initial cost, it is verified that the payback period is 8 years.

Answer 7

Chapter 13, Problem 32P

(a):

To determine

Calculate the payback period.

Answer 8

(a):

Expert Solution

Explanation of Solution

Investment (C) is $245,000. Expense (AE) is $38,000 per year. Income (AI) is $92,000. MARR (i) is 15%. Salvage value (SV) is 15% of the first cost.

Payback period (n) can be calculated as follows:

(AI−AE)((1+i)n−1i(1+i)n)+SV(1+i)n=C(92,000−38,000)((1+0.15)n−10.15(1+0.15)n)+0.15×245,000(1+0.15)n=245,00054,000((1+0.15)n−10.15(1+0.15)n)+36,750(1+i)n=245,00054,000((1+0.15)n−10.15(1+0.15)n)+36,750(1+i)n=245,000

Substitute n as 7 by trial and error method to verify the time period in the above calculation.

−54,000((1+0.15)7−10.15(1+0.15)7)+36,750(1+0.15)7=−245,000−54,000(2.6600−10.15(2.6600))+36,7502.6600=−245,000−54,000(1.66000.399)+36,7502.6600=−245,000−54,000(4.1604)+13,815.79=−245,000−224,661.6+13,815.79=−245,000−210,845.81<−245,000

Since the calculated present value of the cost is less than the initial cost, increase the payback period to 8.

−54,000((1+0.15)8−10.15(1+0.15)8)+36,750(1+0.15)8=−245,000−54,000(3.05902−10.15(3.05902))+36,7503.05902=−245,000−54,000(2.059020.45885)+12,013.65=−245,000−54,000×4.4873+12,013.65=−245,000−242,314.2+12,013.65=−245,000−230,300.55≈−245,000

Since the calculated value is nearly equal to the initial cost, it is verified that the payback period is 8 years.

Answer 9

(a):

Expert Solution

Answer 10

(a):

Expert Solution

Answer 11

Expert Solution

Answer 12

(b):

To determine

Calculate the payback period using spreadsheet.

(b):

Expert Solution

Explanation of Solution

The spreadsheet function for payback period is given below:

= NPER(15%,54000,-245000,0.15*245000)

The above function gives the value of 7.4 years.

Answer 13

(b):

To determine

Calculate the payback period using spreadsheet.

Answer 14

(b):

Expert Solution

Explanation of Solution

The spreadsheet function for payback period is given below:

= NPER(15%,54000,-245000,0.15*245000)

The above function gives the value of 7.4 years.

Answer 15

(b):

Expert Solution

Answer 16

(b):

Expert Solution

Answer 17

Expert Solution

Answer 18

Ch. 13 - Prob. 1P Ch. 13 - Prob. 2P Ch. 13 - Prob. 3P Ch. 13 - Prob. 4P Ch. 13 - Prob. 5P Ch. 13 - Prob. 6P Ch. 13 - Prob. 7P Ch. 13 - Prob. 8P Ch. 13 - Prob. 9P Ch. 13 - Prob. 10P

Calculate the payback period.

Calculate the payback period.

Explanation of Solution

Calculate the payback period using spreadsheet.

Explanation of Solution

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Chapter 13 Solutions