Calculate the equivalent annual worth.

Question

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Answer 1

Question

Chapter 6, Problem 22P

(a)

To determine

Calculate the equivalent annual worth.

(a)

Expert Solution

Explanation of Solution

Table -1 shows the cash flow of different models.

Table -1

Models	LA	IN	CO
First cost (C)	-150,000	-900,000
AOC (MO) per year	-95,000	-60,000	-140,000
Salvage value (SV)	25,000	300,000
Time period (n)	4	6	2
Interest (i)	10%	10%	10%

The equivalent annual worth of project LA (AWL) can be calculated as follows:

AWL=C(i(1+i)n(1+i)n−1)+MO+SV(i(1+i)n−1)=−150,000(0.1(1+0.1)4(1+0.1)4−1)−95,000+25,000(0.1(1+0.1)4−1)=−150,000(0.1(1.4641)1.4641−1)−95,000+25,000(0.11.4641−1)=−150,000(0.146410.4641)−95,000+25,000(0.10.4641)=−150,000(0.315471)−95,000+25,000(0.215471)=−47,320.65−95,000+5,386.775=−136,933.88

The annual worth of the project LA is -$136,933.88.

The equivalent annual worth of model IN (AWI) can be calculated as follows:

AWI=C(i(1+i)n(1+i)n−1)+MO+SV(i(1+i)n−1)=−900,000(0.1(1+0.1)6(1+0.1)6−1)−60,000+300,000(0.1(1+0.1)6−1)=−900,000(0.1(1.771561)1.771561−1)−60,000+300,000(0.11.771561−1)=−900,000(0.17715610.771561)−60,000+300,000(0.10.771561)=−900,000(0.229607)−60,000+300,000(0.129607)=−206,646.3−60,000+38,882.1=−227,764.2

The annual worth of the model IN is -$227,764.2.

Since the annual worth of the project LA is greater than the other two project, select the project LA.

(b)

To determine

Calculate the present worth.

(b)

Expert Solution

Explanation of Solution

The time period for project LA should be equated with the time period of project IN and CO to compare the present worth. The common time period for all the projects is 12 years. The present worth of project LA (PWL) can be calculated as follows:

PWL=AWL((1+i)n−1i(1+i)n)=−136,933.88((1+0.1)12−10.1(1+0.1)12)=−136,933.88(3.138428−10.1(3.138428))=−136,933.88(2.1384280.313843)=−136,933.88(6.813687)=−933,024.6

The present worth of the project LA is -$933,024.6.

The time period for project IN should be equated with time period of project LA and CO to compare the present worth. The common time period for all the projects is 12 years. The present worth of project LA (PWL) can be calculated as follows:

PWI=AWI((1+i)n−1i(1+i)n)=−227,764.2((1+0.1)12−10.1(1+0.1)12)=−227,764.2(3.138428−10.1(3.138428))=−227,764.2(2.1384280.313843)=−227,764.2(6.813687)=−1,551,913.97

The present worth of the project IN is -$1,551,913.97.

The time period for project CO should be equated with time period of project LA and IN to compare the present worth. The common time period for all the projects is 12 years. The present worth of project CO (PWC) can be calculated as follows:

PWC=AWC((1+i)n−1i(1+i)n)=−140,000((1+0.1)12−10.1(1+0.1)12)=−140,000(3.138428−10.1(3.138428))=−140,000(2.1384280.313843)=−140,000(6.813687)=−953,916.18

The present worth of the project CO is -$953,916.18.

Since the present worth of the project LA is greater than the other two project, select the project LA.

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Answer 2

Question

Chapter 6, Problem 22P

(a)

To determine

Calculate the equivalent annual worth.

(a)

Expert Solution

Explanation of Solution

Table -1 shows the cash flow of different models.

Table -1

Models	LA	IN	CO
First cost (C)	-150,000	-900,000
AOC (MO) per year	-95,000	-60,000	-140,000
Salvage value (SV)	25,000	300,000
Time period (n)	4	6	2
Interest (i)	10%	10%	10%

The equivalent annual worth of project LA (AWL) can be calculated as follows:

AWL=C(i(1+i)n(1+i)n−1)+MO+SV(i(1+i)n−1)=−150,000(0.1(1+0.1)4(1+0.1)4−1)−95,000+25,000(0.1(1+0.1)4−1)=−150,000(0.1(1.4641)1.4641−1)−95,000+25,000(0.11.4641−1)=−150,000(0.146410.4641)−95,000+25,000(0.10.4641)=−150,000(0.315471)−95,000+25,000(0.215471)=−47,320.65−95,000+5,386.775=−136,933.88

The annual worth of the project LA is -$136,933.88.

The equivalent annual worth of model IN (AWI) can be calculated as follows:

AWI=C(i(1+i)n(1+i)n−1)+MO+SV(i(1+i)n−1)=−900,000(0.1(1+0.1)6(1+0.1)6−1)−60,000+300,000(0.1(1+0.1)6−1)=−900,000(0.1(1.771561)1.771561−1)−60,000+300,000(0.11.771561−1)=−900,000(0.17715610.771561)−60,000+300,000(0.10.771561)=−900,000(0.229607)−60,000+300,000(0.129607)=−206,646.3−60,000+38,882.1=−227,764.2

The annual worth of the model IN is -$227,764.2.

Since the annual worth of the project LA is greater than the other two project, select the project LA.

(b)

To determine

Calculate the present worth.

(b)

Expert Solution

Explanation of Solution

The time period for project LA should be equated with the time period of project IN and CO to compare the present worth. The common time period for all the projects is 12 years. The present worth of project LA (PWL) can be calculated as follows:

PWL=AWL((1+i)n−1i(1+i)n)=−136,933.88((1+0.1)12−10.1(1+0.1)12)=−136,933.88(3.138428−10.1(3.138428))=−136,933.88(2.1384280.313843)=−136,933.88(6.813687)=−933,024.6

The present worth of the project LA is -$933,024.6.

The time period for project IN should be equated with time period of project LA and CO to compare the present worth. The common time period for all the projects is 12 years. The present worth of project LA (PWL) can be calculated as follows:

PWI=AWI((1+i)n−1i(1+i)n)=−227,764.2((1+0.1)12−10.1(1+0.1)12)=−227,764.2(3.138428−10.1(3.138428))=−227,764.2(2.1384280.313843)=−227,764.2(6.813687)=−1,551,913.97

The present worth of the project IN is -$1,551,913.97.

The time period for project CO should be equated with time period of project LA and IN to compare the present worth. The common time period for all the projects is 12 years. The present worth of project CO (PWC) can be calculated as follows:

PWC=AWC((1+i)n−1i(1+i)n)=−140,000((1+0.1)12−10.1(1+0.1)12)=−140,000(3.138428−10.1(3.138428))=−140,000(2.1384280.313843)=−140,000(6.813687)=−953,916.18

The present worth of the project CO is -$953,916.18.

Since the present worth of the project LA is greater than the other two project, select the project LA.

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Answer 3

Question

Chapter 6, Problem 22P

(a)

To determine

Calculate the equivalent annual worth.

(a)

Expert Solution

Explanation of Solution

Table -1 shows the cash flow of different models.

Table -1

Models	LA	IN	CO
First cost (C)	-150,000	-900,000
AOC (MO) per year	-95,000	-60,000	-140,000
Salvage value (SV)	25,000	300,000
Time period (n)	4	6	2
Interest (i)	10%	10%	10%

The equivalent annual worth of project LA (AWL) can be calculated as follows:

AWL=C(i(1+i)n(1+i)n−1)+MO+SV(i(1+i)n−1)=−150,000(0.1(1+0.1)4(1+0.1)4−1)−95,000+25,000(0.1(1+0.1)4−1)=−150,000(0.1(1.4641)1.4641−1)−95,000+25,000(0.11.4641−1)=−150,000(0.146410.4641)−95,000+25,000(0.10.4641)=−150,000(0.315471)−95,000+25,000(0.215471)=−47,320.65−95,000+5,386.775=−136,933.88

The annual worth of the project LA is -$136,933.88.

The equivalent annual worth of model IN (AWI) can be calculated as follows:

AWI=C(i(1+i)n(1+i)n−1)+MO+SV(i(1+i)n−1)=−900,000(0.1(1+0.1)6(1+0.1)6−1)−60,000+300,000(0.1(1+0.1)6−1)=−900,000(0.1(1.771561)1.771561−1)−60,000+300,000(0.11.771561−1)=−900,000(0.17715610.771561)−60,000+300,000(0.10.771561)=−900,000(0.229607)−60,000+300,000(0.129607)=−206,646.3−60,000+38,882.1=−227,764.2

The annual worth of the model IN is -$227,764.2.

Since the annual worth of the project LA is greater than the other two project, select the project LA.

(b)

To determine

Calculate the present worth.

(b)

Expert Solution

Explanation of Solution

The time period for project LA should be equated with the time period of project IN and CO to compare the present worth. The common time period for all the projects is 12 years. The present worth of project LA (PWL) can be calculated as follows:

PWL=AWL((1+i)n−1i(1+i)n)=−136,933.88((1+0.1)12−10.1(1+0.1)12)=−136,933.88(3.138428−10.1(3.138428))=−136,933.88(2.1384280.313843)=−136,933.88(6.813687)=−933,024.6

The present worth of the project LA is -$933,024.6.

The time period for project IN should be equated with time period of project LA and CO to compare the present worth. The common time period for all the projects is 12 years. The present worth of project LA (PWL) can be calculated as follows:

PWI=AWI((1+i)n−1i(1+i)n)=−227,764.2((1+0.1)12−10.1(1+0.1)12)=−227,764.2(3.138428−10.1(3.138428))=−227,764.2(2.1384280.313843)=−227,764.2(6.813687)=−1,551,913.97

The present worth of the project IN is -$1,551,913.97.

The time period for project CO should be equated with time period of project LA and IN to compare the present worth. The common time period for all the projects is 12 years. The present worth of project CO (PWC) can be calculated as follows:

PWC=AWC((1+i)n−1i(1+i)n)=−140,000((1+0.1)12−10.1(1+0.1)12)=−140,000(3.138428−10.1(3.138428))=−140,000(2.1384280.313843)=−140,000(6.813687)=−953,916.18

The present worth of the project CO is -$953,916.18.

Since the present worth of the project LA is greater than the other two project, select the project LA.

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Answer 4

Question

Chapter 6, Problem 22P

(a)

To determine

Calculate the equivalent annual worth.

(a)

Expert Solution

Explanation of Solution

Table -1 shows the cash flow of different models.

Table -1

Models	LA	IN	CO
First cost (C)	-150,000	-900,000
AOC (MO) per year	-95,000	-60,000	-140,000
Salvage value (SV)	25,000	300,000
Time period (n)	4	6	2
Interest (i)	10%	10%	10%

The equivalent annual worth of project LA (AWL) can be calculated as follows:

AWL=C(i(1+i)n(1+i)n−1)+MO+SV(i(1+i)n−1)=−150,000(0.1(1+0.1)4(1+0.1)4−1)−95,000+25,000(0.1(1+0.1)4−1)=−150,000(0.1(1.4641)1.4641−1)−95,000+25,000(0.11.4641−1)=−150,000(0.146410.4641)−95,000+25,000(0.10.4641)=−150,000(0.315471)−95,000+25,000(0.215471)=−47,320.65−95,000+5,386.775=−136,933.88

The annual worth of the project LA is -$136,933.88.

The equivalent annual worth of model IN (AWI) can be calculated as follows:

AWI=C(i(1+i)n(1+i)n−1)+MO+SV(i(1+i)n−1)=−900,000(0.1(1+0.1)6(1+0.1)6−1)−60,000+300,000(0.1(1+0.1)6−1)=−900,000(0.1(1.771561)1.771561−1)−60,000+300,000(0.11.771561−1)=−900,000(0.17715610.771561)−60,000+300,000(0.10.771561)=−900,000(0.229607)−60,000+300,000(0.129607)=−206,646.3−60,000+38,882.1=−227,764.2

The annual worth of the model IN is -$227,764.2.

Since the annual worth of the project LA is greater than the other two project, select the project LA.

(b)

To determine

Calculate the present worth.

(b)

Expert Solution

Explanation of Solution

The time period for project LA should be equated with the time period of project IN and CO to compare the present worth. The common time period for all the projects is 12 years. The present worth of project LA (PWL) can be calculated as follows:

PWL=AWL((1+i)n−1i(1+i)n)=−136,933.88((1+0.1)12−10.1(1+0.1)12)=−136,933.88(3.138428−10.1(3.138428))=−136,933.88(2.1384280.313843)=−136,933.88(6.813687)=−933,024.6

The present worth of the project LA is -$933,024.6.

The time period for project IN should be equated with time period of project LA and CO to compare the present worth. The common time period for all the projects is 12 years. The present worth of project LA (PWL) can be calculated as follows:

PWI=AWI((1+i)n−1i(1+i)n)=−227,764.2((1+0.1)12−10.1(1+0.1)12)=−227,764.2(3.138428−10.1(3.138428))=−227,764.2(2.1384280.313843)=−227,764.2(6.813687)=−1,551,913.97

The present worth of the project IN is -$1,551,913.97.

The time period for project CO should be equated with time period of project LA and IN to compare the present worth. The common time period for all the projects is 12 years. The present worth of project CO (PWC) can be calculated as follows:

PWC=AWC((1+i)n−1i(1+i)n)=−140,000((1+0.1)12−10.1(1+0.1)12)=−140,000(3.138428−10.1(3.138428))=−140,000(2.1384280.313843)=−140,000(6.813687)=−953,916.18

The present worth of the project CO is -$953,916.18.

Since the present worth of the project LA is greater than the other two project, select the project LA.

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Answer 5

Chapter 6, Problem 22P

(a)

To determine

Calculate the equivalent annual worth.

(a)

Expert Solution

Explanation of Solution

Table -1 shows the cash flow of different models.

Table -1

Models	LA	IN	CO
First cost (C)	-150,000	-900,000
AOC (MO) per year	-95,000	-60,000	-140,000
Salvage value (SV)	25,000	300,000
Time period (n)	4	6	2
Interest (i)	10%	10%	10%

The equivalent annual worth of project LA (AWL) can be calculated as follows:

AWL=C(i(1+i)n(1+i)n−1)+MO+SV(i(1+i)n−1)=−150,000(0.1(1+0.1)4(1+0.1)4−1)−95,000+25,000(0.1(1+0.1)4−1)=−150,000(0.1(1.4641)1.4641−1)−95,000+25,000(0.11.4641−1)=−150,000(0.146410.4641)−95,000+25,000(0.10.4641)=−150,000(0.315471)−95,000+25,000(0.215471)=−47,320.65−95,000+5,386.775=−136,933.88

The annual worth of the project LA is -$136,933.88.

The equivalent annual worth of model IN (AWI) can be calculated as follows:

AWI=C(i(1+i)n(1+i)n−1)+MO+SV(i(1+i)n−1)=−900,000(0.1(1+0.1)6(1+0.1)6−1)−60,000+300,000(0.1(1+0.1)6−1)=−900,000(0.1(1.771561)1.771561−1)−60,000+300,000(0.11.771561−1)=−900,000(0.17715610.771561)−60,000+300,000(0.10.771561)=−900,000(0.229607)−60,000+300,000(0.129607)=−206,646.3−60,000+38,882.1=−227,764.2

The annual worth of the model IN is -$227,764.2.

Since the annual worth of the project LA is greater than the other two project, select the project LA.

(b)

To determine

Calculate the present worth.

(b)

Expert Solution

Explanation of Solution

The time period for project LA should be equated with the time period of project IN and CO to compare the present worth. The common time period for all the projects is 12 years. The present worth of project LA (PWL) can be calculated as follows:

PWL=AWL((1+i)n−1i(1+i)n)=−136,933.88((1+0.1)12−10.1(1+0.1)12)=−136,933.88(3.138428−10.1(3.138428))=−136,933.88(2.1384280.313843)=−136,933.88(6.813687)=−933,024.6

The present worth of the project LA is -$933,024.6.

The time period for project IN should be equated with time period of project LA and CO to compare the present worth. The common time period for all the projects is 12 years. The present worth of project LA (PWL) can be calculated as follows:

PWI=AWI((1+i)n−1i(1+i)n)=−227,764.2((1+0.1)12−10.1(1+0.1)12)=−227,764.2(3.138428−10.1(3.138428))=−227,764.2(2.1384280.313843)=−227,764.2(6.813687)=−1,551,913.97

The present worth of the project IN is -$1,551,913.97.

The time period for project CO should be equated with time period of project LA and IN to compare the present worth. The common time period for all the projects is 12 years. The present worth of project CO (PWC) can be calculated as follows:

PWC=AWC((1+i)n−1i(1+i)n)=−140,000((1+0.1)12−10.1(1+0.1)12)=−140,000(3.138428−10.1(3.138428))=−140,000(2.1384280.313843)=−140,000(6.813687)=−953,916.18

The present worth of the project CO is -$953,916.18.

Since the present worth of the project LA is greater than the other two project, select the project LA.

Answer 6

Chapter 6, Problem 22P

(a)

To determine

Calculate the equivalent annual worth.

(a)

Expert Solution

Explanation of Solution

Table -1 shows the cash flow of different models.

Table -1

Models	LA	IN	CO
First cost (C)	-150,000	-900,000
AOC (MO) per year	-95,000	-60,000	-140,000
Salvage value (SV)	25,000	300,000
Time period (n)	4	6	2
Interest (i)	10%	10%	10%

The equivalent annual worth of project LA (AWL) can be calculated as follows:

AWL=C(i(1+i)n(1+i)n−1)+MO+SV(i(1+i)n−1)=−150,000(0.1(1+0.1)4(1+0.1)4−1)−95,000+25,000(0.1(1+0.1)4−1)=−150,000(0.1(1.4641)1.4641−1)−95,000+25,000(0.11.4641−1)=−150,000(0.146410.4641)−95,000+25,000(0.10.4641)=−150,000(0.315471)−95,000+25,000(0.215471)=−47,320.65−95,000+5,386.775=−136,933.88

The annual worth of the project LA is -$136,933.88.

The equivalent annual worth of model IN (AWI) can be calculated as follows:

AWI=C(i(1+i)n(1+i)n−1)+MO+SV(i(1+i)n−1)=−900,000(0.1(1+0.1)6(1+0.1)6−1)−60,000+300,000(0.1(1+0.1)6−1)=−900,000(0.1(1.771561)1.771561−1)−60,000+300,000(0.11.771561−1)=−900,000(0.17715610.771561)−60,000+300,000(0.10.771561)=−900,000(0.229607)−60,000+300,000(0.129607)=−206,646.3−60,000+38,882.1=−227,764.2

The annual worth of the model IN is -$227,764.2.

Since the annual worth of the project LA is greater than the other two project, select the project LA.

Answer 7

Chapter 6, Problem 22P

(a)

To determine

Calculate the equivalent annual worth.

Answer 8

(a)

Expert Solution

Explanation of Solution

Table -1 shows the cash flow of different models.

Table -1

Models	LA	IN	CO
First cost (C)	-150,000	-900,000
AOC (MO) per year	-95,000	-60,000	-140,000
Salvage value (SV)	25,000	300,000
Time period (n)	4	6	2
Interest (i)	10%	10%	10%

The equivalent annual worth of project LA (AWL) can be calculated as follows:

AWL=C(i(1+i)n(1+i)n−1)+MO+SV(i(1+i)n−1)=−150,000(0.1(1+0.1)4(1+0.1)4−1)−95,000+25,000(0.1(1+0.1)4−1)=−150,000(0.1(1.4641)1.4641−1)−95,000+25,000(0.11.4641−1)=−150,000(0.146410.4641)−95,000+25,000(0.10.4641)=−150,000(0.315471)−95,000+25,000(0.215471)=−47,320.65−95,000+5,386.775=−136,933.88

The annual worth of the project LA is -$136,933.88.

The equivalent annual worth of model IN (AWI) can be calculated as follows:

AWI=C(i(1+i)n(1+i)n−1)+MO+SV(i(1+i)n−1)=−900,000(0.1(1+0.1)6(1+0.1)6−1)−60,000+300,000(0.1(1+0.1)6−1)=−900,000(0.1(1.771561)1.771561−1)−60,000+300,000(0.11.771561−1)=−900,000(0.17715610.771561)−60,000+300,000(0.10.771561)=−900,000(0.229607)−60,000+300,000(0.129607)=−206,646.3−60,000+38,882.1=−227,764.2

The annual worth of the model IN is -$227,764.2.

Since the annual worth of the project LA is greater than the other two project, select the project LA.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

(b)

To determine

Calculate the present worth.

(b)

Expert Solution

Explanation of Solution

The time period for project LA should be equated with the time period of project IN and CO to compare the present worth. The common time period for all the projects is 12 years. The present worth of project LA (PWL) can be calculated as follows:

PWL=AWL((1+i)n−1i(1+i)n)=−136,933.88((1+0.1)12−10.1(1+0.1)12)=−136,933.88(3.138428−10.1(3.138428))=−136,933.88(2.1384280.313843)=−136,933.88(6.813687)=−933,024.6

The present worth of the project LA is -$933,024.6.

The time period for project IN should be equated with time period of project LA and CO to compare the present worth. The common time period for all the projects is 12 years. The present worth of project LA (PWL) can be calculated as follows:

PWI=AWI((1+i)n−1i(1+i)n)=−227,764.2((1+0.1)12−10.1(1+0.1)12)=−227,764.2(3.138428−10.1(3.138428))=−227,764.2(2.1384280.313843)=−227,764.2(6.813687)=−1,551,913.97

The present worth of the project IN is -$1,551,913.97.

The time period for project CO should be equated with time period of project LA and IN to compare the present worth. The common time period for all the projects is 12 years. The present worth of project CO (PWC) can be calculated as follows:

PWC=AWC((1+i)n−1i(1+i)n)=−140,000((1+0.1)12−10.1(1+0.1)12)=−140,000(3.138428−10.1(3.138428))=−140,000(2.1384280.313843)=−140,000(6.813687)=−953,916.18

The present worth of the project CO is -$953,916.18.

Since the present worth of the project LA is greater than the other two project, select the project LA.

Answer 13

(b)

To determine

Calculate the present worth.

Answer 14

(b)

Expert Solution

Explanation of Solution

The time period for project LA should be equated with the time period of project IN and CO to compare the present worth. The common time period for all the projects is 12 years. The present worth of project LA (PWL) can be calculated as follows:

PWL=AWL((1+i)n−1i(1+i)n)=−136,933.88((1+0.1)12−10.1(1+0.1)12)=−136,933.88(3.138428−10.1(3.138428))=−136,933.88(2.1384280.313843)=−136,933.88(6.813687)=−933,024.6

The present worth of the project LA is -$933,024.6.

The time period for project IN should be equated with time period of project LA and CO to compare the present worth. The common time period for all the projects is 12 years. The present worth of project LA (PWL) can be calculated as follows:

PWI=AWI((1+i)n−1i(1+i)n)=−227,764.2((1+0.1)12−10.1(1+0.1)12)=−227,764.2(3.138428−10.1(3.138428))=−227,764.2(2.1384280.313843)=−227,764.2(6.813687)=−1,551,913.97

The present worth of the project IN is -$1,551,913.97.

The time period for project CO should be equated with time period of project LA and IN to compare the present worth. The common time period for all the projects is 12 years. The present worth of project CO (PWC) can be calculated as follows:

PWC=AWC((1+i)n−1i(1+i)n)=−140,000((1+0.1)12−10.1(1+0.1)12)=−140,000(3.138428−10.1(3.138428))=−140,000(2.1384280.313843)=−140,000(6.813687)=−953,916.18