Calculate the present worth analysis.

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Answer 1

Question

Chapter 18, Problem 1CS1

To determine

Calculate the present worth analysis.

Expert Solution & Answer

Explanation of Solution

Time period is denoted by ‘n’ and MARR is denoted by ‘i’. Time period 1 (n) is 40. Time period 2 (n1) is 20.

The present worth (PW) of Plan A can be calculated using the following formula:

PW=First cost+AOC×((1+i)n−1i(1+i)n)+Salvage value×(1(1+i)n) (1)

Substitute the respective values in Equation (1) to calculate the present worth of Plan A with the actual time period.

PW=−10,000−500((1+0.1)40−10.1(1+0.1)40)+1,000×(1(1+0.1)40)=−10,000−500(9.7791)+1,000×(0.0221)=−14,867

Thus, the present worth is -$14,867.

Location is denoted by ‘L’. Present worth (PW) of Plan B can be calculated using the following formula:

PW=(First costL 1+AOCL 1×((1+i)n−1i(1+i)n)+Salvage valueL 1×(1(1+i)n)+First costL 2+AOCL 2×(1(1+i)n1)+First costL 2(1(1+i)n1)+Salvage valueL 2×(1(1+i)n)+AOCL 2×((1+i)n−1i(1+i)n)) (2)

Substitute the respective values in Equation (1) to calculate the present worth of Plan B with the actual time period.

PW=(−30,000−100×((1+0.1)40−10.1(1+0.1)40)+5000(1(1+0.1)40)−5,000−200×(1(1+0.1)20)−5,000(1(1+0.1)20)−200×(1(1+0.1)40)−200×((1+0.1)40−10.1(1+0.1)40))=(−30,000−100×(9.7791)+5000(0.0221)−5,000−200×(0.1486)−5,000(0.1486)−200×(0.0221)−200×(9.7791))=−38,600

Thus, the present worth is -$38,600.

Table 1 shows the value of present worth by changing the time period to different percentages that is obtained using Equations (1) and (2):

Table 1

MARR	PW A	PW B
0.1	-14,867	-38,600
0.07	-16,599	-40,023
0.04	-19,688	-42,311

Table 1 reveals that at different levels of MARR, the present worth of alternate A is greater than alternate B. Thus, there is no sensitivity. Plan A is selected for different levels of MARR.

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Answer 2

Question

Chapter 18, Problem 1CS1

To determine

Calculate the present worth analysis.

Expert Solution & Answer

Explanation of Solution

Time period is denoted by ‘n’ and MARR is denoted by ‘i’. Time period 1 (n) is 40. Time period 2 (n1) is 20.

The present worth (PW) of Plan A can be calculated using the following formula:

PW=First cost+AOC×((1+i)n−1i(1+i)n)+Salvage value×(1(1+i)n) (1)

Substitute the respective values in Equation (1) to calculate the present worth of Plan A with the actual time period.

PW=−10,000−500((1+0.1)40−10.1(1+0.1)40)+1,000×(1(1+0.1)40)=−10,000−500(9.7791)+1,000×(0.0221)=−14,867

Thus, the present worth is -$14,867.

Location is denoted by ‘L’. Present worth (PW) of Plan B can be calculated using the following formula:

PW=(First costL 1+AOCL 1×((1+i)n−1i(1+i)n)+Salvage valueL 1×(1(1+i)n)+First costL 2+AOCL 2×(1(1+i)n1)+First costL 2(1(1+i)n1)+Salvage valueL 2×(1(1+i)n)+AOCL 2×((1+i)n−1i(1+i)n)) (2)

Substitute the respective values in Equation (1) to calculate the present worth of Plan B with the actual time period.

PW=(−30,000−100×((1+0.1)40−10.1(1+0.1)40)+5000(1(1+0.1)40)−5,000−200×(1(1+0.1)20)−5,000(1(1+0.1)20)−200×(1(1+0.1)40)−200×((1+0.1)40−10.1(1+0.1)40))=(−30,000−100×(9.7791)+5000(0.0221)−5,000−200×(0.1486)−5,000(0.1486)−200×(0.0221)−200×(9.7791))=−38,600

Thus, the present worth is -$38,600.

Table 1 shows the value of present worth by changing the time period to different percentages that is obtained using Equations (1) and (2):

Table 1

MARR	PW A	PW B
0.1	-14,867	-38,600
0.07	-16,599	-40,023
0.04	-19,688	-42,311

Table 1 reveals that at different levels of MARR, the present worth of alternate A is greater than alternate B. Thus, there is no sensitivity. Plan A is selected for different levels of MARR.

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Answer 3

Question

Chapter 18, Problem 1CS1

To determine

Calculate the present worth analysis.

Expert Solution & Answer

Explanation of Solution

Time period is denoted by ‘n’ and MARR is denoted by ‘i’. Time period 1 (n) is 40. Time period 2 (n1) is 20.

The present worth (PW) of Plan A can be calculated using the following formula:

PW=First cost+AOC×((1+i)n−1i(1+i)n)+Salvage value×(1(1+i)n) (1)

Substitute the respective values in Equation (1) to calculate the present worth of Plan A with the actual time period.

PW=−10,000−500((1+0.1)40−10.1(1+0.1)40)+1,000×(1(1+0.1)40)=−10,000−500(9.7791)+1,000×(0.0221)=−14,867

Thus, the present worth is -$14,867.

Location is denoted by ‘L’. Present worth (PW) of Plan B can be calculated using the following formula:

PW=(First costL 1+AOCL 1×((1+i)n−1i(1+i)n)+Salvage valueL 1×(1(1+i)n)+First costL 2+AOCL 2×(1(1+i)n1)+First costL 2(1(1+i)n1)+Salvage valueL 2×(1(1+i)n)+AOCL 2×((1+i)n−1i(1+i)n)) (2)

Substitute the respective values in Equation (1) to calculate the present worth of Plan B with the actual time period.

PW=(−30,000−100×((1+0.1)40−10.1(1+0.1)40)+5000(1(1+0.1)40)−5,000−200×(1(1+0.1)20)−5,000(1(1+0.1)20)−200×(1(1+0.1)40)−200×((1+0.1)40−10.1(1+0.1)40))=(−30,000−100×(9.7791)+5000(0.0221)−5,000−200×(0.1486)−5,000(0.1486)−200×(0.0221)−200×(9.7791))=−38,600

Thus, the present worth is -$38,600.

Table 1 shows the value of present worth by changing the time period to different percentages that is obtained using Equations (1) and (2):

Table 1

MARR	PW A	PW B
0.1	-14,867	-38,600
0.07	-16,599	-40,023
0.04	-19,688	-42,311

Table 1 reveals that at different levels of MARR, the present worth of alternate A is greater than alternate B. Thus, there is no sensitivity. Plan A is selected for different levels of MARR.

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Answer 4

Question

Chapter 18, Problem 1CS1

To determine

Calculate the present worth analysis.

Expert Solution & Answer

Explanation of Solution

Time period is denoted by ‘n’ and MARR is denoted by ‘i’. Time period 1 (n) is 40. Time period 2 (n1) is 20.

The present worth (PW) of Plan A can be calculated using the following formula:

PW=First cost+AOC×((1+i)n−1i(1+i)n)+Salvage value×(1(1+i)n) (1)

Substitute the respective values in Equation (1) to calculate the present worth of Plan A with the actual time period.

PW=−10,000−500((1+0.1)40−10.1(1+0.1)40)+1,000×(1(1+0.1)40)=−10,000−500(9.7791)+1,000×(0.0221)=−14,867

Thus, the present worth is -$14,867.

Location is denoted by ‘L’. Present worth (PW) of Plan B can be calculated using the following formula:

PW=(First costL 1+AOCL 1×((1+i)n−1i(1+i)n)+Salvage valueL 1×(1(1+i)n)+First costL 2+AOCL 2×(1(1+i)n1)+First costL 2(1(1+i)n1)+Salvage valueL 2×(1(1+i)n)+AOCL 2×((1+i)n−1i(1+i)n)) (2)

Substitute the respective values in Equation (1) to calculate the present worth of Plan B with the actual time period.

PW=(−30,000−100×((1+0.1)40−10.1(1+0.1)40)+5000(1(1+0.1)40)−5,000−200×(1(1+0.1)20)−5,000(1(1+0.1)20)−200×(1(1+0.1)40)−200×((1+0.1)40−10.1(1+0.1)40))=(−30,000−100×(9.7791)+5000(0.0221)−5,000−200×(0.1486)−5,000(0.1486)−200×(0.0221)−200×(9.7791))=−38,600

Thus, the present worth is -$38,600.

Table 1 shows the value of present worth by changing the time period to different percentages that is obtained using Equations (1) and (2):

Table 1

MARR	PW A	PW B
0.1	-14,867	-38,600
0.07	-16,599	-40,023
0.04	-19,688	-42,311

Table 1 reveals that at different levels of MARR, the present worth of alternate A is greater than alternate B. Thus, there is no sensitivity. Plan A is selected for different levels of MARR.

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Answer 5

Chapter 18, Problem 1CS1

To determine

Calculate the present worth analysis.

Expert Solution & Answer

Explanation of Solution

Time period is denoted by ‘n’ and MARR is denoted by ‘i’. Time period 1 (n) is 40. Time period 2 (n1) is 20.

The present worth (PW) of Plan A can be calculated using the following formula:

PW=First cost+AOC×((1+i)n−1i(1+i)n)+Salvage value×(1(1+i)n) (1)

Substitute the respective values in Equation (1) to calculate the present worth of Plan A with the actual time period.

PW=−10,000−500((1+0.1)40−10.1(1+0.1)40)+1,000×(1(1+0.1)40)=−10,000−500(9.7791)+1,000×(0.0221)=−14,867

Thus, the present worth is -$14,867.

Location is denoted by ‘L’. Present worth (PW) of Plan B can be calculated using the following formula:

PW=(First costL 1+AOCL 1×((1+i)n−1i(1+i)n)+Salvage valueL 1×(1(1+i)n)+First costL 2+AOCL 2×(1(1+i)n1)+First costL 2(1(1+i)n1)+Salvage valueL 2×(1(1+i)n)+AOCL 2×((1+i)n−1i(1+i)n)) (2)

Substitute the respective values in Equation (1) to calculate the present worth of Plan B with the actual time period.

PW=(−30,000−100×((1+0.1)40−10.1(1+0.1)40)+5000(1(1+0.1)40)−5,000−200×(1(1+0.1)20)−5,000(1(1+0.1)20)−200×(1(1+0.1)40)−200×((1+0.1)40−10.1(1+0.1)40))=(−30,000−100×(9.7791)+5000(0.0221)−5,000−200×(0.1486)−5,000(0.1486)−200×(0.0221)−200×(9.7791))=−38,600

Thus, the present worth is -$38,600.

Table 1 shows the value of present worth by changing the time period to different percentages that is obtained using Equations (1) and (2):

Table 1

MARR	PW A	PW B
0.1	-14,867	-38,600
0.07	-16,599	-40,023
0.04	-19,688	-42,311

Table 1 reveals that at different levels of MARR, the present worth of alternate A is greater than alternate B. Thus, there is no sensitivity. Plan A is selected for different levels of MARR.

Answer 6

Chapter 18, Problem 1CS1

To determine

Calculate the present worth analysis.

Expert Solution & Answer

Explanation of Solution

Time period is denoted by ‘n’ and MARR is denoted by ‘i’. Time period 1 (n) is 40. Time period 2 (n1) is 20.

The present worth (PW) of Plan A can be calculated using the following formula:

PW=First cost+AOC×((1+i)n−1i(1+i)n)+Salvage value×(1(1+i)n) (1)

Substitute the respective values in Equation (1) to calculate the present worth of Plan A with the actual time period.

PW=−10,000−500((1+0.1)40−10.1(1+0.1)40)+1,000×(1(1+0.1)40)=−10,000−500(9.7791)+1,000×(0.0221)=−14,867

Thus, the present worth is -$14,867.

Location is denoted by ‘L’. Present worth (PW) of Plan B can be calculated using the following formula:

PW=(First costL 1+AOCL 1×((1+i)n−1i(1+i)n)+Salvage valueL 1×(1(1+i)n)+First costL 2+AOCL 2×(1(1+i)n1)+First costL 2(1(1+i)n1)+Salvage valueL 2×(1(1+i)n)+AOCL 2×((1+i)n−1i(1+i)n)) (2)

Substitute the respective values in Equation (1) to calculate the present worth of Plan B with the actual time period.

PW=(−30,000−100×((1+0.1)40−10.1(1+0.1)40)+5000(1(1+0.1)40)−5,000−200×(1(1+0.1)20)−5,000(1(1+0.1)20)−200×(1(1+0.1)40)−200×((1+0.1)40−10.1(1+0.1)40))=(−30,000−100×(9.7791)+5000(0.0221)−5,000−200×(0.1486)−5,000(0.1486)−200×(0.0221)−200×(9.7791))=−38,600

Thus, the present worth is -$38,600.

Table 1 shows the value of present worth by changing the time period to different percentages that is obtained using Equations (1) and (2):

Table 1

MARR	PW A	PW B
0.1	-14,867	-38,600
0.07	-16,599	-40,023
0.04	-19,688	-42,311

Table 1 reveals that at different levels of MARR, the present worth of alternate A is greater than alternate B. Thus, there is no sensitivity. Plan A is selected for different levels of MARR.

Answer 7

Chapter 18, Problem 1CS1

To determine

Calculate the present worth analysis.

Answer 8

Expert Solution & Answer

Explanation of Solution

Time period is denoted by ‘n’ and MARR is denoted by ‘i’. Time period 1 (n) is 40. Time period 2 (n1) is 20.

The present worth (PW) of Plan A can be calculated using the following formula:

PW=First cost+AOC×((1+i)n−1i(1+i)n)+Salvage value×(1(1+i)n) (1)

Substitute the respective values in Equation (1) to calculate the present worth of Plan A with the actual time period.

PW=−10,000−500((1+0.1)40−10.1(1+0.1)40)+1,000×(1(1+0.1)40)=−10,000−500(9.7791)+1,000×(0.0221)=−14,867

Thus, the present worth is -$14,867.

Location is denoted by ‘L’. Present worth (PW) of Plan B can be calculated using the following formula:

PW=(First costL 1+AOCL 1×((1+i)n−1i(1+i)n)+Salvage valueL 1×(1(1+i)n)+First costL 2+AOCL 2×(1(1+i)n1)+First costL 2(1(1+i)n1)+Salvage valueL 2×(1(1+i)n)+AOCL 2×((1+i)n−1i(1+i)n)) (2)

Substitute the respective values in Equation (1) to calculate the present worth of Plan B with the actual time period.

PW=(−30,000−100×((1+0.1)40−10.1(1+0.1)40)+5000(1(1+0.1)40)−5,000−200×(1(1+0.1)20)−5,000(1(1+0.1)20)−200×(1(1+0.1)40)−200×((1+0.1)40−10.1(1+0.1)40))=(−30,000−100×(9.7791)+5000(0.0221)−5,000−200×(0.1486)−5,000(0.1486)−200×(0.0221)−200×(9.7791))=−38,600

Thus, the present worth is -$38,600.

Table 1 shows the value of present worth by changing the time period to different percentages that is obtained using Equations (1) and (2):

Table 1

MARR	PW A	PW B
0.1	-14,867	-38,600
0.07	-16,599	-40,023
0.04	-19,688	-42,311

Table 1 reveals that at different levels of MARR, the present worth of alternate A is greater than alternate B. Thus, there is no sensitivity. Plan A is selected for different levels of MARR.