Calculate the annual worth.

Question

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Answer 1

Question

Chapter 11, Problem 37P

(a):

To determine

Calculate the annual worth.

(a):

Expert Solution

Explanation of Solution

Defender: The first cost (FC) is $160,000. The annual operating cost (AC) is $7,000. The salvage value for the first year (SV1) is $50,000 and for the second year (SV2) is $40,000. The interest rate is 12% compounded monthly. Thus, the effective interest rate (i) is 1%(0.1212) .

Challenger: The first cost (FC) is $210,000. The annual operating cost (AC) is $5,000. The salvage values for first year (SV1) is $100,000, second year (SV2) is $7,000, and third year (SV3) is $45,000. The interest rate is 12% compounded monthly. Thus, the effective interest rate (i) is 1%(0.1212).

The annual worth (AV) is calculated using the following formula:

AV=−FC(i(1+i)n(1+i)n−1)−AC+SVn(i(1+i)n−1) (1)

Substitute the respective values in Equation (1) to calculate the annual worth (AV) of defender in 12-month period.

AV=−160,000(0.01(1+0.01)12(1+0.01)12−1)−7,000+50,000(0.01(1+0.01)12−1)=−160,000(0.01(1.12683)1.12683−1)−7,000+50,000(0.011.12683−1)=−160,000(0.011270.12683)−7,000+50,000(0.010.12683)=−160,000(0.08885)−7,000+50,000(0.07885)=−14,216−7,000+3,942.5=−17,274

The annual worth of the defender for 12 months is -$17,2754.

Substitute the respective values in Equation (1) to calculate the annual worth (AV) of challenger in 12-month period.

AV=−210,000(0.01(1+0.01)12(1+0.01)12−1)−5,000+100,000(0.01(1+0.01)12−1)=−210,000(0.01(1.12683)1.12683−1)−5,000+100,000(0.011.12683−1)=−210,000(0.011270.12683)−5,000+100,000(0.010.12683)=−210,000(0.08885)−5,000+100,000(0.07885)=−18,658.5−5,000+7,885=−15,774

The annual worth of the challenger for 12 months is -$15,774.

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

(b):

To determine

Calculate the annual worth for 2 years.

(b):

Expert Solution

Explanation of Solution

Table 1 shows the annual worth of the defender and challenger for 2 years (24 months), which were obtained using Equation (1).

Table 1

Project	AV
Defender	-13,048
Challenger	-12,290

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

(c):

To determine

Calculate the annual worth for 3 years.

(c):

Expert Solution

Explanation of Solution

Table 1 shows the annual worth of the defender and challenger for 3 years (36 months), which were obtained using Equation (1).

Table 1

Project	AV
Defender	-14,292
Challenger	-10,349

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

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Answer 2

Question

Chapter 11, Problem 37P

(a):

To determine

Calculate the annual worth.

(a):

Expert Solution

Explanation of Solution

Defender: The first cost (FC) is $160,000. The annual operating cost (AC) is $7,000. The salvage value for the first year (SV1) is $50,000 and for the second year (SV2) is $40,000. The interest rate is 12% compounded monthly. Thus, the effective interest rate (i) is 1%(0.1212) .

Challenger: The first cost (FC) is $210,000. The annual operating cost (AC) is $5,000. The salvage values for first year (SV1) is $100,000, second year (SV2) is $7,000, and third year (SV3) is $45,000. The interest rate is 12% compounded monthly. Thus, the effective interest rate (i) is 1%(0.1212).

The annual worth (AV) is calculated using the following formula:

AV=−FC(i(1+i)n(1+i)n−1)−AC+SVn(i(1+i)n−1) (1)

Substitute the respective values in Equation (1) to calculate the annual worth (AV) of defender in 12-month period.

AV=−160,000(0.01(1+0.01)12(1+0.01)12−1)−7,000+50,000(0.01(1+0.01)12−1)=−160,000(0.01(1.12683)1.12683−1)−7,000+50,000(0.011.12683−1)=−160,000(0.011270.12683)−7,000+50,000(0.010.12683)=−160,000(0.08885)−7,000+50,000(0.07885)=−14,216−7,000+3,942.5=−17,274

The annual worth of the defender for 12 months is -$17,2754.

Substitute the respective values in Equation (1) to calculate the annual worth (AV) of challenger in 12-month period.

AV=−210,000(0.01(1+0.01)12(1+0.01)12−1)−5,000+100,000(0.01(1+0.01)12−1)=−210,000(0.01(1.12683)1.12683−1)−5,000+100,000(0.011.12683−1)=−210,000(0.011270.12683)−5,000+100,000(0.010.12683)=−210,000(0.08885)−5,000+100,000(0.07885)=−18,658.5−5,000+7,885=−15,774

The annual worth of the challenger for 12 months is -$15,774.

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

(b):

To determine

Calculate the annual worth for 2 years.

(b):

Expert Solution

Explanation of Solution

Table 1 shows the annual worth of the defender and challenger for 2 years (24 months), which were obtained using Equation (1).

Table 1

Project	AV
Defender	-13,048
Challenger	-12,290

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

(c):

To determine

Calculate the annual worth for 3 years.

(c):

Expert Solution

Explanation of Solution

Table 1 shows the annual worth of the defender and challenger for 3 years (36 months), which were obtained using Equation (1).

Table 1

Project	AV
Defender	-14,292
Challenger	-10,349

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

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Answer 3

Question

Chapter 11, Problem 37P

(a):

To determine

Calculate the annual worth.

(a):

Expert Solution

Explanation of Solution

Defender: The first cost (FC) is $160,000. The annual operating cost (AC) is $7,000. The salvage value for the first year (SV1) is $50,000 and for the second year (SV2) is $40,000. The interest rate is 12% compounded monthly. Thus, the effective interest rate (i) is 1%(0.1212) .

Challenger: The first cost (FC) is $210,000. The annual operating cost (AC) is $5,000. The salvage values for first year (SV1) is $100,000, second year (SV2) is $7,000, and third year (SV3) is $45,000. The interest rate is 12% compounded monthly. Thus, the effective interest rate (i) is 1%(0.1212).

The annual worth (AV) is calculated using the following formula:

AV=−FC(i(1+i)n(1+i)n−1)−AC+SVn(i(1+i)n−1) (1)

Substitute the respective values in Equation (1) to calculate the annual worth (AV) of defender in 12-month period.

AV=−160,000(0.01(1+0.01)12(1+0.01)12−1)−7,000+50,000(0.01(1+0.01)12−1)=−160,000(0.01(1.12683)1.12683−1)−7,000+50,000(0.011.12683−1)=−160,000(0.011270.12683)−7,000+50,000(0.010.12683)=−160,000(0.08885)−7,000+50,000(0.07885)=−14,216−7,000+3,942.5=−17,274

The annual worth of the defender for 12 months is -$17,2754.

Substitute the respective values in Equation (1) to calculate the annual worth (AV) of challenger in 12-month period.

AV=−210,000(0.01(1+0.01)12(1+0.01)12−1)−5,000+100,000(0.01(1+0.01)12−1)=−210,000(0.01(1.12683)1.12683−1)−5,000+100,000(0.011.12683−1)=−210,000(0.011270.12683)−5,000+100,000(0.010.12683)=−210,000(0.08885)−5,000+100,000(0.07885)=−18,658.5−5,000+7,885=−15,774

The annual worth of the challenger for 12 months is -$15,774.

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

(b):

To determine

Calculate the annual worth for 2 years.

(b):

Expert Solution

Explanation of Solution

Table 1 shows the annual worth of the defender and challenger for 2 years (24 months), which were obtained using Equation (1).

Table 1

Project	AV
Defender	-13,048
Challenger	-12,290

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

(c):

To determine

Calculate the annual worth for 3 years.

(c):

Expert Solution

Explanation of Solution

Table 1 shows the annual worth of the defender and challenger for 3 years (36 months), which were obtained using Equation (1).

Table 1

Project	AV
Defender	-14,292
Challenger	-10,349

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

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Answer 4

Question

Chapter 11, Problem 37P

(a):

To determine

Calculate the annual worth.

(a):

Expert Solution

Explanation of Solution

Defender: The first cost (FC) is $160,000. The annual operating cost (AC) is $7,000. The salvage value for the first year (SV1) is $50,000 and for the second year (SV2) is $40,000. The interest rate is 12% compounded monthly. Thus, the effective interest rate (i) is 1%(0.1212) .

Challenger: The first cost (FC) is $210,000. The annual operating cost (AC) is $5,000. The salvage values for first year (SV1) is $100,000, second year (SV2) is $7,000, and third year (SV3) is $45,000. The interest rate is 12% compounded monthly. Thus, the effective interest rate (i) is 1%(0.1212).

The annual worth (AV) is calculated using the following formula:

AV=−FC(i(1+i)n(1+i)n−1)−AC+SVn(i(1+i)n−1) (1)

Substitute the respective values in Equation (1) to calculate the annual worth (AV) of defender in 12-month period.

AV=−160,000(0.01(1+0.01)12(1+0.01)12−1)−7,000+50,000(0.01(1+0.01)12−1)=−160,000(0.01(1.12683)1.12683−1)−7,000+50,000(0.011.12683−1)=−160,000(0.011270.12683)−7,000+50,000(0.010.12683)=−160,000(0.08885)−7,000+50,000(0.07885)=−14,216−7,000+3,942.5=−17,274

The annual worth of the defender for 12 months is -$17,2754.

Substitute the respective values in Equation (1) to calculate the annual worth (AV) of challenger in 12-month period.

AV=−210,000(0.01(1+0.01)12(1+0.01)12−1)−5,000+100,000(0.01(1+0.01)12−1)=−210,000(0.01(1.12683)1.12683−1)−5,000+100,000(0.011.12683−1)=−210,000(0.011270.12683)−5,000+100,000(0.010.12683)=−210,000(0.08885)−5,000+100,000(0.07885)=−18,658.5−5,000+7,885=−15,774

The annual worth of the challenger for 12 months is -$15,774.

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

(b):

To determine

Calculate the annual worth for 2 years.

(b):

Expert Solution

Explanation of Solution

Table 1 shows the annual worth of the defender and challenger for 2 years (24 months), which were obtained using Equation (1).

Table 1

Project	AV
Defender	-13,048
Challenger	-12,290

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

(c):

To determine

Calculate the annual worth for 3 years.

(c):

Expert Solution

Explanation of Solution

Table 1 shows the annual worth of the defender and challenger for 3 years (36 months), which were obtained using Equation (1).

Table 1

Project	AV
Defender	-14,292
Challenger	-10,349

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

Want to see more full solutions like this?

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

Answer 5

Chapter 11, Problem 37P

(a):

To determine

Calculate the annual worth.

(a):

Expert Solution

Explanation of Solution

Defender: The first cost (FC) is $160,000. The annual operating cost (AC) is $7,000. The salvage value for the first year (SV1) is $50,000 and for the second year (SV2) is $40,000. The interest rate is 12% compounded monthly. Thus, the effective interest rate (i) is 1%(0.1212) .

Challenger: The first cost (FC) is $210,000. The annual operating cost (AC) is $5,000. The salvage values for first year (SV1) is $100,000, second year (SV2) is $7,000, and third year (SV3) is $45,000. The interest rate is 12% compounded monthly. Thus, the effective interest rate (i) is 1%(0.1212).

The annual worth (AV) is calculated using the following formula:

AV=−FC(i(1+i)n(1+i)n−1)−AC+SVn(i(1+i)n−1) (1)

Substitute the respective values in Equation (1) to calculate the annual worth (AV) of defender in 12-month period.

AV=−160,000(0.01(1+0.01)12(1+0.01)12−1)−7,000+50,000(0.01(1+0.01)12−1)=−160,000(0.01(1.12683)1.12683−1)−7,000+50,000(0.011.12683−1)=−160,000(0.011270.12683)−7,000+50,000(0.010.12683)=−160,000(0.08885)−7,000+50,000(0.07885)=−14,216−7,000+3,942.5=−17,274

The annual worth of the defender for 12 months is -$17,2754.

Substitute the respective values in Equation (1) to calculate the annual worth (AV) of challenger in 12-month period.

AV=−210,000(0.01(1+0.01)12(1+0.01)12−1)−5,000+100,000(0.01(1+0.01)12−1)=−210,000(0.01(1.12683)1.12683−1)−5,000+100,000(0.011.12683−1)=−210,000(0.011270.12683)−5,000+100,000(0.010.12683)=−210,000(0.08885)−5,000+100,000(0.07885)=−18,658.5−5,000+7,885=−15,774

The annual worth of the challenger for 12 months is -$15,774.

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

(b):

To determine

Calculate the annual worth for 2 years.

(b):

Expert Solution

Explanation of Solution

Table 1 shows the annual worth of the defender and challenger for 2 years (24 months), which were obtained using Equation (1).

Table 1

Project	AV
Defender	-13,048
Challenger	-12,290

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

(c):

To determine

Calculate the annual worth for 3 years.

(c):

Expert Solution

Explanation of Solution

Table 1 shows the annual worth of the defender and challenger for 3 years (36 months), which were obtained using Equation (1).

Table 1

Project	AV
Defender	-14,292
Challenger	-10,349

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

Answer 6

Chapter 11, Problem 37P

(a):

To determine

Calculate the annual worth.

(a):

Expert Solution

Explanation of Solution

Defender: The first cost (FC) is $160,000. The annual operating cost (AC) is $7,000. The salvage value for the first year (SV1) is $50,000 and for the second year (SV2) is $40,000. The interest rate is 12% compounded monthly. Thus, the effective interest rate (i) is 1%(0.1212) .

Challenger: The first cost (FC) is $210,000. The annual operating cost (AC) is $5,000. The salvage values for first year (SV1) is $100,000, second year (SV2) is $7,000, and third year (SV3) is $45,000. The interest rate is 12% compounded monthly. Thus, the effective interest rate (i) is 1%(0.1212).

The annual worth (AV) is calculated using the following formula:

AV=−FC(i(1+i)n(1+i)n−1)−AC+SVn(i(1+i)n−1) (1)

Substitute the respective values in Equation (1) to calculate the annual worth (AV) of defender in 12-month period.

AV=−160,000(0.01(1+0.01)12(1+0.01)12−1)−7,000+50,000(0.01(1+0.01)12−1)=−160,000(0.01(1.12683)1.12683−1)−7,000+50,000(0.011.12683−1)=−160,000(0.011270.12683)−7,000+50,000(0.010.12683)=−160,000(0.08885)−7,000+50,000(0.07885)=−14,216−7,000+3,942.5=−17,274

The annual worth of the defender for 12 months is -$17,2754.

Substitute the respective values in Equation (1) to calculate the annual worth (AV) of challenger in 12-month period.

AV=−210,000(0.01(1+0.01)12(1+0.01)12−1)−5,000+100,000(0.01(1+0.01)12−1)=−210,000(0.01(1.12683)1.12683−1)−5,000+100,000(0.011.12683−1)=−210,000(0.011270.12683)−5,000+100,000(0.010.12683)=−210,000(0.08885)−5,000+100,000(0.07885)=−18,658.5−5,000+7,885=−15,774

The annual worth of the challenger for 12 months is -$15,774.

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

Answer 7

Chapter 11, Problem 37P

(a):

To determine

Calculate the annual worth.

Answer 8

(a):

Expert Solution

Explanation of Solution

Defender: The first cost (FC) is $160,000. The annual operating cost (AC) is $7,000. The salvage value for the first year (SV1) is $50,000 and for the second year (SV2) is $40,000. The interest rate is 12% compounded monthly. Thus, the effective interest rate (i) is 1%(0.1212) .

Challenger: The first cost (FC) is $210,000. The annual operating cost (AC) is $5,000. The salvage values for first year (SV1) is $100,000, second year (SV2) is $7,000, and third year (SV3) is $45,000. The interest rate is 12% compounded monthly. Thus, the effective interest rate (i) is 1%(0.1212).

The annual worth (AV) is calculated using the following formula:

AV=−FC(i(1+i)n(1+i)n−1)−AC+SVn(i(1+i)n−1) (1)

Substitute the respective values in Equation (1) to calculate the annual worth (AV) of defender in 12-month period.

AV=−160,000(0.01(1+0.01)12(1+0.01)12−1)−7,000+50,000(0.01(1+0.01)12−1)=−160,000(0.01(1.12683)1.12683−1)−7,000+50,000(0.011.12683−1)=−160,000(0.011270.12683)−7,000+50,000(0.010.12683)=−160,000(0.08885)−7,000+50,000(0.07885)=−14,216−7,000+3,942.5=−17,274

The annual worth of the defender for 12 months is -$17,2754.

Substitute the respective values in Equation (1) to calculate the annual worth (AV) of challenger in 12-month period.

AV=−210,000(0.01(1+0.01)12(1+0.01)12−1)−5,000+100,000(0.01(1+0.01)12−1)=−210,000(0.01(1.12683)1.12683−1)−5,000+100,000(0.011.12683−1)=−210,000(0.011270.12683)−5,000+100,000(0.010.12683)=−210,000(0.08885)−5,000+100,000(0.07885)=−18,658.5−5,000+7,885=−15,774

The annual worth of the challenger for 12 months is -$15,774.

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

Answer 9

(a):

Expert Solution

Answer 10

(a):

Expert Solution

Answer 11

Expert Solution

Answer 12

(b):

To determine

Calculate the annual worth for 2 years.

(b):

Expert Solution

Explanation of Solution

Table 1 shows the annual worth of the defender and challenger for 2 years (24 months), which were obtained using Equation (1).

Table 1

Project	AV
Defender	-13,048
Challenger	-12,290

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

Answer 13

(b):

To determine

Calculate the annual worth for 2 years.

Answer 14

(b):

Expert Solution

Explanation of Solution

Table 1 shows the annual worth of the defender and challenger for 2 years (24 months), which were obtained using Equation (1).

Table 1

Project	AV
Defender	-13,048
Challenger	-12,290

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

Answer 15

(b):

Expert Solution

Answer 16

(b):

Expert Solution

Answer 17

Expert Solution

Answer 18

(c):

To determine

Calculate the annual worth for 3 years.

(c):

Expert Solution

Explanation of Solution

Table 1 shows the annual worth of the defender and challenger for 3 years (36 months), which were obtained using Equation (1).

Table 1

Project	AV
Defender	-14,292
Challenger	-10,349

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

Answer 19

(c):

To determine

Calculate the annual worth for 3 years.

Answer 20

(c):

Expert Solution

Explanation of Solution

Table 1 shows the annual worth of the defender and challenger for 3 years (36 months), which were obtained using Equation (1).

Table 1

Project	AV
Defender	-14,292
Challenger	-10,349

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

Answer 21

(c):

Expert Solution

Answer 22

(c):

Expert Solution

Answer 23

Expert Solution

Answer 24

Ch. 11 - Prob. 1P Ch. 11 - Prob. 2P Ch. 11 - Prob. 3P Ch. 11 - Prob. 4P Ch. 11 - Prob. 5P Ch. 11 - Prob. 6P Ch. 11 - Prob. 7P Ch. 11 - Prob. 8P Ch. 11 - Prob. 9P Ch. 11 - Prob. 10P

Calculate the annual worth.

Calculate the annual worth.

Explanation of Solution

Calculate the annual worth for 2 years.

Explanation of Solution

Calculate the annual worth for 3 years.

Explanation of Solution

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Chapter 11 Solutions