Calculate the annual worth.

Question

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Answer 1

Question

Chapter 11, Problem 33P

To determine

Calculate the annual worth.

Expert Solution & Answer

Explanation of Solution

Defender: At the beginning of each year, payment (BP) is $180,000. Time period (n) is 5. Interest (i) is 15%.

Challenger: Initial cost is $1,600,000. Annual operating cost (AC) is $58,000. Annual saving (AS) is $220,000. Salvage value (SV) is 30% to the initial cost. Thus, it is 480,000(1,600,000×0.3) Time period (n) is 5. Interest (i) is 15%.

Annual worth (AV) of the defender can be calculated as follows:

AV=(−BP−BP((1+n)n−1−1i(1+n)n−1))(i(1+i)n(1+i)n−1)=(−180,000−180,000((1+0.15)5−1−10.15(1+0.15)5−1))(0.15(1+0.15)5(1+0.15)5−1)=(−180,000−180,000(1.74901−10.15(1.74901)))(0.15(2.01136)(2.01136)−1)=(−180,000−180,000(0.749010.26235))(0.30171.01136)=(−180,000−513,900)(0.29831)=−206,997.31

The annual worth of the defender is -$206,997.31.

Annual worth (AV) of the challenger can be calculated as follows:

AV=−FC((1+n)n−1i(1+n)n)−AC+AS+SV(i(1+i)n−1)=−1,600,000(0.15(1+0.15)5(1+0.15)5−1)−58,000+220,000+480,000(0.15(1+0.15)5−1)=−1,600,000(0.15(2.01136)(2.01136)−1)−58,000+220,000+480,000(0.152.01136−1)=−1,600,000(0.30171.01136)−58,000+220,000+480,000(0.151.01136)=−1,600,000(0.29831)−58,000+220,000+480,000(0.14831)=−477,296−58,000+220,000+71,188.8=−244,107.2

The annual worth of the defender is -$244,107.2.

Since the annual cost of the defender is lower than challenger, retain the defender.

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Answer 2

Question

Chapter 11, Problem 33P

To determine

Calculate the annual worth.

Expert Solution & Answer

Explanation of Solution

Defender: At the beginning of each year, payment (BP) is $180,000. Time period (n) is 5. Interest (i) is 15%.

Challenger: Initial cost is $1,600,000. Annual operating cost (AC) is $58,000. Annual saving (AS) is $220,000. Salvage value (SV) is 30% to the initial cost. Thus, it is 480,000(1,600,000×0.3) Time period (n) is 5. Interest (i) is 15%.

Annual worth (AV) of the defender can be calculated as follows:

AV=(−BP−BP((1+n)n−1−1i(1+n)n−1))(i(1+i)n(1+i)n−1)=(−180,000−180,000((1+0.15)5−1−10.15(1+0.15)5−1))(0.15(1+0.15)5(1+0.15)5−1)=(−180,000−180,000(1.74901−10.15(1.74901)))(0.15(2.01136)(2.01136)−1)=(−180,000−180,000(0.749010.26235))(0.30171.01136)=(−180,000−513,900)(0.29831)=−206,997.31

The annual worth of the defender is -$206,997.31.

Annual worth (AV) of the challenger can be calculated as follows:

AV=−FC((1+n)n−1i(1+n)n)−AC+AS+SV(i(1+i)n−1)=−1,600,000(0.15(1+0.15)5(1+0.15)5−1)−58,000+220,000+480,000(0.15(1+0.15)5−1)=−1,600,000(0.15(2.01136)(2.01136)−1)−58,000+220,000+480,000(0.152.01136−1)=−1,600,000(0.30171.01136)−58,000+220,000+480,000(0.151.01136)=−1,600,000(0.29831)−58,000+220,000+480,000(0.14831)=−477,296−58,000+220,000+71,188.8=−244,107.2

The annual worth of the defender is -$244,107.2.

Since the annual cost of the defender is lower than challenger, retain the defender.

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Answer 3

Question

Chapter 11, Problem 33P

To determine

Calculate the annual worth.

Expert Solution & Answer

Explanation of Solution

Defender: At the beginning of each year, payment (BP) is $180,000. Time period (n) is 5. Interest (i) is 15%.

Challenger: Initial cost is $1,600,000. Annual operating cost (AC) is $58,000. Annual saving (AS) is $220,000. Salvage value (SV) is 30% to the initial cost. Thus, it is 480,000(1,600,000×0.3) Time period (n) is 5. Interest (i) is 15%.

Annual worth (AV) of the defender can be calculated as follows:

AV=(−BP−BP((1+n)n−1−1i(1+n)n−1))(i(1+i)n(1+i)n−1)=(−180,000−180,000((1+0.15)5−1−10.15(1+0.15)5−1))(0.15(1+0.15)5(1+0.15)5−1)=(−180,000−180,000(1.74901−10.15(1.74901)))(0.15(2.01136)(2.01136)−1)=(−180,000−180,000(0.749010.26235))(0.30171.01136)=(−180,000−513,900)(0.29831)=−206,997.31

The annual worth of the defender is -$206,997.31.

Annual worth (AV) of the challenger can be calculated as follows:

AV=−FC((1+n)n−1i(1+n)n)−AC+AS+SV(i(1+i)n−1)=−1,600,000(0.15(1+0.15)5(1+0.15)5−1)−58,000+220,000+480,000(0.15(1+0.15)5−1)=−1,600,000(0.15(2.01136)(2.01136)−1)−58,000+220,000+480,000(0.152.01136−1)=−1,600,000(0.30171.01136)−58,000+220,000+480,000(0.151.01136)=−1,600,000(0.29831)−58,000+220,000+480,000(0.14831)=−477,296−58,000+220,000+71,188.8=−244,107.2

The annual worth of the defender is -$244,107.2.

Since the annual cost of the defender is lower than challenger, retain the defender.

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Answer 4

Question

Chapter 11, Problem 33P

To determine

Calculate the annual worth.

Expert Solution & Answer

Explanation of Solution

Defender: At the beginning of each year, payment (BP) is $180,000. Time period (n) is 5. Interest (i) is 15%.

Challenger: Initial cost is $1,600,000. Annual operating cost (AC) is $58,000. Annual saving (AS) is $220,000. Salvage value (SV) is 30% to the initial cost. Thus, it is 480,000(1,600,000×0.3) Time period (n) is 5. Interest (i) is 15%.

Annual worth (AV) of the defender can be calculated as follows:

AV=(−BP−BP((1+n)n−1−1i(1+n)n−1))(i(1+i)n(1+i)n−1)=(−180,000−180,000((1+0.15)5−1−10.15(1+0.15)5−1))(0.15(1+0.15)5(1+0.15)5−1)=(−180,000−180,000(1.74901−10.15(1.74901)))(0.15(2.01136)(2.01136)−1)=(−180,000−180,000(0.749010.26235))(0.30171.01136)=(−180,000−513,900)(0.29831)=−206,997.31

The annual worth of the defender is -$206,997.31.

Annual worth (AV) of the challenger can be calculated as follows:

AV=−FC((1+n)n−1i(1+n)n)−AC+AS+SV(i(1+i)n−1)=−1,600,000(0.15(1+0.15)5(1+0.15)5−1)−58,000+220,000+480,000(0.15(1+0.15)5−1)=−1,600,000(0.15(2.01136)(2.01136)−1)−58,000+220,000+480,000(0.152.01136−1)=−1,600,000(0.30171.01136)−58,000+220,000+480,000(0.151.01136)=−1,600,000(0.29831)−58,000+220,000+480,000(0.14831)=−477,296−58,000+220,000+71,188.8=−244,107.2

The annual worth of the defender is -$244,107.2.

Since the annual cost of the defender is lower than challenger, retain the defender.

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Answer 5

Chapter 11, Problem 33P

To determine

Calculate the annual worth.

Expert Solution & Answer

Explanation of Solution

Defender: At the beginning of each year, payment (BP) is $180,000. Time period (n) is 5. Interest (i) is 15%.

Challenger: Initial cost is $1,600,000. Annual operating cost (AC) is $58,000. Annual saving (AS) is $220,000. Salvage value (SV) is 30% to the initial cost. Thus, it is 480,000(1,600,000×0.3) Time period (n) is 5. Interest (i) is 15%.

Annual worth (AV) of the defender can be calculated as follows:

AV=(−BP−BP((1+n)n−1−1i(1+n)n−1))(i(1+i)n(1+i)n−1)=(−180,000−180,000((1+0.15)5−1−10.15(1+0.15)5−1))(0.15(1+0.15)5(1+0.15)5−1)=(−180,000−180,000(1.74901−10.15(1.74901)))(0.15(2.01136)(2.01136)−1)=(−180,000−180,000(0.749010.26235))(0.30171.01136)=(−180,000−513,900)(0.29831)=−206,997.31

The annual worth of the defender is -$206,997.31.

Annual worth (AV) of the challenger can be calculated as follows:

AV=−FC((1+n)n−1i(1+n)n)−AC+AS+SV(i(1+i)n−1)=−1,600,000(0.15(1+0.15)5(1+0.15)5−1)−58,000+220,000+480,000(0.15(1+0.15)5−1)=−1,600,000(0.15(2.01136)(2.01136)−1)−58,000+220,000+480,000(0.152.01136−1)=−1,600,000(0.30171.01136)−58,000+220,000+480,000(0.151.01136)=−1,600,000(0.29831)−58,000+220,000+480,000(0.14831)=−477,296−58,000+220,000+71,188.8=−244,107.2

The annual worth of the defender is -$244,107.2.

Since the annual cost of the defender is lower than challenger, retain the defender.

Answer 6

Chapter 11, Problem 33P

To determine

Calculate the annual worth.

Expert Solution & Answer

Explanation of Solution

Defender: At the beginning of each year, payment (BP) is $180,000. Time period (n) is 5. Interest (i) is 15%.

Challenger: Initial cost is $1,600,000. Annual operating cost (AC) is $58,000. Annual saving (AS) is $220,000. Salvage value (SV) is 30% to the initial cost. Thus, it is 480,000(1,600,000×0.3) Time period (n) is 5. Interest (i) is 15%.

Annual worth (AV) of the defender can be calculated as follows:

AV=(−BP−BP((1+n)n−1−1i(1+n)n−1))(i(1+i)n(1+i)n−1)=(−180,000−180,000((1+0.15)5−1−10.15(1+0.15)5−1))(0.15(1+0.15)5(1+0.15)5−1)=(−180,000−180,000(1.74901−10.15(1.74901)))(0.15(2.01136)(2.01136)−1)=(−180,000−180,000(0.749010.26235))(0.30171.01136)=(−180,000−513,900)(0.29831)=−206,997.31

The annual worth of the defender is -$206,997.31.

Annual worth (AV) of the challenger can be calculated as follows:

AV=−FC((1+n)n−1i(1+n)n)−AC+AS+SV(i(1+i)n−1)=−1,600,000(0.15(1+0.15)5(1+0.15)5−1)−58,000+220,000+480,000(0.15(1+0.15)5−1)=−1,600,000(0.15(2.01136)(2.01136)−1)−58,000+220,000+480,000(0.152.01136−1)=−1,600,000(0.30171.01136)−58,000+220,000+480,000(0.151.01136)=−1,600,000(0.29831)−58,000+220,000+480,000(0.14831)=−477,296−58,000+220,000+71,188.8=−244,107.2

The annual worth of the defender is -$244,107.2.

Since the annual cost of the defender is lower than challenger, retain the defender.

Answer 7

Chapter 11, Problem 33P

To determine

Calculate the annual worth.

Answer 8

Expert Solution & Answer

Explanation of Solution

Defender: At the beginning of each year, payment (BP) is $180,000. Time period (n) is 5. Interest (i) is 15%.

Challenger: Initial cost is $1,600,000. Annual operating cost (AC) is $58,000. Annual saving (AS) is $220,000. Salvage value (SV) is 30% to the initial cost. Thus, it is 480,000(1,600,000×0.3) Time period (n) is 5. Interest (i) is 15%.

Annual worth (AV) of the defender can be calculated as follows:

AV=(−BP−BP((1+n)n−1−1i(1+n)n−1))(i(1+i)n(1+i)n−1)=(−180,000−180,000((1+0.15)5−1−10.15(1+0.15)5−1))(0.15(1+0.15)5(1+0.15)5−1)=(−180,000−180,000(1.74901−10.15(1.74901)))(0.15(2.01136)(2.01136)−1)=(−180,000−180,000(0.749010.26235))(0.30171.01136)=(−180,000−513,900)(0.29831)=−206,997.31

The annual worth of the defender is -$206,997.31.

Annual worth (AV) of the challenger can be calculated as follows:

AV=−FC((1+n)n−1i(1+n)n)−AC+AS+SV(i(1+i)n−1)=−1,600,000(0.15(1+0.15)5(1+0.15)5−1)−58,000+220,000+480,000(0.15(1+0.15)5−1)=−1,600,000(0.15(2.01136)(2.01136)−1)−58,000+220,000+480,000(0.152.01136−1)=−1,600,000(0.30171.01136)−58,000+220,000+480,000(0.151.01136)=−1,600,000(0.29831)−58,000+220,000+480,000(0.14831)=−477,296−58,000+220,000+71,188.8=−244,107.2