Calculate the annual worth.

Question

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Answer 1

Question

Chapter 11, Problem 26P

(a):

To determine

Calculate the annual worth.

(a):

Expert Solution

Explanation of Solution

Defender: Market value (MV) is $7,000. Upgrade cost (UC) is $22,000. Annual operating cost (AC) is $27,000. Salvage value (SV) is $21,000. Time period (n) is 3. Interest rate (i) is 10%.

Challenger: First cost (FC) is $65,000. Annual operating cost (AC) is $14,000. Salvage value (SV) is $123,000. Time period (n) is 3. Interest rate (i) is 10%.

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

AV=−(MV+UC)(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−(7,000+22,000)(0.1(1+0.1)3(1+0.1)3−1)−27,000+12,000(0.1(1+0.1)3−1)=−29,000(0.1(1.331)1.331−1)−27,000+12,000(0.11.331−1)=−29,000(0.13310.331)−27,000+12,000(0.10.331)=−29,000(0.402115)−27,000+12,000(0.302115)=−11,661.34−27,000+3,625.38=−35,035.96

The annual worth of the defender is -$35,035.96.

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

AV=−FC(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−65,000(0.1(1+0.1)3(1+0.1)3−1)−14,000+23,000(0.1(1+0.1)3−1)=−65,000(0.1(1.331)1.331−1)−14,000+23,000(0.11.331−1)=−65,000(0.13310.331)−14,000+23,000(0.10.331)=−65,000(0.402115)−14,000+23,000(0.302115)=−26,137.48−14,000+6,948.65=−33,188.83

The annual worth of the challenger is -$33,188.83. Since the annual worth of cost for challenger is lesser than the defender, replace the defender with the challenger.

(b):

To determine

Calculate the annual worth for 2 year.

(b):

Expert Solution

Explanation of Solution

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

AV=−FC(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−65,000(0.1(1+0.1)2(1+0.1)2−1)−14,000+23,000(0.1(1+0.1)2−1)=−65,000(0.1(1.21)1.21−1)−14,000+23,000(0.11.21−1)=−65,000(0.1210.21)−14,000+23,000(0.10.21)=−65,000(0.57619)−14,000+23,000(0.47619)=−37,452.35−14,000+10,952.37=−40,499.98

The annual worth of the challenger is -$40,499.98. Since the annual worth of 2 year cost for challenger is greater than the defender for 3 year cost, retain the defender.

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Answer 2

Question

Chapter 11, Problem 26P

(a):

To determine

Calculate the annual worth.

(a):

Expert Solution

Explanation of Solution

Defender: Market value (MV) is $7,000. Upgrade cost (UC) is $22,000. Annual operating cost (AC) is $27,000. Salvage value (SV) is $21,000. Time period (n) is 3. Interest rate (i) is 10%.

Challenger: First cost (FC) is $65,000. Annual operating cost (AC) is $14,000. Salvage value (SV) is $123,000. Time period (n) is 3. Interest rate (i) is 10%.

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

AV=−(MV+UC)(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−(7,000+22,000)(0.1(1+0.1)3(1+0.1)3−1)−27,000+12,000(0.1(1+0.1)3−1)=−29,000(0.1(1.331)1.331−1)−27,000+12,000(0.11.331−1)=−29,000(0.13310.331)−27,000+12,000(0.10.331)=−29,000(0.402115)−27,000+12,000(0.302115)=−11,661.34−27,000+3,625.38=−35,035.96

The annual worth of the defender is -$35,035.96.

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

AV=−FC(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−65,000(0.1(1+0.1)3(1+0.1)3−1)−14,000+23,000(0.1(1+0.1)3−1)=−65,000(0.1(1.331)1.331−1)−14,000+23,000(0.11.331−1)=−65,000(0.13310.331)−14,000+23,000(0.10.331)=−65,000(0.402115)−14,000+23,000(0.302115)=−26,137.48−14,000+6,948.65=−33,188.83

The annual worth of the challenger is -$33,188.83. Since the annual worth of cost for challenger is lesser than the defender, replace the defender with the challenger.

(b):

To determine

Calculate the annual worth for 2 year.

(b):

Expert Solution

Explanation of Solution

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

AV=−FC(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−65,000(0.1(1+0.1)2(1+0.1)2−1)−14,000+23,000(0.1(1+0.1)2−1)=−65,000(0.1(1.21)1.21−1)−14,000+23,000(0.11.21−1)=−65,000(0.1210.21)−14,000+23,000(0.10.21)=−65,000(0.57619)−14,000+23,000(0.47619)=−37,452.35−14,000+10,952.37=−40,499.98

The annual worth of the challenger is -$40,499.98. Since the annual worth of 2 year cost for challenger is greater than the defender for 3 year cost, retain the defender.

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Answer 3

Question

Chapter 11, Problem 26P

(a):

To determine

Calculate the annual worth.

(a):

Expert Solution

Explanation of Solution

Defender: Market value (MV) is $7,000. Upgrade cost (UC) is $22,000. Annual operating cost (AC) is $27,000. Salvage value (SV) is $21,000. Time period (n) is 3. Interest rate (i) is 10%.

Challenger: First cost (FC) is $65,000. Annual operating cost (AC) is $14,000. Salvage value (SV) is $123,000. Time period (n) is 3. Interest rate (i) is 10%.

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

AV=−(MV+UC)(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−(7,000+22,000)(0.1(1+0.1)3(1+0.1)3−1)−27,000+12,000(0.1(1+0.1)3−1)=−29,000(0.1(1.331)1.331−1)−27,000+12,000(0.11.331−1)=−29,000(0.13310.331)−27,000+12,000(0.10.331)=−29,000(0.402115)−27,000+12,000(0.302115)=−11,661.34−27,000+3,625.38=−35,035.96

The annual worth of the defender is -$35,035.96.

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

AV=−FC(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−65,000(0.1(1+0.1)3(1+0.1)3−1)−14,000+23,000(0.1(1+0.1)3−1)=−65,000(0.1(1.331)1.331−1)−14,000+23,000(0.11.331−1)=−65,000(0.13310.331)−14,000+23,000(0.10.331)=−65,000(0.402115)−14,000+23,000(0.302115)=−26,137.48−14,000+6,948.65=−33,188.83

The annual worth of the challenger is -$33,188.83. Since the annual worth of cost for challenger is lesser than the defender, replace the defender with the challenger.

(b):

To determine

Calculate the annual worth for 2 year.

(b):

Expert Solution

Explanation of Solution

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

AV=−FC(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−65,000(0.1(1+0.1)2(1+0.1)2−1)−14,000+23,000(0.1(1+0.1)2−1)=−65,000(0.1(1.21)1.21−1)−14,000+23,000(0.11.21−1)=−65,000(0.1210.21)−14,000+23,000(0.10.21)=−65,000(0.57619)−14,000+23,000(0.47619)=−37,452.35−14,000+10,952.37=−40,499.98

The annual worth of the challenger is -$40,499.98. Since the annual worth of 2 year cost for challenger is greater than the defender for 3 year cost, retain the defender.

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Answer 4

Question

Chapter 11, Problem 26P

(a):

To determine

Calculate the annual worth.

(a):

Expert Solution

Explanation of Solution

Defender: Market value (MV) is $7,000. Upgrade cost (UC) is $22,000. Annual operating cost (AC) is $27,000. Salvage value (SV) is $21,000. Time period (n) is 3. Interest rate (i) is 10%.

Challenger: First cost (FC) is $65,000. Annual operating cost (AC) is $14,000. Salvage value (SV) is $123,000. Time period (n) is 3. Interest rate (i) is 10%.

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

AV=−(MV+UC)(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−(7,000+22,000)(0.1(1+0.1)3(1+0.1)3−1)−27,000+12,000(0.1(1+0.1)3−1)=−29,000(0.1(1.331)1.331−1)−27,000+12,000(0.11.331−1)=−29,000(0.13310.331)−27,000+12,000(0.10.331)=−29,000(0.402115)−27,000+12,000(0.302115)=−11,661.34−27,000+3,625.38=−35,035.96

The annual worth of the defender is -$35,035.96.

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

AV=−FC(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−65,000(0.1(1+0.1)3(1+0.1)3−1)−14,000+23,000(0.1(1+0.1)3−1)=−65,000(0.1(1.331)1.331−1)−14,000+23,000(0.11.331−1)=−65,000(0.13310.331)−14,000+23,000(0.10.331)=−65,000(0.402115)−14,000+23,000(0.302115)=−26,137.48−14,000+6,948.65=−33,188.83

The annual worth of the challenger is -$33,188.83. Since the annual worth of cost for challenger is lesser than the defender, replace the defender with the challenger.

(b):

To determine

Calculate the annual worth for 2 year.

(b):

Expert Solution

Explanation of Solution

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

AV=−FC(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−65,000(0.1(1+0.1)2(1+0.1)2−1)−14,000+23,000(0.1(1+0.1)2−1)=−65,000(0.1(1.21)1.21−1)−14,000+23,000(0.11.21−1)=−65,000(0.1210.21)−14,000+23,000(0.10.21)=−65,000(0.57619)−14,000+23,000(0.47619)=−37,452.35−14,000+10,952.37=−40,499.98

The annual worth of the challenger is -$40,499.98. Since the annual worth of 2 year cost for challenger is greater than the defender for 3 year cost, retain the defender.

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Answer 5

Chapter 11, Problem 26P

(a):

To determine

Calculate the annual worth.

(a):

Expert Solution

Explanation of Solution

Defender: Market value (MV) is $7,000. Upgrade cost (UC) is $22,000. Annual operating cost (AC) is $27,000. Salvage value (SV) is $21,000. Time period (n) is 3. Interest rate (i) is 10%.

Challenger: First cost (FC) is $65,000. Annual operating cost (AC) is $14,000. Salvage value (SV) is $123,000. Time period (n) is 3. Interest rate (i) is 10%.

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

AV=−(MV+UC)(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−(7,000+22,000)(0.1(1+0.1)3(1+0.1)3−1)−27,000+12,000(0.1(1+0.1)3−1)=−29,000(0.1(1.331)1.331−1)−27,000+12,000(0.11.331−1)=−29,000(0.13310.331)−27,000+12,000(0.10.331)=−29,000(0.402115)−27,000+12,000(0.302115)=−11,661.34−27,000+3,625.38=−35,035.96

The annual worth of the defender is -$35,035.96.

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

AV=−FC(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−65,000(0.1(1+0.1)3(1+0.1)3−1)−14,000+23,000(0.1(1+0.1)3−1)=−65,000(0.1(1.331)1.331−1)−14,000+23,000(0.11.331−1)=−65,000(0.13310.331)−14,000+23,000(0.10.331)=−65,000(0.402115)−14,000+23,000(0.302115)=−26,137.48−14,000+6,948.65=−33,188.83

The annual worth of the challenger is -$33,188.83. Since the annual worth of cost for challenger is lesser than the defender, replace the defender with the challenger.

(b):

To determine

Calculate the annual worth for 2 year.

(b):

Expert Solution

Explanation of Solution

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

AV=−FC(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−65,000(0.1(1+0.1)2(1+0.1)2−1)−14,000+23,000(0.1(1+0.1)2−1)=−65,000(0.1(1.21)1.21−1)−14,000+23,000(0.11.21−1)=−65,000(0.1210.21)−14,000+23,000(0.10.21)=−65,000(0.57619)−14,000+23,000(0.47619)=−37,452.35−14,000+10,952.37=−40,499.98

The annual worth of the challenger is -$40,499.98. Since the annual worth of 2 year cost for challenger is greater than the defender for 3 year cost, retain the defender.

Answer 6

Chapter 11, Problem 26P

(a):

To determine

Calculate the annual worth.

(a):

Expert Solution

Explanation of Solution

Defender: Market value (MV) is $7,000. Upgrade cost (UC) is $22,000. Annual operating cost (AC) is $27,000. Salvage value (SV) is $21,000. Time period (n) is 3. Interest rate (i) is 10%.

Challenger: First cost (FC) is $65,000. Annual operating cost (AC) is $14,000. Salvage value (SV) is $123,000. Time period (n) is 3. Interest rate (i) is 10%.

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

AV=−(MV+UC)(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−(7,000+22,000)(0.1(1+0.1)3(1+0.1)3−1)−27,000+12,000(0.1(1+0.1)3−1)=−29,000(0.1(1.331)1.331−1)−27,000+12,000(0.11.331−1)=−29,000(0.13310.331)−27,000+12,000(0.10.331)=−29,000(0.402115)−27,000+12,000(0.302115)=−11,661.34−27,000+3,625.38=−35,035.96

The annual worth of the defender is -$35,035.96.

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

AV=−FC(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−65,000(0.1(1+0.1)3(1+0.1)3−1)−14,000+23,000(0.1(1+0.1)3−1)=−65,000(0.1(1.331)1.331−1)−14,000+23,000(0.11.331−1)=−65,000(0.13310.331)−14,000+23,000(0.10.331)=−65,000(0.402115)−14,000+23,000(0.302115)=−26,137.48−14,000+6,948.65=−33,188.83

The annual worth of the challenger is -$33,188.83. Since the annual worth of cost for challenger is lesser than the defender, replace the defender with the challenger.

Answer 7

Chapter 11, Problem 26P

(a):

To determine

Calculate the annual worth.

Answer 8

(a):

Expert Solution

Explanation of Solution

Defender: Market value (MV) is $7,000. Upgrade cost (UC) is $22,000. Annual operating cost (AC) is $27,000. Salvage value (SV) is $21,000. Time period (n) is 3. Interest rate (i) is 10%.

Challenger: First cost (FC) is $65,000. Annual operating cost (AC) is $14,000. Salvage value (SV) is $123,000. Time period (n) is 3. Interest rate (i) is 10%.

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

AV=−(MV+UC)(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−(7,000+22,000)(0.1(1+0.1)3(1+0.1)3−1)−27,000+12,000(0.1(1+0.1)3−1)=−29,000(0.1(1.331)1.331−1)−27,000+12,000(0.11.331−1)=−29,000(0.13310.331)−27,000+12,000(0.10.331)=−29,000(0.402115)−27,000+12,000(0.302115)=−11,661.34−27,000+3,625.38=−35,035.96

The annual worth of the defender is -$35,035.96.

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

AV=−FC(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−65,000(0.1(1+0.1)3(1+0.1)3−1)−14,000+23,000(0.1(1+0.1)3−1)=−65,000(0.1(1.331)1.331−1)−14,000+23,000(0.11.331−1)=−65,000(0.13310.331)−14,000+23,000(0.10.331)=−65,000(0.402115)−14,000+23,000(0.302115)=−26,137.48−14,000+6,948.65=−33,188.83

The annual worth of the challenger is -$33,188.83. Since the annual worth of cost for challenger is lesser than the defender, replace the defender with the 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 year.

(b):

Expert Solution

Explanation of Solution

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

AV=−FC(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−65,000(0.1(1+0.1)2(1+0.1)2−1)−14,000+23,000(0.1(1+0.1)2−1)=−65,000(0.1(1.21)1.21−1)−14,000+23,000(0.11.21−1)=−65,000(0.1210.21)−14,000+23,000(0.10.21)=−65,000(0.57619)−14,000+23,000(0.47619)=−37,452.35−14,000+10,952.37=−40,499.98

The annual worth of the challenger is -$40,499.98. Since the annual worth of 2 year cost for challenger is greater than the defender for 3 year cost, retain the defender.

Answer 13

(b):

To determine

Calculate the annual worth for 2 year.

Answer 14

(b):

Expert Solution

Explanation of Solution

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

AV=−FC(i(1+i)n(1+i)n−1)−AC+SV(i(1+i)n−1)=−65,000(0.1(1+0.1)2(1+0.1)2−1)−14,000+23,000(0.1(1+0.1)2−1)=−65,000(0.1(1.21)1.21−1)−14,000+23,000(0.11.21−1)=−65,000(0.1210.21)−14,000+23,000(0.10.21)=−65,000(0.57619)−14,000+23,000(0.47619)=−37,452.35−14,000+10,952.37=−40,499.98

The annual worth of the challenger is -$40,499.98. Since the annual worth of 2 year cost for challenger is greater than the defender for 3 year cost, retain the defender.