Benefit–cost ratio.

Question

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Answer 1

Question

Chapter 9, Problem 70APQ

To determine

Benefit–cost ratio.

Expert Solution & Answer

Explanation of Solution

Benefit (B) is $10,000 per year forever. Cost (C1) is $50,000 at year zero and (C2) $50,000 at the end of year (n) 2. Interest rate (i) is 10%.

Option (b):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.1=10,0000.1(50,000+(50,000(1+0.1)2))1.1=100,000(50,000+(50,0001.21))1.1=100,000(50,000+41,322.31)1.1=100,000(91,322.31)1.1≈1.095

The calculated BC value is nearly equal to the given value. Thus, option ‘b’ is correct.

Option (a):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))0.93=10,0000.1(50,000+(50,000(1+0.1)2))0.93=100,000(50,000+(50,0001.21))0.93=100,000(50,000+41,322.31)0.93=100,000(91,322.31)0.93<1.095

The calculated BC value is greater than the given value. Thus, option ‘a’ is incorrect.

Option (c):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.24=10,0000.1(50,000+(50,000(1+0.1)2))1.24=100,000(50,000+(50,0001.21))1.24=100,000(50,000+41,322.31)1.24=100,000(91,322.31)1.24>1.095

The calculated BC value is less than the given value. Thus, option ‘c’ is incorrect.

Option (d):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.73=10,0000.1(50,000+(50,000(1+0.1)2))1.73=100,000(50,000+(50,0001.21))1.73=100,000(50,000+41,322.31)1.73=100,000(91,322.31)1.73>1.095

The calculated BC value is less than the given value. Thus, option ‘d’ is incorrect.

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Answer 2

Question

Chapter 9, Problem 70APQ

To determine

Benefit–cost ratio.

Expert Solution & Answer

Explanation of Solution

Benefit (B) is $10,000 per year forever. Cost (C1) is $50,000 at year zero and (C2) $50,000 at the end of year (n) 2. Interest rate (i) is 10%.

Option (b):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.1=10,0000.1(50,000+(50,000(1+0.1)2))1.1=100,000(50,000+(50,0001.21))1.1=100,000(50,000+41,322.31)1.1=100,000(91,322.31)1.1≈1.095

The calculated BC value is nearly equal to the given value. Thus, option ‘b’ is correct.

Option (a):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))0.93=10,0000.1(50,000+(50,000(1+0.1)2))0.93=100,000(50,000+(50,0001.21))0.93=100,000(50,000+41,322.31)0.93=100,000(91,322.31)0.93<1.095

The calculated BC value is greater than the given value. Thus, option ‘a’ is incorrect.

Option (c):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.24=10,0000.1(50,000+(50,000(1+0.1)2))1.24=100,000(50,000+(50,0001.21))1.24=100,000(50,000+41,322.31)1.24=100,000(91,322.31)1.24>1.095

The calculated BC value is less than the given value. Thus, option ‘c’ is incorrect.

Option (d):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.73=10,0000.1(50,000+(50,000(1+0.1)2))1.73=100,000(50,000+(50,0001.21))1.73=100,000(50,000+41,322.31)1.73=100,000(91,322.31)1.73>1.095

The calculated BC value is less than the given value. Thus, option ‘d’ is incorrect.

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Answer 3

Question

Chapter 9, Problem 70APQ

To determine

Benefit–cost ratio.

Expert Solution & Answer

Explanation of Solution

Benefit (B) is $10,000 per year forever. Cost (C1) is $50,000 at year zero and (C2) $50,000 at the end of year (n) 2. Interest rate (i) is 10%.

Option (b):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.1=10,0000.1(50,000+(50,000(1+0.1)2))1.1=100,000(50,000+(50,0001.21))1.1=100,000(50,000+41,322.31)1.1=100,000(91,322.31)1.1≈1.095

The calculated BC value is nearly equal to the given value. Thus, option ‘b’ is correct.

Option (a):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))0.93=10,0000.1(50,000+(50,000(1+0.1)2))0.93=100,000(50,000+(50,0001.21))0.93=100,000(50,000+41,322.31)0.93=100,000(91,322.31)0.93<1.095

The calculated BC value is greater than the given value. Thus, option ‘a’ is incorrect.

Option (c):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.24=10,0000.1(50,000+(50,000(1+0.1)2))1.24=100,000(50,000+(50,0001.21))1.24=100,000(50,000+41,322.31)1.24=100,000(91,322.31)1.24>1.095

The calculated BC value is less than the given value. Thus, option ‘c’ is incorrect.

Option (d):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.73=10,0000.1(50,000+(50,000(1+0.1)2))1.73=100,000(50,000+(50,0001.21))1.73=100,000(50,000+41,322.31)1.73=100,000(91,322.31)1.73>1.095

The calculated BC value is less than the given value. Thus, option ‘d’ is incorrect.

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Answer 4

Question

Chapter 9, Problem 70APQ

To determine

Benefit–cost ratio.

Expert Solution & Answer

Explanation of Solution

Benefit (B) is $10,000 per year forever. Cost (C1) is $50,000 at year zero and (C2) $50,000 at the end of year (n) 2. Interest rate (i) is 10%.

Option (b):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.1=10,0000.1(50,000+(50,000(1+0.1)2))1.1=100,000(50,000+(50,0001.21))1.1=100,000(50,000+41,322.31)1.1=100,000(91,322.31)1.1≈1.095

The calculated BC value is nearly equal to the given value. Thus, option ‘b’ is correct.

Option (a):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))0.93=10,0000.1(50,000+(50,000(1+0.1)2))0.93=100,000(50,000+(50,0001.21))0.93=100,000(50,000+41,322.31)0.93=100,000(91,322.31)0.93<1.095

The calculated BC value is greater than the given value. Thus, option ‘a’ is incorrect.

Option (c):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.24=10,0000.1(50,000+(50,000(1+0.1)2))1.24=100,000(50,000+(50,0001.21))1.24=100,000(50,000+41,322.31)1.24=100,000(91,322.31)1.24>1.095

The calculated BC value is less than the given value. Thus, option ‘c’ is incorrect.

Option (d):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.73=10,0000.1(50,000+(50,000(1+0.1)2))1.73=100,000(50,000+(50,0001.21))1.73=100,000(50,000+41,322.31)1.73=100,000(91,322.31)1.73>1.095

The calculated BC value is less than the given value. Thus, option ‘d’ is incorrect.

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Answer 5

Chapter 9, Problem 70APQ

To determine

Benefit–cost ratio.

Expert Solution & Answer

Explanation of Solution

Benefit (B) is $10,000 per year forever. Cost (C1) is $50,000 at year zero and (C2) $50,000 at the end of year (n) 2. Interest rate (i) is 10%.

Option (b):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.1=10,0000.1(50,000+(50,000(1+0.1)2))1.1=100,000(50,000+(50,0001.21))1.1=100,000(50,000+41,322.31)1.1=100,000(91,322.31)1.1≈1.095

The calculated BC value is nearly equal to the given value. Thus, option ‘b’ is correct.

Option (a):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))0.93=10,0000.1(50,000+(50,000(1+0.1)2))0.93=100,000(50,000+(50,0001.21))0.93=100,000(50,000+41,322.31)0.93=100,000(91,322.31)0.93<1.095

The calculated BC value is greater than the given value. Thus, option ‘a’ is incorrect.

Option (c):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.24=10,0000.1(50,000+(50,000(1+0.1)2))1.24=100,000(50,000+(50,0001.21))1.24=100,000(50,000+41,322.31)1.24=100,000(91,322.31)1.24>1.095

The calculated BC value is less than the given value. Thus, option ‘c’ is incorrect.

Option (d):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.73=10,0000.1(50,000+(50,000(1+0.1)2))1.73=100,000(50,000+(50,0001.21))1.73=100,000(50,000+41,322.31)1.73=100,000(91,322.31)1.73>1.095

The calculated BC value is less than the given value. Thus, option ‘d’ is incorrect.

Answer 6

Chapter 9, Problem 70APQ

To determine

Benefit–cost ratio.

Expert Solution & Answer

Explanation of Solution

Benefit (B) is $10,000 per year forever. Cost (C1) is $50,000 at year zero and (C2) $50,000 at the end of year (n) 2. Interest rate (i) is 10%.

Option (b):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.1=10,0000.1(50,000+(50,000(1+0.1)2))1.1=100,000(50,000+(50,0001.21))1.1=100,000(50,000+41,322.31)1.1=100,000(91,322.31)1.1≈1.095

The calculated BC value is nearly equal to the given value. Thus, option ‘b’ is correct.

Option (a):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))0.93=10,0000.1(50,000+(50,000(1+0.1)2))0.93=100,000(50,000+(50,0001.21))0.93=100,000(50,000+41,322.31)0.93=100,000(91,322.31)0.93<1.095

The calculated BC value is greater than the given value. Thus, option ‘a’ is incorrect.

Option (c):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.24=10,0000.1(50,000+(50,000(1+0.1)2))1.24=100,000(50,000+(50,0001.21))1.24=100,000(50,000+41,322.31)1.24=100,000(91,322.31)1.24>1.095

The calculated BC value is less than the given value. Thus, option ‘c’ is incorrect.

Option (d):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.73=10,0000.1(50,000+(50,000(1+0.1)2))1.73=100,000(50,000+(50,0001.21))1.73=100,000(50,000+41,322.31)1.73=100,000(91,322.31)1.73>1.095

The calculated BC value is less than the given value. Thus, option ‘d’ is incorrect.

Answer 7

Chapter 9, Problem 70APQ

To determine

Benefit–cost ratio.

Answer 8

Expert Solution & Answer

Explanation of Solution

Benefit (B) is $10,000 per year forever. Cost (C1) is $50,000 at year zero and (C2) $50,000 at the end of year (n) 2. Interest rate (i) is 10%.

Option (b):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.1=10,0000.1(50,000+(50,000(1+0.1)2))1.1=100,000(50,000+(50,0001.21))1.1=100,000(50,000+41,322.31)1.1=100,000(91,322.31)1.1≈1.095

The calculated BC value is nearly equal to the given value. Thus, option ‘b’ is correct.

Option (a):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))0.93=10,0000.1(50,000+(50,000(1+0.1)2))0.93=100,000(50,000+(50,0001.21))0.93=100,000(50,000+41,322.31)0.93=100,000(91,322.31)0.93<1.095

The calculated BC value is greater than the given value. Thus, option ‘a’ is incorrect.

Option (c):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.24=10,0000.1(50,000+(50,000(1+0.1)2))1.24=100,000(50,000+(50,0001.21))1.24=100,000(50,000+41,322.31)1.24=100,000(91,322.31)1.24>1.095

The calculated BC value is less than the given value. Thus, option ‘c’ is incorrect.

Option (d):

The benefit–cost ratio (BC) can be calculated as follows:

BC=Bi(C1+(C2(1+i)n))1.73=10,0000.1(50,000+(50,000(1+0.1)2))1.73=100,000(50,000+(50,0001.21))1.73=100,000(50,000+41,322.31)1.73=100,000(91,322.31)1.73>1.095