Calculate the equivalent annual value.

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Answer 1

Question

Chapter 4, Problem 63P

To determine

Calculate the equivalent annual value.

Expert Solution & Answer

Explanation of Solution

Equivalent cash flow (CF1) from year 1 to 3 is $5,000. Interest rate 1 (i1) is 10%. Time period 1 is 3 years. Cash flow (CF2) from year 4 to 5 is $7,000. Time period 2 (n2) is 5 years. Interest rate (i2) is 12%.

Present value (P) in year can be calculated as follows:

P=(CF1((1+i1)n1−1i1(1+i1)n1))+CF1((1+i2)n2−n1−1i2(1+i2)n2−n1)(1(1+i1)n1)=(5,000((1+0.1)3−10.1(1+0.1)3))+7,000((1+0.12)5−3−10.12(1+0.12)5−3)(1(1+0.1)3)=(5,000(1.331−10.1(1.331)))+7,000(1.2544−10.12(1.2544))(11.331)=(5,000(0.3310.1331))+7,000(0.25440.150528)(0.751315)=(5,000(2.486852))+7,000(1.690051)(0.751315)=12,434.26+8,888.32=21,322.58

Present value is $21,322.58.

Equivalent annual value (A) can be calculated as follows:

21,322.58=(A((1+i1)n1−1i1(1+i1)n1))+A((1+i2)n2−n1−1i2(1+i2)n2−n1)(1(1+i1)n1)21,322.58=(A((1+0.1)3−10.1(1+0.1)3))+A((1+0.12)5−3−10.12(1+0.12)5−3)(1(1+0.1)3)21,322.58=(A(1.331−10.1(1.331)))+A(1.2544−10.12(1.2544))(11.331)21,322.58=(A(0.3310.1331))+A(0.25440.150528)(0.751315)21,322.58=(A(2.486852))+A(1.690051)(0.751315)21,322.58=2.486852A+1.269761A21,322.58=3.756613AA=21,322.583.756613=5,676.01

Equivalent annual value is $5,6786.01.

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Answer 2

Question

Chapter 4, Problem 63P

To determine

Calculate the equivalent annual value.

Expert Solution & Answer

Explanation of Solution

Equivalent cash flow (CF1) from year 1 to 3 is $5,000. Interest rate 1 (i1) is 10%. Time period 1 is 3 years. Cash flow (CF2) from year 4 to 5 is $7,000. Time period 2 (n2) is 5 years. Interest rate (i2) is 12%.

Present value (P) in year can be calculated as follows:

P=(CF1((1+i1)n1−1i1(1+i1)n1))+CF1((1+i2)n2−n1−1i2(1+i2)n2−n1)(1(1+i1)n1)=(5,000((1+0.1)3−10.1(1+0.1)3))+7,000((1+0.12)5−3−10.12(1+0.12)5−3)(1(1+0.1)3)=(5,000(1.331−10.1(1.331)))+7,000(1.2544−10.12(1.2544))(11.331)=(5,000(0.3310.1331))+7,000(0.25440.150528)(0.751315)=(5,000(2.486852))+7,000(1.690051)(0.751315)=12,434.26+8,888.32=21,322.58

Present value is $21,322.58.

Equivalent annual value (A) can be calculated as follows:

21,322.58=(A((1+i1)n1−1i1(1+i1)n1))+A((1+i2)n2−n1−1i2(1+i2)n2−n1)(1(1+i1)n1)21,322.58=(A((1+0.1)3−10.1(1+0.1)3))+A((1+0.12)5−3−10.12(1+0.12)5−3)(1(1+0.1)3)21,322.58=(A(1.331−10.1(1.331)))+A(1.2544−10.12(1.2544))(11.331)21,322.58=(A(0.3310.1331))+A(0.25440.150528)(0.751315)21,322.58=(A(2.486852))+A(1.690051)(0.751315)21,322.58=2.486852A+1.269761A21,322.58=3.756613AA=21,322.583.756613=5,676.01

Equivalent annual value is $5,6786.01.

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Answer 3

Question

Chapter 4, Problem 63P

To determine

Calculate the equivalent annual value.

Expert Solution & Answer

Explanation of Solution

Equivalent cash flow (CF1) from year 1 to 3 is $5,000. Interest rate 1 (i1) is 10%. Time period 1 is 3 years. Cash flow (CF2) from year 4 to 5 is $7,000. Time period 2 (n2) is 5 years. Interest rate (i2) is 12%.

Present value (P) in year can be calculated as follows:

P=(CF1((1+i1)n1−1i1(1+i1)n1))+CF1((1+i2)n2−n1−1i2(1+i2)n2−n1)(1(1+i1)n1)=(5,000((1+0.1)3−10.1(1+0.1)3))+7,000((1+0.12)5−3−10.12(1+0.12)5−3)(1(1+0.1)3)=(5,000(1.331−10.1(1.331)))+7,000(1.2544−10.12(1.2544))(11.331)=(5,000(0.3310.1331))+7,000(0.25440.150528)(0.751315)=(5,000(2.486852))+7,000(1.690051)(0.751315)=12,434.26+8,888.32=21,322.58

Present value is $21,322.58.

Equivalent annual value (A) can be calculated as follows:

21,322.58=(A((1+i1)n1−1i1(1+i1)n1))+A((1+i2)n2−n1−1i2(1+i2)n2−n1)(1(1+i1)n1)21,322.58=(A((1+0.1)3−10.1(1+0.1)3))+A((1+0.12)5−3−10.12(1+0.12)5−3)(1(1+0.1)3)21,322.58=(A(1.331−10.1(1.331)))+A(1.2544−10.12(1.2544))(11.331)21,322.58=(A(0.3310.1331))+A(0.25440.150528)(0.751315)21,322.58=(A(2.486852))+A(1.690051)(0.751315)21,322.58=2.486852A+1.269761A21,322.58=3.756613AA=21,322.583.756613=5,676.01

Equivalent annual value is $5,6786.01.

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Answer 4

Question

Chapter 4, Problem 63P

To determine

Calculate the equivalent annual value.

Expert Solution & Answer

Explanation of Solution

Equivalent cash flow (CF1) from year 1 to 3 is $5,000. Interest rate 1 (i1) is 10%. Time period 1 is 3 years. Cash flow (CF2) from year 4 to 5 is $7,000. Time period 2 (n2) is 5 years. Interest rate (i2) is 12%.

Present value (P) in year can be calculated as follows:

P=(CF1((1+i1)n1−1i1(1+i1)n1))+CF1((1+i2)n2−n1−1i2(1+i2)n2−n1)(1(1+i1)n1)=(5,000((1+0.1)3−10.1(1+0.1)3))+7,000((1+0.12)5−3−10.12(1+0.12)5−3)(1(1+0.1)3)=(5,000(1.331−10.1(1.331)))+7,000(1.2544−10.12(1.2544))(11.331)=(5,000(0.3310.1331))+7,000(0.25440.150528)(0.751315)=(5,000(2.486852))+7,000(1.690051)(0.751315)=12,434.26+8,888.32=21,322.58

Present value is $21,322.58.

Equivalent annual value (A) can be calculated as follows:

21,322.58=(A((1+i1)n1−1i1(1+i1)n1))+A((1+i2)n2−n1−1i2(1+i2)n2−n1)(1(1+i1)n1)21,322.58=(A((1+0.1)3−10.1(1+0.1)3))+A((1+0.12)5−3−10.12(1+0.12)5−3)(1(1+0.1)3)21,322.58=(A(1.331−10.1(1.331)))+A(1.2544−10.12(1.2544))(11.331)21,322.58=(A(0.3310.1331))+A(0.25440.150528)(0.751315)21,322.58=(A(2.486852))+A(1.690051)(0.751315)21,322.58=2.486852A+1.269761A21,322.58=3.756613AA=21,322.583.756613=5,676.01

Equivalent annual value is $5,6786.01.

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Answer 5

Chapter 4, Problem 63P

To determine

Calculate the equivalent annual value.

Expert Solution & Answer

Explanation of Solution

Equivalent cash flow (CF1) from year 1 to 3 is $5,000. Interest rate 1 (i1) is 10%. Time period 1 is 3 years. Cash flow (CF2) from year 4 to 5 is $7,000. Time period 2 (n2) is 5 years. Interest rate (i2) is 12%.

Present value (P) in year can be calculated as follows:

P=(CF1((1+i1)n1−1i1(1+i1)n1))+CF1((1+i2)n2−n1−1i2(1+i2)n2−n1)(1(1+i1)n1)=(5,000((1+0.1)3−10.1(1+0.1)3))+7,000((1+0.12)5−3−10.12(1+0.12)5−3)(1(1+0.1)3)=(5,000(1.331−10.1(1.331)))+7,000(1.2544−10.12(1.2544))(11.331)=(5,000(0.3310.1331))+7,000(0.25440.150528)(0.751315)=(5,000(2.486852))+7,000(1.690051)(0.751315)=12,434.26+8,888.32=21,322.58

Present value is $21,322.58.

Equivalent annual value (A) can be calculated as follows:

21,322.58=(A((1+i1)n1−1i1(1+i1)n1))+A((1+i2)n2−n1−1i2(1+i2)n2−n1)(1(1+i1)n1)21,322.58=(A((1+0.1)3−10.1(1+0.1)3))+A((1+0.12)5−3−10.12(1+0.12)5−3)(1(1+0.1)3)21,322.58=(A(1.331−10.1(1.331)))+A(1.2544−10.12(1.2544))(11.331)21,322.58=(A(0.3310.1331))+A(0.25440.150528)(0.751315)21,322.58=(A(2.486852))+A(1.690051)(0.751315)21,322.58=2.486852A+1.269761A21,322.58=3.756613AA=21,322.583.756613=5,676.01

Equivalent annual value is $5,6786.01.

Answer 6

Chapter 4, Problem 63P

To determine

Calculate the equivalent annual value.

Expert Solution & Answer

Explanation of Solution

Equivalent cash flow (CF1) from year 1 to 3 is $5,000. Interest rate 1 (i1) is 10%. Time period 1 is 3 years. Cash flow (CF2) from year 4 to 5 is $7,000. Time period 2 (n2) is 5 years. Interest rate (i2) is 12%.

Present value (P) in year can be calculated as follows:

P=(CF1((1+i1)n1−1i1(1+i1)n1))+CF1((1+i2)n2−n1−1i2(1+i2)n2−n1)(1(1+i1)n1)=(5,000((1+0.1)3−10.1(1+0.1)3))+7,000((1+0.12)5−3−10.12(1+0.12)5−3)(1(1+0.1)3)=(5,000(1.331−10.1(1.331)))+7,000(1.2544−10.12(1.2544))(11.331)=(5,000(0.3310.1331))+7,000(0.25440.150528)(0.751315)=(5,000(2.486852))+7,000(1.690051)(0.751315)=12,434.26+8,888.32=21,322.58

Present value is $21,322.58.

Equivalent annual value (A) can be calculated as follows:

21,322.58=(A((1+i1)n1−1i1(1+i1)n1))+A((1+i2)n2−n1−1i2(1+i2)n2−n1)(1(1+i1)n1)21,322.58=(A((1+0.1)3−10.1(1+0.1)3))+A((1+0.12)5−3−10.12(1+0.12)5−3)(1(1+0.1)3)21,322.58=(A(1.331−10.1(1.331)))+A(1.2544−10.12(1.2544))(11.331)21,322.58=(A(0.3310.1331))+A(0.25440.150528)(0.751315)21,322.58=(A(2.486852))+A(1.690051)(0.751315)21,322.58=2.486852A+1.269761A21,322.58=3.756613AA=21,322.583.756613=5,676.01

Equivalent annual value is $5,6786.01.

Answer 7

Chapter 4, Problem 63P

To determine

Calculate the equivalent annual value.

Answer 8

Expert Solution & Answer

Explanation of Solution

Equivalent cash flow (CF1) from year 1 to 3 is $5,000. Interest rate 1 (i1) is 10%. Time period 1 is 3 years. Cash flow (CF2) from year 4 to 5 is $7,000. Time period 2 (n2) is 5 years. Interest rate (i2) is 12%.

Present value (P) in year can be calculated as follows:

P=(CF1((1+i1)n1−1i1(1+i1)n1))+CF1((1+i2)n2−n1−1i2(1+i2)n2−n1)(1(1+i1)n1)=(5,000((1+0.1)3−10.1(1+0.1)3))+7,000((1+0.12)5−3−10.12(1+0.12)5−3)(1(1+0.1)3)=(5,000(1.331−10.1(1.331)))+7,000(1.2544−10.12(1.2544))(11.331)=(5,000(0.3310.1331))+7,000(0.25440.150528)(0.751315)=(5,000(2.486852))+7,000(1.690051)(0.751315)=12,434.26+8,888.32=21,322.58

Present value is $21,322.58.

Equivalent annual value (A) can be calculated as follows:

21,322.58=(A((1+i1)n1−1i1(1+i1)n1))+A((1+i2)n2−n1−1i2(1+i2)n2−n1)(1(1+i1)n1)21,322.58=(A((1+0.1)3−10.1(1+0.1)3))+A((1+0.12)5−3−10.12(1+0.12)5−3)(1(1+0.1)3)21,322.58=(A(1.331−10.1(1.331)))+A(1.2544−10.12(1.2544))(11.331)21,322.58=(A(0.3310.1331))+A(0.25440.150528)(0.751315)21,322.58=(A(2.486852))+A(1.690051)(0.751315)21,322.58=2.486852A+1.269761A21,322.58=3.756613AA=21,322.583.756613=5,676.01