Calculate the present, future, and equivalent annual value.

Question

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Answer 1

Question

Chapter 4, Problem 61P

To determine

Calculate the present, future, and equivalent annual value.

Expert Solution & Answer

Explanation of Solution

Equivalent cash flow (CF1) from year 1 to 5 is -$100. Time period 1 (n1) is 5. Interest rate 1 (i1) is 14%. Equivalent cash flow (CF2) from year 6 to 8 is -$160. Interest rate 2 (i2) is 10%. Time period 2 (n2) is 3.

Present value (P) can be calculated as follows:

P=CF1((1+i1)n1−1i1(1+i1)n1)+CF2((1+i2)n2−1(1+i2)n2i2)(1(1+i1)n1)=−100((1+0.14)5−1(1+0.14)50.14)+(−160)((1+0.1)3−10.1(1+0.1)3)(1(1+0.14)5)=−100(1.925415−10.14(1.925415))+(−160)(1.331−10.1(1.331))(11.925145)=−100(0.9254150.269558)+(−160)(0.3310.1331)(0.5194)=−100(3.4331)+(−160)(2.4869)(0.5194)=−343.31−206.67=−549.98

Present value is -$549.98.

Future value (F) can be calculated as follows:

F=CF1((1+i1)n1−1i1)(1+i2)n2+CF2((1+i2)n2−1i2)=−100((1+0.14)5−10.14)(1+0.1)3+(−160)((1+0.1)3−10.1)=−100(1.925415−10.14)(1.331)+(−160)(1.331−10.1)=−100(0.9254150.14)(1.331)+(−160)(0.3310.1)=−100(6.6101)(1.331)+(−160)(3.31)=−879.8−529.6=−1,409.4

Future value is -$1,409.4.

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

F=A((1+i1)n1−1i1)(1+i2)n2+A((1+i2)n2−1i2)−1,409.4=A((1+0.14)5−10.14)(1+0.1)3+A((1+0.1)3−10.1)−1,409.4=A(1.925415−10.14)(1.331)+A(1.331−10.1)−1,409.4=A(0.9254150.14)(1.331)+A(0.3310.1)−1,409.4=A(6.6101)(1.331)+A(3.31)−1,409.4=8.798A+3.31A12.108A=−1,409.4A=−1,409.412.108=−116.4

Equivalent annual value is -$116.4.

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Answer 2

Question

Chapter 4, Problem 61P

To determine

Calculate the present, future, and equivalent annual value.

Expert Solution & Answer

Explanation of Solution

Equivalent cash flow (CF1) from year 1 to 5 is -$100. Time period 1 (n1) is 5. Interest rate 1 (i1) is 14%. Equivalent cash flow (CF2) from year 6 to 8 is -$160. Interest rate 2 (i2) is 10%. Time period 2 (n2) is 3.

Present value (P) can be calculated as follows:

P=CF1((1+i1)n1−1i1(1+i1)n1)+CF2((1+i2)n2−1(1+i2)n2i2)(1(1+i1)n1)=−100((1+0.14)5−1(1+0.14)50.14)+(−160)((1+0.1)3−10.1(1+0.1)3)(1(1+0.14)5)=−100(1.925415−10.14(1.925415))+(−160)(1.331−10.1(1.331))(11.925145)=−100(0.9254150.269558)+(−160)(0.3310.1331)(0.5194)=−100(3.4331)+(−160)(2.4869)(0.5194)=−343.31−206.67=−549.98

Present value is -$549.98.

Future value (F) can be calculated as follows:

F=CF1((1+i1)n1−1i1)(1+i2)n2+CF2((1+i2)n2−1i2)=−100((1+0.14)5−10.14)(1+0.1)3+(−160)((1+0.1)3−10.1)=−100(1.925415−10.14)(1.331)+(−160)(1.331−10.1)=−100(0.9254150.14)(1.331)+(−160)(0.3310.1)=−100(6.6101)(1.331)+(−160)(3.31)=−879.8−529.6=−1,409.4

Future value is -$1,409.4.

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

F=A((1+i1)n1−1i1)(1+i2)n2+A((1+i2)n2−1i2)−1,409.4=A((1+0.14)5−10.14)(1+0.1)3+A((1+0.1)3−10.1)−1,409.4=A(1.925415−10.14)(1.331)+A(1.331−10.1)−1,409.4=A(0.9254150.14)(1.331)+A(0.3310.1)−1,409.4=A(6.6101)(1.331)+A(3.31)−1,409.4=8.798A+3.31A12.108A=−1,409.4A=−1,409.412.108=−116.4

Equivalent annual value is -$116.4.

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Answer 3

Question

Chapter 4, Problem 61P

To determine

Calculate the present, future, and equivalent annual value.

Expert Solution & Answer

Explanation of Solution

Equivalent cash flow (CF1) from year 1 to 5 is -$100. Time period 1 (n1) is 5. Interest rate 1 (i1) is 14%. Equivalent cash flow (CF2) from year 6 to 8 is -$160. Interest rate 2 (i2) is 10%. Time period 2 (n2) is 3.

Present value (P) can be calculated as follows:

P=CF1((1+i1)n1−1i1(1+i1)n1)+CF2((1+i2)n2−1(1+i2)n2i2)(1(1+i1)n1)=−100((1+0.14)5−1(1+0.14)50.14)+(−160)((1+0.1)3−10.1(1+0.1)3)(1(1+0.14)5)=−100(1.925415−10.14(1.925415))+(−160)(1.331−10.1(1.331))(11.925145)=−100(0.9254150.269558)+(−160)(0.3310.1331)(0.5194)=−100(3.4331)+(−160)(2.4869)(0.5194)=−343.31−206.67=−549.98

Present value is -$549.98.

Future value (F) can be calculated as follows:

F=CF1((1+i1)n1−1i1)(1+i2)n2+CF2((1+i2)n2−1i2)=−100((1+0.14)5−10.14)(1+0.1)3+(−160)((1+0.1)3−10.1)=−100(1.925415−10.14)(1.331)+(−160)(1.331−10.1)=−100(0.9254150.14)(1.331)+(−160)(0.3310.1)=−100(6.6101)(1.331)+(−160)(3.31)=−879.8−529.6=−1,409.4

Future value is -$1,409.4.

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

F=A((1+i1)n1−1i1)(1+i2)n2+A((1+i2)n2−1i2)−1,409.4=A((1+0.14)5−10.14)(1+0.1)3+A((1+0.1)3−10.1)−1,409.4=A(1.925415−10.14)(1.331)+A(1.331−10.1)−1,409.4=A(0.9254150.14)(1.331)+A(0.3310.1)−1,409.4=A(6.6101)(1.331)+A(3.31)−1,409.4=8.798A+3.31A12.108A=−1,409.4A=−1,409.412.108=−116.4

Equivalent annual value is -$116.4.

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Answer 4

Question

Chapter 4, Problem 61P

To determine

Calculate the present, future, and equivalent annual value.

Expert Solution & Answer

Explanation of Solution

Equivalent cash flow (CF1) from year 1 to 5 is -$100. Time period 1 (n1) is 5. Interest rate 1 (i1) is 14%. Equivalent cash flow (CF2) from year 6 to 8 is -$160. Interest rate 2 (i2) is 10%. Time period 2 (n2) is 3.

Present value (P) can be calculated as follows:

P=CF1((1+i1)n1−1i1(1+i1)n1)+CF2((1+i2)n2−1(1+i2)n2i2)(1(1+i1)n1)=−100((1+0.14)5−1(1+0.14)50.14)+(−160)((1+0.1)3−10.1(1+0.1)3)(1(1+0.14)5)=−100(1.925415−10.14(1.925415))+(−160)(1.331−10.1(1.331))(11.925145)=−100(0.9254150.269558)+(−160)(0.3310.1331)(0.5194)=−100(3.4331)+(−160)(2.4869)(0.5194)=−343.31−206.67=−549.98

Present value is -$549.98.

Future value (F) can be calculated as follows:

F=CF1((1+i1)n1−1i1)(1+i2)n2+CF2((1+i2)n2−1i2)=−100((1+0.14)5−10.14)(1+0.1)3+(−160)((1+0.1)3−10.1)=−100(1.925415−10.14)(1.331)+(−160)(1.331−10.1)=−100(0.9254150.14)(1.331)+(−160)(0.3310.1)=−100(6.6101)(1.331)+(−160)(3.31)=−879.8−529.6=−1,409.4

Future value is -$1,409.4.

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

F=A((1+i1)n1−1i1)(1+i2)n2+A((1+i2)n2−1i2)−1,409.4=A((1+0.14)5−10.14)(1+0.1)3+A((1+0.1)3−10.1)−1,409.4=A(1.925415−10.14)(1.331)+A(1.331−10.1)−1,409.4=A(0.9254150.14)(1.331)+A(0.3310.1)−1,409.4=A(6.6101)(1.331)+A(3.31)−1,409.4=8.798A+3.31A12.108A=−1,409.4A=−1,409.412.108=−116.4

Equivalent annual value is -$116.4.

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Answer 5

Chapter 4, Problem 61P

To determine

Calculate the present, future, and equivalent annual value.

Expert Solution & Answer

Explanation of Solution

Equivalent cash flow (CF1) from year 1 to 5 is -$100. Time period 1 (n1) is 5. Interest rate 1 (i1) is 14%. Equivalent cash flow (CF2) from year 6 to 8 is -$160. Interest rate 2 (i2) is 10%. Time period 2 (n2) is 3.

Present value (P) can be calculated as follows:

P=CF1((1+i1)n1−1i1(1+i1)n1)+CF2((1+i2)n2−1(1+i2)n2i2)(1(1+i1)n1)=−100((1+0.14)5−1(1+0.14)50.14)+(−160)((1+0.1)3−10.1(1+0.1)3)(1(1+0.14)5)=−100(1.925415−10.14(1.925415))+(−160)(1.331−10.1(1.331))(11.925145)=−100(0.9254150.269558)+(−160)(0.3310.1331)(0.5194)=−100(3.4331)+(−160)(2.4869)(0.5194)=−343.31−206.67=−549.98

Present value is -$549.98.

Future value (F) can be calculated as follows:

F=CF1((1+i1)n1−1i1)(1+i2)n2+CF2((1+i2)n2−1i2)=−100((1+0.14)5−10.14)(1+0.1)3+(−160)((1+0.1)3−10.1)=−100(1.925415−10.14)(1.331)+(−160)(1.331−10.1)=−100(0.9254150.14)(1.331)+(−160)(0.3310.1)=−100(6.6101)(1.331)+(−160)(3.31)=−879.8−529.6=−1,409.4

Future value is -$1,409.4.

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

F=A((1+i1)n1−1i1)(1+i2)n2+A((1+i2)n2−1i2)−1,409.4=A((1+0.14)5−10.14)(1+0.1)3+A((1+0.1)3−10.1)−1,409.4=A(1.925415−10.14)(1.331)+A(1.331−10.1)−1,409.4=A(0.9254150.14)(1.331)+A(0.3310.1)−1,409.4=A(6.6101)(1.331)+A(3.31)−1,409.4=8.798A+3.31A12.108A=−1,409.4A=−1,409.412.108=−116.4

Equivalent annual value is -$116.4.

Answer 6

Chapter 4, Problem 61P

To determine

Calculate the present, future, and equivalent annual value.

Expert Solution & Answer

Explanation of Solution

Equivalent cash flow (CF1) from year 1 to 5 is -$100. Time period 1 (n1) is 5. Interest rate 1 (i1) is 14%. Equivalent cash flow (CF2) from year 6 to 8 is -$160. Interest rate 2 (i2) is 10%. Time period 2 (n2) is 3.

Present value (P) can be calculated as follows:

P=CF1((1+i1)n1−1i1(1+i1)n1)+CF2((1+i2)n2−1(1+i2)n2i2)(1(1+i1)n1)=−100((1+0.14)5−1(1+0.14)50.14)+(−160)((1+0.1)3−10.1(1+0.1)3)(1(1+0.14)5)=−100(1.925415−10.14(1.925415))+(−160)(1.331−10.1(1.331))(11.925145)=−100(0.9254150.269558)+(−160)(0.3310.1331)(0.5194)=−100(3.4331)+(−160)(2.4869)(0.5194)=−343.31−206.67=−549.98

Present value is -$549.98.

Future value (F) can be calculated as follows:

F=CF1((1+i1)n1−1i1)(1+i2)n2+CF2((1+i2)n2−1i2)=−100((1+0.14)5−10.14)(1+0.1)3+(−160)((1+0.1)3−10.1)=−100(1.925415−10.14)(1.331)+(−160)(1.331−10.1)=−100(0.9254150.14)(1.331)+(−160)(0.3310.1)=−100(6.6101)(1.331)+(−160)(3.31)=−879.8−529.6=−1,409.4

Future value is -$1,409.4.

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

F=A((1+i1)n1−1i1)(1+i2)n2+A((1+i2)n2−1i2)−1,409.4=A((1+0.14)5−10.14)(1+0.1)3+A((1+0.1)3−10.1)−1,409.4=A(1.925415−10.14)(1.331)+A(1.331−10.1)−1,409.4=A(0.9254150.14)(1.331)+A(0.3310.1)−1,409.4=A(6.6101)(1.331)+A(3.31)−1,409.4=8.798A+3.31A12.108A=−1,409.4A=−1,409.412.108=−116.4

Equivalent annual value is -$116.4.

Answer 7

Chapter 4, Problem 61P

To determine

Calculate the present, future, and equivalent annual value.

Answer 8

Expert Solution & Answer

Explanation of Solution

Equivalent cash flow (CF1) from year 1 to 5 is -$100. Time period 1 (n1) is 5. Interest rate 1 (i1) is 14%. Equivalent cash flow (CF2) from year 6 to 8 is -$160. Interest rate 2 (i2) is 10%. Time period 2 (n2) is 3.

Present value (P) can be calculated as follows:

P=CF1((1+i1)n1−1i1(1+i1)n1)+CF2((1+i2)n2−1(1+i2)n2i2)(1(1+i1)n1)=−100((1+0.14)5−1(1+0.14)50.14)+(−160)((1+0.1)3−10.1(1+0.1)3)(1(1+0.14)5)=−100(1.925415−10.14(1.925415))+(−160)(1.331−10.1(1.331))(11.925145)=−100(0.9254150.269558)+(−160)(0.3310.1331)(0.5194)=−100(3.4331)+(−160)(2.4869)(0.5194)=−343.31−206.67=−549.98

Present value is -$549.98.

Future value (F) can be calculated as follows:

F=CF1((1+i1)n1−1i1)(1+i2)n2+CF2((1+i2)n2−1i2)=−100((1+0.14)5−10.14)(1+0.1)3+(−160)((1+0.1)3−10.1)=−100(1.925415−10.14)(1.331)+(−160)(1.331−10.1)=−100(0.9254150.14)(1.331)+(−160)(0.3310.1)=−100(6.6101)(1.331)+(−160)(3.31)=−879.8−529.6=−1,409.4

Future value is -$1,409.4.

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

F=A((1+i1)n1−1i1)(1+i2)n2+A((1+i2)n2−1i2)−1,409.4=A((1+0.14)5−10.14)(1+0.1)3+A((1+0.1)3−10.1)−1,409.4=A(1.925415−10.14)(1.331)+A(1.331−10.1)−1,409.4=A(0.9254150.14)(1.331)+A(0.3310.1)−1,409.4=A(6.6101)(1.331)+A(3.31)−1,409.4=8.798A+3.31A12.108A=−1,409.4A=−1,409.412.108=−116.4