Calculate the present, future, and equivalent annual value.

Question

Want to see more full solutions like this?

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

Answer

M” method Given the following model, solve by the method of “M”. (see image)

As indicated in the attached image, U.S. earnings for high- and low-skill workers as measured by educational attainment began diverging in the 1980s. The remaining questions in this problem set use the model for the labor market developed in class to walk through potential explanations for this trend. 1. Assume that there are just two types of workers, low- and high-skill. As a result, there are two labor markets: supply and demand for low-skill workers and supply and demand for high-skill workers. Using two carefully drawn labor-market figures, show that an increase in the demand for high skill workers can explain an increase in the relative wage of high-skill workers. 2. Using the same assumptions as in the previous question, use two carefully drawn labor-market figures to show that an increase in the supply of low-skill workers can explain an increase in the relative wage of high-skill workers.

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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