ENGINEERING ECO ANALYSIS W/STUDY GUIDE
ENGINEERING ECO ANALYSIS W/STUDY GUIDE
13th Edition
ISBN: 9780190693053
Author: NEWNAN
Publisher: Oxford University Press
Question
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Chapter 3, Problem 9P
To determine

The explanation of the choice made by each woman.

Expert Solution & Answer
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Answer to Problem 9P

Magdalen made a correct choice if the annual interest is greater than 25.99%.

Miriam made a correct choice if the annual interest is less than 25.99%.

Mary June made a correct choice if the annual interest rate is equal to 25.99%.

Explanation of Solution

Given:

Two different cash flows.

  • $500
  • will be received today.
  • $1000
  • will be received after 3 years.
  • Concept used:

    There are two available options.

    Either take

    $500 today or $1000 after 3 years.

    Calculation:

    Write the expression to calculate the present value of $1000

    PV=$1000(1+i)n

    Here, interest is i, and number of years is n.

    Explanation for the choice made by Magdalen:

    Magdalen choose to take $500 in spite of taking $1000 after three years. Magdalen’s choice will be rational if the present value of

    $1000 received after three years is less than $500.

    500>1000(1+i)n ...... (I)

    Substitute, 3 for n in Equation (I) and calculate the interest rate.

    500>1000(1+i)3500(1+i)3>1000(1+i)3>1000500(1+i)3>2

    1+i>231+i>1.2599i>1.25991i>0.2599

    i>25.99%

    Therefore Magdalen made a correct choice if the annual interest is greater than 25.99%.

    Explanation for the choice made by Miriam:

    Miriam chooses to take $1000 after 3 years in spite of $500 today. Miriam choice will be rational if the present value of

    $1000 after 3 years is greater than the

    $500.

    500<1000(1+i)n ...... (II)

    Substitute, 3 for n in Equation (II) and calculate the interest rate.

    500<1000(1+i)3500(1+i)3<1000(1+i)3<1000500(1+i)3<2

    1+i<231+i<1.2599i<1.25991i<0.2599

    i<25.99%

    Therefore Miriam made a correct choice if the annual interest is less than 25.99%.

    Explanation for the choice made by Mary June Mary June choice is indifferent between taking $500 today or $1000 after three years can be considered a rational choice if the present value of $1000 after three years is equal to $500 today.

    500=1000(1+i)n ...... (III)

    Substitute, 3 for n in Equation (III) and calculate the interest rate.

    500=1000(1+i)3500(1+i)3=1000(1+i)3=1000500(1+i)3=2

    1+i=231+i=1.2599i=1.25991i=0.2599

    i=25.99%

    Therefore, Mary June made a correct choice if the annual interest rate is equal to 25.99%.

    Conclusion:

    Magdalen made a correct choice if the annual interest is greater than 25.99%.

    Miriam made a correct choice if the annual interest is less than 25.99%.

    Mary June made a correct choice if the annual interest rate is equal to 25.99%.

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