Chapter 14, Problem 11P

(a)

To determine

Annual expenditure.

Explanation of Solution

The given information:

Miles traveled per year is 1000.

Milles per gallon is 15.

Price per gallon is 5.

Calculation:

The general formula for calculating annual expenditure is shown below:

$\text{AE}=\left(\frac{\text{Miles travelled per year}}{\text{Miles per gallon}}\right)\times \text{Price per gallon}$ (1)

Substitute the respective values in Equation (1) to calculate the annual expenditure on fuel for the Oldsmobuick.

$\begin{array}{c}\text{AE}=\left(\frac{\$10,000}{15}\right)\times 5\\ =666.66\times 5\\ =3,333.3\end{array}$

Annual expenditure is $3,333.3.

By using the same Equation (1), the calculation of annual expenditure on fuel for Prius is shown below:

$\begin{array}{c}\text{AE}=\left(\frac{\$10,000}{45}\right)\times 5\\ =222.22\times 5\\ =1,111.1\end{array}$

Annual expenditure is $1,111.1.

(b)

To determine

Present value.

Explanation of Solution

The given information:

Rate of interest (r) is 7%.

Cost of Prius is $25,000.

Calculation:

The general formula for calculating present value is shown below:

$\text{PV}=\left(\frac{\text{Annual expenditure}}{{\left(1+\text{Interest rate}\right)}^1}\right)+\left(\frac{\text{Annual expenditure}}{{\left(1+\text{Interest rate}\right)}^2}\right)+\mathrm{...}+\left(\frac{\text{Annual expenditure}}{{\left(1+\text{Interest rate}\right)}^5}\right)$ (2)

Substitute the respective values in Equation (2) to calculate the present value.

Assume that the fuel cost expenditure is the only one cost for using car and end of the fifth year, the consumer purchase a new Prius.

$\begin{array}{c}\text{PV}=\left(\begin{array}{l}\left(\frac{3,333.33}{{\left(1+\text{0}\text{.07}\right)}^{\text{1}}}\right)+\left(\frac{3,333.33}{{\left(1+\text{0}\text{.07}\right)}^2}\right)+\left(\frac{3,333.33}{{\left(1+\text{0}\text{.07}\right)}^3}\right)+\left(\frac{3,333.33}{{\left(1+\text{0}\text{.07}\right)}^4}\right)\\ +\left(\frac{3,333.33}{{\left(1+\text{0}\text{.07}\right)}^5}\right)+\left(\frac{25,000}{{\left(1+\text{0}\text{.07}\right)}^5}\right)\end{array}\right)\\ =\left(\begin{array}{l}\left(\frac{3,333.33}{1.07}\right)+\left(\frac{3,333.33}{1.1449}\right)+\left(\frac{3,333.33}{1.225043}\right)+\left(\frac{3,333.33}{1.31079601}\right)\\ +\left(\frac{3,333.33}{1.4025517307}\right)+\left(\frac{25,000}{1.4025517307}\right)\end{array}\right)\\ =3,115.27+2,911.45+2,720.99+2,542.98+2,376.61+17,824.65\\ =31,491.9\end{array}$

Present value is $31,419.9.

(c)

To determine

Present value.

Explanation of Solution

The given information:

Rate of interest (r) is 7%.

Cost of Prius is $25,000.

Calculation:

By using the same Equation (2), the present value of cost if the consumer buys new Prius is calculated as follows:

$\begin{array}{c}\text{PV}=\left(\begin{array}{l}\left(\frac{1,111.11}{{\left(1+\text{0}\text{.07}\right)}^{\text{1}}}\right)+\left(\frac{1,111.11}{{\left(1+\text{0}\text{.07}\right)}^2}\right)+\left(\frac{1,111.11}{{\left(1+\text{0}\text{.07}\right)}^3}\right)+\left(\frac{1,111.11}{{\left(1+\text{0}\text{.07}\right)}^4}\right)\\ +\left(\frac{1,111.11}{{\left(1+\text{0}\text{.07}\right)}^5}\right)+\left(\frac{1,111.11}{{\left(1+\text{0}\text{.07}\right)}^5}\right)\end{array}\right)\\ =\left(\frac{1,111.11}{1.07}\right)+\left(\frac{1,111.11}{1.1449}\right)+\left(\frac{1,111.11}{1.225043}\right)+\left(\frac{1,111.11}{1.31079601}\right)+\left(\frac{1,111.11}{1.4025517307}\right)+25,000\\ =1,038.42+970.48+906.99+847.66+792.21+25,000\\ =29,555.76\end{array}$

Present value is $70,557.65.

(d)

To determine

Decision making regarding consumption of Prius.

Explanation of Solution

By comparing the present value obtained in part (b) and in part (c), it is lower in second case. Thus, the consumer always prefers the least cost. Therefore, the consumer purchases the Prius today.

(e)

To determine

Annual expenditure.

Explanation of Solution

The given information:

Miles traveled per year is 1000.

Milles per gallon is 30.

Price per gallon is 5.

Calculation:

By using the same Equation (1), the calculation of annual expenditure on fuel for

Oldsmobuick is shown below:

$\begin{array}{c}\text{AE}=\left(\frac{\$10,000}{30}\right)\times 5\\ =333.33\times 5\\ =1,666.6\end{array}$

Annual expenditure is $1,666.6.

By using the same Equation (2), the present value of cost if the consumer continues to drive the Oldsmobuick is calculated as follows:

$\begin{array}{c}\text{PV}=\left(\begin{array}{l}\left(\frac{1,666.67}{{\left(1+\text{0}\text{.07}\right)}^{\text{1}}}\right)+\left(\frac{1,666.67}{{\left(1+\text{0}\text{.07}\right)}^2}\right)+\left(\frac{1,666.67}{{\left(1+\text{0}\text{.07}\right)}^3}\right)+\left(\frac{1,666.67}{{\left(1+\text{0}\text{.07}\right)}^4}\right)\\ +\left(\frac{1,666.67}{{\left(1+\text{0}\text{.07}\right)}^5}\right)+\left(\frac{25,000}{{\left(1+\text{0}\text{.07}\right)}^5}\right)\end{array}\right)\\ =\left(\begin{array}{l}\left(\frac{1,666.67}{1.07}\right)+\left(\frac{1,666.67}{1.1449}\right)+\left(\frac{1,666.67}{1.225043}\right)+\left(\frac{1,666.67}{1.31079601}\right)\\ +\left(\frac{1,666.67}{1.4025517307}\right)+\left(\frac{25,000}{1.4025517307}\right)\end{array}\right)\\ =1,557.63+1,455.73+1,360.499+1,271.49+1,188.31+17,824.65\\ =24,658.3\end{array}$

Present value is $24,658.3.