Chapter 4, Problem 58QP

Summary Introduction

To compute: The purchase of the car under buying and leasing and to buy it or not.

Purchasing Power:

It refers to the ability of the person to buy something. Purchasing power decreases with an increase in inflation and increase with the decrease in inflation.

Explanation of Solution

Given,

Initial payment is $2,400.

Monthly payment is $380.

Purchase cost of the car is $28,000.

Present value of resale price is $14,263.

Formula to calculate the present value under leasing option,

$\text{Present}\text{value}=\text{Initial}\text{payment}+\left(\text{Monthly}\text{payment}\times PVIF{A}_{5\%,3\text{years}\times 12\text{months}}\right)$

Where,

• PVIFA refers to present value interest factor annuity.

Substitute $2,400 for the initial payment, $380 for the monthly payment,

$\begin{array}{c}\text{Present}\text{value}=\$2,400+\left(\$380\times 32.871\right)\\ =\$2,400+\$12,491\\ =\$14,891\end{array}$

Hence, the present value under leasing option is $14,891.

Formula to calculate the present value under the purchasing option,

$\text{Present}\text{value}=\text{Purchase}\text{}\text{cost}-\text{Present}\text{value}\text{of}\text{resale}\text{price}$

Substitute $28,000 for the purchase cost and $14,263 for the present value of the resale price.

$\begin{array}{c}\text{Present}\text{value}=\$28,000-\$14,273\\ =\$13,727\end{array}$

Hence, the present value under purchasing option is $13,727.

Hence, it is preferred to buy the car on lease as the value of the option of purchasing is very less as compared to the option of leasing.

Given,

Resale price is $17,000.

Annual interest rate is 6%.

Computation of the present value of the resale price,

$\text{Present}\text{value}=\text{Resale}\text{price}\times \frac{1}{{\left(1+\text{Annual}\text{interest}\text{rate}\right)}^3}$

Substitute $17,000 for the re sale price and 6% for annual interest rate.

$\begin{array}{c}\text{Present}\text{value}=\$17,000\times \frac{1}{{\left(1+0.06\right)}^3}\\ =\$17,000\times 0.839\\ =\$14,273\end{array}$

Hence, the present value of the resale priceis $14,273.

Computation of the break even point,

Formula to calculate the breakeven point,

$\text{Future}\text{value}=\text{Present}\text{value}\times {\left(1+\text{rate}\text{of}\text{interest}\right)}^{\text{Time}}$

Substitute $13,109 for the present value and 0.5% for rate of interest.

$\begin{array}{c}\text{Future}\text{value}=\$13,109\times {\left(1+0.005\right)}^{3\text{years}\times 12\text{}\text{months}}\\ =\$13,109\times 1.197\\ =\$15,691\end{array}$

Hence, the break even sale price of the car is $15,691.

Working notes:

Given,

Annual percentage rate is 6%.

Computation of monthly interest rate,

$\begin{array}{c}\text{Monthly}\text{interest}\text{rate}=\frac{\text{Annual}\text{percentage}\text{}\text{rate}}{\text{Number}\text{of}\text{months}}\\ =\frac{6\%}{12\text{months}}\\ =0.5\%\end{array}$

Hence, the monthly interest rate is 0.5%.

Given,

Purchase cost is $28,000.

Computation of present value under leasing option,

$\begin{array}{c}\text{Present}\text{value}\text{under}\text{leasing}\text{option}=\text{Purchase}\text{cost}-\text{Present}\text{value}\text{of}\text{re}\text{sale}\text{price}\\ \$14,981=\$28,000-\text{Present}\text{value}\text{of}\text{re}\text{sale}\text{price}\\ \text{Present}\text{value}\text{of}\text{re}\text{sale}\text{price}=\$13,109\end{array}$

Hence, the present value of the resale price is $13,109.

Conclusion

The car should be purchased on lease.