Chapter 27, Problem 13CQ

To determine

Check whether buying of a refrigerator is profitable or not.

Explanation of Solution

The market value of a product is determined by its present value. With the given information, the buying price (P) of a refrigerator is $700, the salvage value (SV) is $200, rate of interest is 8 per cent, and reduction in the electricity bill (ED) is $150. Assume that the electricity bill is $350. After deducting the ED, electricity bill is $200$\left(\text{350}-150\right)$. The present worth (PV) of using the owner’s refrigerator can be calculated as follows:

$\begin{array}{c}\text{PV}=-\frac{{\text{EB}}_1}{{\left(1+\text{i}\right)}^1}-\frac{{\text{EB}}_2}{{\left(1+\text{i}\right)}^2}\mathrm{...}-\frac{{\text{EB}}_{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}}\\ =-\frac{350}{{\left(1+0.08\right)}^1}-\frac{350}{{\left(1+0.08\right)}^2}-\frac{\text{350}}{{\left(1+0.08\right)}^3}-\frac{350}{{\left(1+0.08\right)}^4}-\frac{\text{350}}{{\left(1+0.08\right)}^5}\\ =-\frac{350}{{\left(1.08\right)}^1}-\frac{350}{{\left(1.08\right)}^2}-\frac{\text{350}}{{\left(1.08\right)}^3}-\frac{350}{{\left(1.08\right)}^4}-\frac{350}{{\left(1.08\right)}^5}\\ =-\frac{350}{1.08}-\frac{350}{1.1664}-\frac{\text{350}}{1.2597}-\frac{350}{1.3605}-\frac{350}{1.4693}\\ =-324.07-300.07-277.84-257.26-238.21\\ =-1,397.45\end{array}$

The PV of using the owner’s refrigerator is -$1,397.45.

The present worth (PV) of buying a new refrigerator can be calculated as follows:

$\begin{array}{c}\text{PV}=-\text{P}-\frac{{\text{EB}}_1}{{\left(1+\text{i}\right)}^1}-\frac{{\text{EB}}_2}{{\left(1+\text{i}\right)}^2}\mathrm{...}-\frac{{\text{EB}}_{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}}+\frac{{\text{SV}}_{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}}\\ =-700-\frac{200}{{\left(1+0.08\right)}^1}-\frac{200}{{\left(1+0.08\right)}^2}-\frac{\text{200}}{{\left(1+0.08\right)}^3}-\frac{200}{{\left(1+0.08\right)}^4}-\frac{200}{{\left(1+0.08\right)}^5}+\frac{200}{{\left(1+0.08\right)}^5}\\ =-700-\frac{200}{{\left(1.08\right)}^1}-\frac{200}{{\left(1.08\right)}^2}-\frac{200}{{\left(1.08\right)}^3}-\frac{200}{{\left(1.08\right)}^4}-\frac{200}{{\left(1.08\right)}^5}+\frac{200}{{\left(1.08\right)}^5}\\ =-700-\frac{200}{1.08}-\frac{200}{1.1664}-\frac{200}{1.2597}-\frac{200}{1.3605}-\frac{200}{1.4693}+\frac{200}{1.46693}\\ =-700-185.185-171.468-158.768-147-136.119+136.119\\ =-1,362.42\end{array}$

The PV of buying a new refrigerator is -$1,362.42. Thus, PV of buying a new refrigerator is greater (lower cost) than using the owner’s refrigerator. Thus, the person chooses to buy a new one.