Question

You are in the market for a new refrigerator for your company’s lounge, and you have narrowed the search down to two models. The energy-efficient model sells for \(700 and will save you \)45 at the end of each of the next five years in the electricity costs. The standard model has features similar to the energy-efficient model but provides no future saving in the electricity costs. It is priced at only $500. Assuming your opportunity cost of funds is 16 percent, which refrigerator should you purchase?

Short answer

The standard model is cheaper one and so it should be purchased.

Step-by-step solution

Determining formula 

First calculate the present value of the returns over the years and then compare the prices of the two appliances.

Use the formula for the present value of the stream as the period is 5 years:

$PV=\frac{F{V}_1}{{(1+i)}^1}+\frac{F{V}_2}{{(1+i)}^2}+\frac{F{V}_3}{{(1+i)}^3}+\frac{F{V}_4}{{(1+i)}^4}+\frac{F{V}_5}{{(1+i)}^5}$

 Step2: Determining which refrigerator to be purchased.

Since the opportunity cost of funds is 6%, it follows that i=6%=0.06.

Therefore,

$\begin{array}{l}Pv=\frac{F{V}_1}{{(1+0.06)}^1}+\frac{F{V}_2}{{(1+0.06)}^2}+\frac{F{V}_3}{{(1+0.06)}^3}+\frac{F{V}_4}{{(1+0.06)}^4}+\frac{F{V}_5}{{(1+0.06)}^5}\\ PV=\frac{F{V}_1}{{\left(1.06\right)}^1}+\frac{F{V}_2}{{\left(1.06\right)}^2}+\frac{F{V}_3}{{\left(1.06\right)}^3}+\frac{F{V}_4}{{\left(1.06\right)}^4}+\frac{F{V}_5}{{\left(1.06\right)}^5}\end{array}$

$F{V}_1=F{V}_2=F{V}_3=F{V}_4=F{V}_5=\$45$because annual return in saving is the same at the end of each year. Therefore,

$\begin{array}{l}PV=\frac{45}{{\left(1.06\right)}^1}+\frac{45}{{\left(1.06\right)}^2}+\frac{45}{{\left(1.06\right)}^3}+\frac{45}{{\left(1.06\right)}^4}+\frac{45}{{\left(1.06\right)}^5}\\ PV=\mathrm{189.74.}\end{array}$

Therefore, present value of the future savings in the next five years is $189.74, not 5.45=$225 as one might think.

The cost of the energy efficient appliance is given by:

$\$700-\$189.74=\$510.26$

The cost of the energy efficient appliance is $510.26 while the cost of the standard model is $500.

Therefore, you should buy the standard model as it is cheaper one.