Chapter 8, Problem 1P

The seasonal energy efficiency ratio (SEER) is 13 for a new heating and air conditioning system that costs $4,400 to install. A higher SEER (14) system is available for $5,200. The more efficient system with a SEER of 14 will save 10,000,000 Btu per year in energy consumption. Assume the cost per million Btu is $10.00. If the warranty on either system is 10 years, is the extra $800 for the more efficient system justified? The inflation-free (real) interest rate is 2% per year. What assumptions did you make in your analysis?

To determine

Calculate the internal rate o return.

Explanation of Solution

The assumption is that the cost of energy is remain the same for the analysis period of 10 years. Also it is assumes that the salvage value of the two system at end of the life time is zero.

Time period is denoted by n and the interest is denoted by i. The internal rate of return (i) between the two systems can be calculated as follows.

$\begin{array}{c}\text{Additional spending}=\text{Saving Btu}\times \text{Cost per Btu}\left(\frac{{\left(\text{1}+\text{i}\right)}^{\text{n}}-\text{1}}{\text{i}{\left(\text{1}+\text{i}\right)}^{\text{n}}}\right)\\ 800=\text{10,000,000}\times \frac{10}{1,000,000}\left(\frac{{\left(\text{1}+\text{i}\right)}^{\text{10}}-\text{1}}{\text{i}{\left(\text{1}+\text{i}\right)}^{\text{10}}}\right)\end{array}$   

Substitute the value of ‘i’ as 4.3% by trial and error method in the above calculation. This makes the calculated value is equal to additional spending. Thus, it is verified that the IRR is 4.3%. Since the IRR is greater than the real interest rate. The additional spending is justified.