Question

You own a rental building in the city and are interested in replacing the heating system. You are faced with the following alternatives:

a. A gas heating system, which will cost $5,000 to install and $1,000 a year to run and will last twenty years.

b. An oil heating system, which will cost $3,500 to install and $1,200 a year to run and will last fifteen years.

If your opportunity cost of capital is 10%, which of these two options is better for you? These two projects have different lives, so use Equivalent Annuity rule to find the answer.

Select one:

a. Choose gas heating system

b. The two projects are equivalent, you'd be indifferent.

c. Choose oil heating system

Answer 1

Calculating NPV of gas heating system, we get -5000+(-1000)/1.1+(-1000)/1.1^2+.....(-1000)/1.1^20. We can make use of present value of annuity formula, which is P*((1-(1+r)^-n)/r). On Substituting, we get -5000+ ((-1000)*(1-(1.1^-20))/0.1= -13513.6

Calculating NPV of oil heating system, we get -3500+(-1200)/1.1+(-1200)/1.1^2+.....(-1200)/1.1^15= -12627.3

Using Equivalent Annuity Rule, we need to find EAA of each project and then select the one with higher EAA. EAA is calculated by the formula: (r*NPV)/(1-(1+r)^-n), where r is the discount rate, n is the number of periods.

So, EAA for gas heating system is (0.1*-13513.6)/(1-(1.1^-20))= -1587.3

EAA for oil heating system is (0.1*-12627.3)/(1-(1.1^-15))= -1660.16

As, EAA for Gas heating system is greater than EAA for oil heating system, we should choose Gas heating system.