Question

Econo-cool air conditioners cost $300 to purchase, result in electricity bills of $150 per year, and last for 5 years. Luxury Air models cost $500, result in electricity bills of $100 per year, and last for 8 years. The discount rate is 21 percent.

a. What are the equivalent annual costs of the Econo-cool and Luxury Air models? Which model is more cost effective?
b. Now you remember that the inflation rate is expected to be 10 percent per year for the foreseeable future. How does the inflation rate affect the evaluation of the two air conditioners? (1 mark)

Answer 1

As per rules I will answer the first 4 sub-parts of this question

Econo Cool AC

Capital recovery = P*i*(1+i)^n/ ((1+i)^n -1)

= 300*0.21*1.21^5/ 1.21^5 -1

= 163.4057/ 1.5937

=$102.53

EAC= 102.53+ 150 = $252.53

Luxury Air

Capital recovery = P*i*(1+i)^n/ ((1+i)^n -1)

= 500*0.21*1.21^8/ 1.21^8 -1

= 482.472/3.5949

=$ 134.21

EAC= 134.21+ 100 = $234.21

Luxury Air is more cost effective.

b) Due to inflation the real cost of capital increases. Hence the rate of discounting will be increased to adjust for inflation. This will increase the total costs. But the decision will be the same.

Inflation adjusted rate= 0.21+ 0.1+ 0.21*0.1 = 0.331 % per year

The EAC for Econo model=

(300*0.331*1.331^5/ (1.331^5 -1 ))+ 150

=$280.55

The EAC for Luxury model =

500*0.331*1.331^8/ (1.331^8 -1) + 100

=$284.20

Thus due to inflation, the EAC of the two options has become similar.