Question

Econo-Cool air conditioners cost $360 to purchase, result in electricity bills of $162 per year, and last for 5 years. Luxury Air models cost $560, result in electricity bills of $124 per year, and last for 8 years. The discount rate is 22%.

a. What is the equivalent annual cost of the Econo-Cool model? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

b. What is the equivalent annual cost of the Luxury Air model? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

c. Which model is more cost-effective?

• Econo-Cool

• Luxury Air

d-1. Now you remember that the inflation rate is expected to be 10% per year for the foreseeable future. What is the equivalent annual cost of the Econo-Cool and Luxury Air model? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

d-2. Which model is more cost-effective?

• Econo-Cool

• Luxury Air

Answer 1

a) The Present value of Cost of Econo Cool = 360+ 162/0.22*(1-1/1.22^5) = $823.91

So, Equivalent Annual Cost A is given by

A/0.22*(1-1/1.22^5) = 823.91

=> A*2.86364= 823.91

=> A = $287.71

b) Similarly

The Present value of Cost of Luxury Air = 560+ 124/0.22*(1-1/1.22^8) = $1008.789

So, Equivalent Annual Cost A is given by

A/0.22*(1-1/1.22^8) = 1008.789

=> A*3.619268= 1008.789

=> A = $278.73

c) The Luxury Air model is more cost effective as its Equivalent Annual Cost is lesser than the Econo Cool Model

d1) If Inflation is 10% per year then electricity bills will increase by 10% every year

So, PV of Total Cost in Econo Cool

= 360+ 162*1.1/1.22+ 162*1.1^2/1.22^2+...+162*1.1^5/1.22^5

=360 + 162*1.1/1.22*(1-(1.1/1.22)^5)/(1-1.1/1.22)

=$960.11

So, Equivalent Annual Cost A is given by

A/0.22*(1-1/1.22^5) = 960.11

=> A*2.86364= 960.11

=> A = $335.28

Similarly

PV of Total Cost in Luxury Air

= 560+ 124*1.1/1.22+ 124*1.1^2/1.22^2+...+124*1.1^5/1.22^8

=560 + 124*1.1/1.22*(1-(1.1/1.22)^8)/(1-1.1/1.22)

=$1200.193

So, Equivalent Annual Cost A is given by

A/0.22*(1-1/1.22^8) = 1200.193

=> A*3.619268= 1200.193

=> A = $331.61

d2) Still the Luxury Air model is more cost effective as its Equivalent Annual cost is still lesser than that of Econo Cool Model