Question

Econo-Cool air conditioners cost $390 to purchase, result in electricity bills of $168 per year, and last for 5 years. Luxury Air models cost $590, result in electricity bills of $136 per year, and last for 8 years. The discount rate is 23%.

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

Equivalent annual cost (EAC) is the annual cost of owning and maintaining an asset determined by dividing the net present value of the asset purchase, operations and maintenance cost by the present value of annuity factor.

Hence Equivalent Annual Cost= NPV/ PVAF

We multiply the cahsflow each year to each year discount factor to find the present value.

Discount Factor = 1/ (1+R)^N For eg Year 1 = 1/1.23^1= 0.8130

			23%
Year	Cahflow Eco	Cahflow Lux	Discount Factor	PV Eco	PV Lux
0	390	590	1.0000	390.00	590.00
1	168	136	0.8130	136.59	110.57
2	168	136	0.6610	111.05	89.89
3	168	136	0.5374	90.28	73.08
4	168	136	0.4369	73.40	59.42
5	168	136	0.3552	59.67	48.31
6		136	0.2888		39.27
7		136	0.2348		31.93
8		136	0.1909		25.96
Total			4.5179	860.98	1,068.44

To find the PVAF for each option, we add the discount factors for the life of the asset.

i.e 5 years for Eco and 8 years for luxury

PVAF Eco = 2.8035 PVAF Lux = 3.5179

EAC= NPV/PVAF

Eco = 860.98/ 2.8035 = 307.11

Lux = 1068.44 / 3.5179= 303.71

Luxury Model is more cost effective

2. If inflation is there @10%, electricity cost per year will increase by 10%. Using the revised electricity cost we do the same calculation as above.

			23%
Year	Cahflow Eco	Cahflow Lux	Discount Factor	PV Eco	PV Lux
0	390	590.00	1.0000	390.00	590.00
1	168.00	136.00	0.8130	136.59	110.57
2	184.80	149.60	0.6610	122.15	98.88
3	203.28	164.56	0.5374	109.24	88.43
4	223.61	181.02	0.4369	97.69	79.09
5	245.97	199.12	0.3552	87.37	70.73
6		219.03	0.2888		63.25
7		240.93	0.2348		56.57
8		265.03	0.1909		50.59
Total				943.04	1,208.10
PVAF	2.8035	3.5179
EAC	336.3815104	343.4142191

Now we observe that, Eco is a better option as EAC is lower.