Question

3.GHI company wants to buy an air conditioner. There are two options in the market. The discount rate is 17%. Option A: Super air conditioner cost $300 to purchase, can be used for 5 years, and the electricity bill is $150 per year. Option B: Excellent air conditioner cost $500 to purchase, can be used for 8 years, and the electricity bill is $100 per year.

a) What are the equivalent annual costs (EAC) of the Super and Excellent air conditioner models?

b) Which model is more cost-effective (with lower cost)?

c) If the inflation rate is expected to be 10% per year, redo a.) and b.)

Answer 1

EAC = Present value of Cost/(PVIF i%,n)

Calculation of Present value of cost (A)

PV (A) = Initial cost + Annual cost(PVIF i%,n)

PV (A) = 300 + 150(PVIF17%,5)

PV (A) = 300 + 150*3.1993

PV (A) = $ 780

Present value of cost for (B)

PV (B) = 500 + 100(PVIF17%,8)

PV (B) = 500 + 100*4.2072 = $921

Calculation of EAC

EAC (A) = 780/3.1993 = $243.80

EAC (B) = 921/4.20716 = $218.91

Based on EAC, Option (B) is the more cost effective , because of lower cost

(C)..Calculation of annual cost inculding inflation

Years	Inflation factor	Option (A)	Option (B)	PVIF17%	PV (A)	PV (B)
1	1.10	165	110	0.8547	141.03	94.02
2	1.21	181.50	121	0.7305	132.59	88.39
3	1.331	199.65	133.10	0.6244	124.66	83.11
4	1.4641	219.62	146.41	0.5337	117.21	78.14
5	1.61051	241.58	161.05	0.4561	110.18	73.45
6	1.771561		177.16	0.3898		69.06
7	1.9487171		194.87	0.3332		64.93
8	2.14358881		214.36	0.2848		61.05
	Sum (ups)				625.67	612.15

Present Value (A) = 300+625.67 = $925.67

Present value (B) = 500 + 612.15 = 1,112.15

EAC (A) = 925.67/3.1993 = $289.33

EAC (B) = 1,112.15/4.20716 = $264.35

Still the option (B) is more cost effective