Question

1. Two refrigerators are available for purchase. One costs more to buy but less to operate as shown below. Both are expected to last 10 years.

	Refrigerator A	Refrigerator B
Purchase Price	$840	$700
Annual Operating
Cost (in each year):	$100	$120

Which is the cheaper source of refrigeration over a ten-year period? Does the prevailing interest rate affect your answer? (Hint: calculate the answer using 3% and again using 12%.)

Answer 1

To determine the cheaper source of refrigeration we will compute NPV (net present value) of the costs.

Purchase price is paid immediatley and I am assuming that annual operating cost occurs at the end of each year.

Calculations using 3% rate:

Refrigerator A						Refrigerator B
Year	Cash flow	1+r	PVIF	PV		Year	Cash flow	1+r	PVIF	PV
0	840.00	1.03	1.0000	840.00		0	700.00	1.03	1.0000	700.00
1	100.00		0.9709	97.09		1	120.00		0.9709	116.50
2	100.00		0.9426	94.26		2	120.00		0.9426	113.11
3	100.00		0.9151	91.51		3	120.00		0.9151	109.82
4	100.00		0.8885	88.85		4	120.00		0.8885	106.62
5	100.00		0.8626	86.26		5	120.00		0.8626	103.51
6	100.00		0.8375	83.75		6	120.00		0.8375	100.50
7	100.00		0.8131	81.31		7	120.00		0.8131	97.57
8	100.00		0.7894	78.94		8	120.00		0.7894	94.73
9	100.00		0.7664	76.64		9	120.00		0.7664	91.97
10	100.00		0.7441	74.41		10	120.00		0.7441	89.29
			Total	1,693.02					Total	1,723.62

Thus Refrigerator A has a lower total cost.

Calculations using 12%:

Refrigerator A						Refrigerator B
Year	Cash flow	1+r	PVIF	PV		Year	Cash flow	1+r	PVIF	PV
0	840.00	1.12	1.0000	840.00		0	700.00	1.12	1.0000	700.00
1	100.00		0.8929	89.29		1	120.00		0.8929	107.14
2	100.00		0.7972	79.72		2	120.00		0.7972	95.66
3	100.00		0.7118	71.18		3	120.00		0.7118	85.41
4	100.00		0.6355	63.55		4	120.00		0.6355	76.26
5	100.00		0.5674	56.74		5	120.00		0.5674	68.09
6	100.00		0.5066	50.66		6	120.00		0.5066	60.80
7	100.00		0.4523	45.23		7	120.00		0.4523	54.28
8	100.00		0.4039	40.39		8	120.00		0.4039	48.47
9	100.00		0.3606	36.06		9	120.00		0.3606	43.27
10	100.00		0.3220	32.20		10	120.00		0.3220	38.64
			Total	1,405.02					Total	1,378.03

At 12% it is Refrigerator B that has a lower total cost.

Thus the cheaper source of refrigeration is Refrigerator A at 3%.

The  cheaper source of refrigeration is Refrigerator B at 12%.