Question

For the business expansion, Atlas Corp. wants to purchase new equipment. Based on the 10% discount rate, there are 3 options:

1. Pay 100,000 at the beginning of the first year and then pay 120,000 semiannually for 4 years.

2. Pay 500,000 at the beginning of the third year and pay 800,000 at the end of the 8th year.

3. At the beginning of the 5th year, pay 300,000 annually for 4 years.

Which option should Atlas Corp choose?

Answer 1

Semi Annual Rate = 10/2 = 5%

1)

Period	Discounting Factor [1/(1.05^period)]	Cash Flow	PV of Cash Flow [Discounting Factor*Cash Flow]
0	1	100000	100000
1	0.952380952	120000	114285.7143
2	0.907029478	120000	108843.5374
3	0.863837599	120000	103660.5118
4	0.822702475	120000	98724.29698
5	0.783526166	120000	94023.13998
		Total PV =	619537.2005

2)

Period	Discounting Factor [1/(1.05^period)]	Cash Flow	PV of Cash Flow [Discounting Factor*Cash Flow]
0	1		0
1	0.952380952		0
2	0.907029478		0
3	0.863837599		0
4	0.822702475	500000	411351.2374
5	0.783526166		0
6	0.746215397		0
7	0.71068133		0
8	0.676839362		0
9	0.644608916		0
10	0.613913254		0
11	0.584679289		0
12	0.556837418		0
13	0.530321351		0
14	0.505067953		0
15	0.481017098		0
16	0.458111522	800000	366489.2176
		Total PV =	777840.455

3)

Period	Discounting Factor [1/(1.05^period)]	Cash Flow	PV of Cash Flow [Discounting Factor*Cash Flow]
0	1		0
1	0.952380952		0
2	0.907029478		0
3	0.863837599		0
4	0.822702475		0
5	0.783526166		0
6	0.746215397		0
7	0.71068133		0
8	0.676839362	300000	203051.8086
9	0.644608916		0
10	0.613913254	300000	184173.9761
11	0.584679289		0
12	0.556837418	300000	167051.2255
13	0.530321351		0
14	0.505067953	300000	151520.3859
		Total PV =	705797.396

Option with LEAST Total PV i.e. Option 1 should be chosen.