Question

Assume you are preparing to move into a new neighborhood. You are considering renting or buying. Here are the information for the renting and buying option.Renting OptionYou are expected to pay $500 per month for the first year, and rent will increase by $50 per month per year for the next 15 years (e.g., $550 per month for the 2nd year, $600 per month for the 3rd year, etc.). Prepare a schedule showing rent payments for the next 15 years. To simplify the problem, assume rent is paid annually at the end of each year. Discount rate is 5%. Buying OptionAnnual payments for the next 15 years will be $10,200 (at the end of each year). Calculate the present value of the buying option, using 5% as the discount rate.

1) Determine the present value of the renting option (rounded to the nearest dollar).

2) Determine the present value of the buying option (rounded to the nearest dollar).

3) Based your calculation, which option is preferred? Any other considerations you think should be considered in the real world?

Answer 1

a.Computation of present vale of Rent option
Year	Per month Rent	Annual Rent	PV factor	Present Value
1	500	6000	0.952	5714.29
2	550	6600	0.907	5986.39
3	600	7200	0.864	6219.63
4	650	7800	0.823	6417.08
5	700	8400	0.784	6581.62
6	750	9000	0.746	6715.94
7	800	9600	0.711	6822.54
8	850	10200	0.677	6903.76
9	900	10800	0.645	6961.78
10	950	11400	0.614	6998.61
11	1000	12000	0.585	7016.15
12	1050	12600	0.557	7016.15
13	1100	13200	0.530	7000.24
14	1150	13800	0.505	6969.94
15	1200	14400	0.481	6926.65
			Total	1,00,250.77

b.Computation of present vale of Buy option
Year	Annual Payments	PV factor	Present Value
1	10200	0.952	9,714.29
2	10200	0.907	9,251.70
3	10200	0.864	8,811.14
4	10200	0.823	8,391.57
5	10200	0.784	7,991.97
6	10200	0.746	7,611.40
7	10200	0.711	7,248.95
8	10200	0.677	6,903.76
9	10200	0.645	6,575.01
10	10200	0.614	6,261.92
11	10200	0.585	5,963.73
12	10200	0.557	5,679.74
13	10200	0.530	5,409.28
14	10200	0.505	5,151.69
15	10200	0.481	4,906.37
		Total	1,05,872.51

C. Based on the above working, It is clearly Evident that its better to take property on Rent as present value of Rent option is lower by $5621 as compared to present value of buy option if we consider only on the basis of financial considerations.

But if we consider real life scenario , by opting buy option we could get depreciation on that buidling if that building is used for business purpose.