Assume a lease for a condo asks for rent of $2,500 per month, paid at the...

Assume a lease for a condo asks for rent of $2,500 per month, paid at the start of each month, and rent is set to increase by 3% every year. Furthermore, assume the current purchase price of that same condo is $500,000, with maintenance fees & taxes currently at $10,000 per year, and increasing annually at a rate of 4%, where fees & taxes are paid at the end of each year. Finally, let the applicable nominal annual interest rate be 3%, compounded monthly. Calculate the present value of the associated expenses over the next 25 years, for

a) renting, or

b) buying the condo (i.e. paying price + fees & taxes).

Expert Solution

Given:

Rate : Compounded monthly @ 3% p.a.

Rate: Compounded annually = (1 + 0.03/12)¹² –1 = 1.0304 – 1 = 0.0304 or 3.04%

a. Rent option

Rent Option
Year	Monthly payments	PV Factors @ 3% p.a. compounded monthly	Present Value ofCash Flows
1	2500.00	11.81	29518.1346
2	2575.00	11.46	29506.21876
3	2652.25	11.12	29494.30773
4	2731.82	10.79	29482.40151
5	2813.77	10.47	29470.50009
6	2898.19	10.16	29458.60348
7	2985.13	9.86	29446.71167
8	3074.68	9.57	29434.82467
10	3166.93	9.29	29422.94246
11	3261.93	9.02	29411.06504
12	3359.79	8.75	29399.19242
13	3460.58	8.49	29387.3246
14	3564.40	8.24	29375.46156
15	3671.33	8.00	29363.60332
16	3781.47	7.76	29351.74986
17	3894.92	7.53	29339.90118
18	4011.77	7.09	28462.34775
19	4132.12	6.89	28450.85811
20	4256.08	6.68	28439.3731
21	4383.77	6.48	28427.89273
22	4515.28	6.29	28416.417
23	4650.74	6.11	28404.9459
24	4790.26	5.93	28393.47943
25	4933.97	5.75	28382.01759
PV of Total Cash Flows	698240.2746

b. Purchase Option

Purchase Option
Year	Purchase Cost	Maintenace Cost	PV factor @ 3.04% p.a	Present value of Cahs outflows
0	500000	0	1	500000
1		10000	0.970496894	9704.97
2		10400	0.941864222	9795.39
3		10816	0.914076302	9886.65
4		11248.64	0.887108213	9978.76
5		11698.5856	0.860935766	10071.73
6		12166.52902	0.835535487	10165.57
7		12653.19018	0.810884595	10260.28
8		13159.31779	0.786960981	10355.87
9		13685.6905	0.763743188	10452.35
10		14233.11812	0.741210392	10549.74
11		14802.44285	0.719342384	10648.02
12		15394.54056	0.69811955	10747.23
13		16010.32219	0.677522855	10847.36
14		16650.73507	0.657533826	10948.42
15		17316.76448	0.638134537	11050.43
16		18009.43506	0.619307586	11153.38
17		18729.81246	0.601036089	11257.29
18		19479.00496	0.583303658	11362.17
19		20258.16515	0.566094388	11468.03
20		21068.49176	0.549392846	11574.88
21		21911.23143	0.533184051	11682.72
22		22787.68069	0.517453465	11791.56
23		23699.18792	0.502186981	11901.42
24		24647.15543	0.487370906	12012.31
25		25633.04165	0.47299195	12124.22
Total PV of Cash flows	771790.76

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