In: Finance
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).
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 |