Question

In: Finance

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).

Solutions

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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