Please analyze from the perspective of finance the choice of

Please analyze, from the perspective of finance, the choice of buying a house vs renting an apartment. To make a quantitative analysis, suppose you have collected the following information: 1. If you rent a 1,000 sq. ft two-bedroom apartment in RTP area, your monthly rent will be $900. The apartment is in move-in condition. You won\'t have any upfront expenses when you move in 2. If you want to buy a house, a 2,000 sq. ft three-bedroom townhouse in RTP area is sold at $200,000. To get your application for mortgage approved by a bank, you need to pay 20% (40,000) down payment. In addition, there is $2,000 closing cost. Your mortgage bank gives you two offers for mortgage. Offer one is a 30-years fixed-rate mortgage at 3.88% (5,540/year) APR. Offer two is a five-year floating- rate mortgage, ARM 5/1, at 2.88% interest rate (32,922/year) 3. A townhouse owner needs to pay $80 HOA (960/year) fee each month. In addition, the property tax and house insurance together are about 1.5% (3,000/year) of house value.

Solution

As per the assumption consider that after 5 years the property if buyed will be sell by the owner with opportunity cost of 8%

Your formula to calculate the present value of cash flows is PV= (1/1+R)^N

Your inputs are correct but the formula stood what said above and also you have taken $900 per year to calculate the annuity value which is not correct as the $900 is per month rent, accordingly the rent per annum will be $10800

Therefore the calculation for the outflow of rental value for the period of Five years will be

Rent per annum = $10800

PVAF which is total of {( 1/1.08)¹ + (1/1.08)² + (1/1.08)³ ............+(1/1.08)⁵ }for period of Five years will be = 3.993 taking 3 decimal value

PVAF of Rental outflow = 10800*3.993= 43124.40

Now,

If you buy the house the option will be calculated as under

Present value of the House to purchase is $ 200000

Considereing inflation to be 3% for the next five years i.e. 3% each year then the value of the house after 5 years will be = 200000(1+3/100)⁵ = $ 231855

Outflow of the cash will be as under for the next five years:-

Year Outflow ($) PVF Present Value of the Outflow Amount

0 42000(40000+2000) 1 42000

1-5 (3000+(80*12=960)=3960) 3.993 15812.28

5 6000 0.681 4086

5 (231855) 0.681 (157893.26) negative as its inflow of sale

Option I

Fixed Rate Mortgage per year = $5540

PVAF of 5 years= $ 5540*3.993= 22121.22

Balance Mortgage amount left to be paid = 5540*30=166200-27700(5540*5)=138500

PVF of balance amount $ 138500 as on today = 138500*.681= 94318.50

Total outflow of the cash if buying the house at Fixed Mortgage Rate

= 42000+15812.28+4086+22121.22+94318.50-157893.26

=20444.74

Option II

Floating Rate Mortgage per year = $ 32922

PVAF of Mortgage for period of Five years= 32922*3.993= 131457.546

Total outflow of the cash if buying the house at Floating Mortgage Rate

=42000+15812.28+4086+131457.546-157893.26

=35462.57

Option i is better for buying i.e. 30 years of Fixed Mortgage Rate

From cash outflow Rental $41923.46 or Buying $20444.74

Buying is better than rental at the opportunity cost of 8%