Question

Sarah would like to purchase a condo in Vancouver. She currently rents an apartment for $4,500 per month. The condo she is looking at costs $1,600,000. She intends to put $300,000 down. The condo has monthly condo fees of $300/month, property taxes of $200/month and repairs of $100/month. She can obtain a 30-year mortgage for 3% per year compounded monthly.

There are the following closing costs at purchase:

Land transfer tax $20,000

Legal fees $1,500

There are the following closing costs when selling:

Real estate commission of 3% of selling price

Legal fees $2,000

(a) What is the principal outstanding for the loan after 10 years? (Calculate the value at year 10 of the remaining 20 years of mortgage payments)

(b) Compute the cost (NPV) under buying and renting over the next 10 years assuming the unit is sold in 10 years for $1,800,000 and rent stays constant. Is it better to rent or buy? Upon sale, you will need to pay off the outstanding loan balance (see part a).

Answer 1

Using equated monthly installement formula

EMI= [P x R x (1+R)^N]/[(1+R)^N-1]

a)Hence, Monthly EMI=$5,481 and principal at the end of 10th year=$9,88,258

Calculation of schedule for loan
Year	Principal	Interest	Total Payment	Balance	Loan Paid To Date
Principal	Interest	(A + B)
2020	$18,004	$25,843	$43,847	$12,81,996	1.38%
2021	$27,689	$38,081	$65,770	$12,54,307	3.51%
2022	$28,531	$37,239	$65,770	$12,25,776	5.71%
2023	$29,399	$36,371	$65,770	$11,96,377	7.97%
2024	$30,293	$35,477	$65,770	$11,66,084	10.30%
2025	$31,215	$34,556	$65,770	$11,34,869	12.70%
2026	$32,164	$33,606	$65,770	$11,02,705	15.18%
2027	$33,142	$32,628	$65,770	$10,69,563	17.73%
2028	$34,150	$31,620	$65,770	$10,35,413	20.35%
2029	$35,189	$30,581	$65,770	$10,00,223	23.06%
2030	$36,259	$29,511	$65,770	$9,63,964	25.85%
Jan	$2,980	$2,501	$5,481	$9,97,243	23.29%
Feb	$2,988	$2,493	$5,481	$9,94,255	23.52%
Mar	$2,995	$2,486	$5,481	$9,91,260	23.75%
Apr	$3,003	$2,478	$5,481	$9,88,258	23.98%
May	$3,010	$2,471	$5,481	$9,85,247	24.21%

b) Calculation of cash outflows under buy option

Year	0	1	2	3	4	5	6	7	8	9	10
Ouflows under buy option	300000	Monthly ouflow of $600 for all months for condo fees, property tax and repairs+5481 as monthly EMI's
Land transfer tax	20000
Legal fees	1500
Selling price											-1800000
Legal fees											2000
Real estate commission(3%)											54000
Oustanding loan											988258

Present cash value of cash outflows is $-390,164.38

Calculation of cash outflows under rent option
Year	0	1	2	3	4	5	6	7	8	9	10
		Monthly outflow of $5100 each month for 10 years
Present value of cash outflows is $-529,178.40

Buying option is more profitable since it has a better NPV of $(390164.38) over rent option which has NPV of $(529178.40)