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 #4).

Answer 1

a) Loan amount = $1,600,000 - $300,000 = $1,300,000

Interest rate per month = 3%/12 = 0.0025

No. of payments = 30*12 = 360

The Loan payments (P) is given by

P/0.0025*(1-1/1.0025^360) = 1300000

=> P = $5480.85

So, loan outstanding after 10 years

= 5480.85/0.0025 * (1-1/1.0025^240) = $988257.51

b) Under Renting, monthly expenses =$4500

So, NPV under renting= -4500/0.0025*(1-1/1.0025^120) = - $466027.89

Under Buying

Initial Expenses = $300000 + $20000+ $1500 = $321500

Monthly expenses =$5480.85+$300+$200+$100 =$6080.85

Closing expenses = 3% of $1800000 + $2000 + Outstanding loan

=$54000+$2000+$988257.51 =$1,044,257.51

So, NPV of Buying

= - 321500 - 6080.85/0.0025*(1-1/1.0025^120) - 1044257.51 + 1800000

= - $195501

As NPV of buying is less negative than Renting , buying the condo will be cheaper than Renting

So, it is better to buy