Real Estate: The BUY vs. RENT Decision

On a crisp morning in February 2022, Julianne Chant was sitting in her chair and enjoying the quiet in her office before a busy day. Turning her chair toward the window, she let her mind drift while sipping a cup of coffee. On the desk behind her lay a piece of paper filled with numbers and calculations. It was the result of a long discussion the night before with her partner of three years, Thomas Wright. They were debating whether they should continue to rent an apartment or could afford to buy their own condominium (condo).

The previous spring, the couple had graduated from the University of Victorias Gustavson School of Business on Canadas west coast. They had both secured good jobs and were finally starting to save money. Having taken the same finance course, they were familiar with the concepts of time value of money, budgeting, and investing. Their finance professor had stressed the importance of compounding, and investing early to allow their wealth to build over time. But both Julianne and Thomas had student loans to pay off. Interest rates were expected to rise, which might cause stock prices and real estate to fall in the coming years. Was now the time to stop paying someone elses mortgage and pay off their own? Or should they continue to rent and invest their monthly savings in the stock market index using an exchange traded fund (ETF)?

A COZY ONE-BEDROOM OF THEIR OWN

Owning an place of her own had always been Juliannes dream but Thomas was sceptical. While in university, they had watched Victoria real estate prices rise steadily. Rents had risen too due to the housing shortage, but had not gone up as much. Julianne had been following real estate listings every morning over her coffee and one had caught her eye yesterday. It was a cozy, one-bedroom condo in a good neighbourhood, with a decent view and only a short walk to the ocean. Browsing the pictures online, she already knew how she wanted the place to look. If they bought a condo, she mused, their monthly rent would go towards paying down a mortgage and accumulating equity in a place of their own, instead of down the drain. But could they afford it, particularly in this hot real estate market?

Unfortunately the pair did not have any savings yet. But wanting to help them out, Juliannes parents had offered to lend the couple the down payment. They suggested that Julianne and Thomas could pay it back in monthly instalments over the next five years. Her parents would charge them the same interest rate they were receiving on a savings account. A university classmate who had recently purchased a place recommended putting down 20% of the sale price to avoid costly and mandatory mortgage insurance. To make the monthly payments more affordable, her friend had opted for a 30-year amortization on the mortgage and monthly payments, with the interest rate fixed for an initial term of five years. Julianne remembered that mortgages in Canada were compounded semi-annually but paid monthly, so she would have to figure out the effective rate when calculating the monthly payment.

A big concern was their student loans. As graduates with paying jobs, these loans began charging interest and needed to be paid off. Julianne planned to pay her loan back over two years. Her loan had a fixed monthly payment with interest compounded quarterly. The annual percentage rate, or APR, on the loan included any fees or other costs associated with the loan but did not take account of compounding. Thomas had made a couple of suboptimal spending decisions and had accumulated more student debt than Julianne. He was paying the same interest rate as her but would take an extra year to pay it off, or 36 months. Thomas had a car loan and was making monthly payments that compounded weekly. He planned to pay off his car loan over the next three years as well.

Julianne began entering all of these assumptions into Excel (Exhibit 1). She knew what monthly income each of them was taking home after taxes and other deductions. The bank called this net disposable income and would use it to assess whether they could qualify for a mortgage. She had the loan amounts. She had a monthly budget for food, utilities and other household expenses. She didnt include rent, however, because it would be compared later against the mortgage payment and other costs from buying. To keep things simple, Julianne decided to keep their incomes and expenses constant for the next five years. She could always change that assumption later.

Julianne created a table with the details for each of their loans, the mortgage, and the returns from investing. Each loan had slightly different terms: the quoted interest rate (or APR), the compounding frequency, the number of payment periods per year, and the time horizon for paying it off. She planned to use the built-in function PMT in Excel to calculate the monthly payment for each loan. It required five inputs: the present value of each loan (PV), the future value (FV), the number of periods (NPER), the effective interest rate (RATE), and the loan type (TYPE). She remembered her finance professor explaining that Excel did not know what each period represented; it could be years, quarters, months, weeks, or days. It was up to her to adjust several of the inputs in order for Excel to spit out the correct monthly payment. Each quoted interest rate had to be adjusted for compounding frequency (m) and number of payments per year (f). She could not remember the formula so looked it up in her finance textbook:

where QR = quoted rate (or APR), m = compounding frequency, and f = number of payments per year. She wanted to calculate the effective monthly rate, so the number of payments would be f=12. She decided to treat all loans as end of period compounding, which was the default setting in Excel (TYPE=0).

Building a Budget Table in Excel

With the monthly loan and mortgage payments laid out at the top of her spreadsheet, Julianne began to build a budget. She entered one month in each row for the next 5 years, numbered from 1 to 60. She added columns for their combined household income, their household expenses (excluding rent), and the payments on their student loans and car loan. The final column showed their Net disposable income, which was equal to household income minus household expenses and payments for the two student loans and car loan (Table 2).

She added four blocks to her Excel spreadsheet: one for the rent scenario, one for the buy scenario, one showing the amortization of the loans and mortgage, and one showing the equity that was accumulating in the condo due to principal repayments on the mortgage and loan from her parents.

Third, she would need to figure out how much equity they were saving in the condo by paying down the mortgage and loan from her parents. She needed to build an amortization table for the mortgage and the loan separately, and recalled that they had built one in class that she could use. By looking at the amounts paid down over five years, she would know how much equity had been added to the house.

Under the Scenario 1: Rent, Julianne calculated their cumulative savings over five years if they stayed where they were (Table 3). By deducting rent from their net disposable income each month, she could figure out their monthly savings. These monthly savings would be invested in an ETF at the start of the next month and hopefully grow over time. She would have to use an assumption for the return on a stock ETF over this time horizon. At the end of five years of renting, their cumulative savings would be the value of their ETF, consisting of the monthly contributions and any increase (or decrease) in the value of the ETF.

Next Julianne set up the Scenario 2: Buy and figured out their cumulative savings if they purchased a condo (Table 4). She would need to deduct the monthly mortgage payment, strata fee, property taxes and insurance. Of course, she would also have to factor in the repayment of the down payment borrowed from her parents. Again, any cumulative savings would be invested in an ETF and grow over time. Julianne set up columns for each of these items with the final column showing their cumulative savings. Again cumulative savings under this scenario was equal to monthly savings plus any increase in the value of the ETF over time.

Next, Julianne created an amortization table for the mortgage and the loan from her parents for the next five years (Table 5). The amortization table would show the principal outstanding at the start of each month, their monthly payment, the portion that was interest expense, the portion that was principal repaid on the mortgage, and the principal outstanding at the end of each month. She recalled that the principal repayment was actually a form of savings that increased their equity in the condo. But how could she figure out how much each month was interest and how much was principal? Her class notes showed that the interest expense was calculated as the principal outstanding at the start of each month times the effective monthly rate on the mortgage. By deducting this interest expense from the monthly payment, Julianne realized she could back out how much of the mortgage was repaid. The principal outstanding at the end of the month was simply the beginning principal less the principal repaid. Given that the mortgage would be repaid over 30 years, she wondered how much would be outstanding at the end of five years?

Julianne built out a second amortization table for the loan from her parents. This loan would be fully paid off over five years. Julianne knew that if she built the table correctly, the principal outstanding at the end of 60 months would be $0. If it wasnt, there was a mistake somewhere.

Once she had the two amortization tables, she had the numbers she needed to figure out how much equity they were saving in the condo. She could figure this out one of two ways:

She could add up the principal repayments over five years on both the mortgage and the loan. This total represented their increased equity in the condo.

If she assumed the condo price had not changed, she could deduct the principal outstanding on the mortgage and the loan at the end of five years from the original amount borrowed.

Realizing that both approaches should give her the same value, Julianne decided to follow the first method and added these columns to her spreadsheet (Table 6).

After working sporadically on her spreadsheet throughout her work day, Julianne saw that it was time to head home. She knew she had most of the calculations needed for her conversation with Thomas that evening. There were still a few pieces she hadnt quite figured out. She needed to figure out which scenario would generate the most wealth over five years. She had columns showing the cumulative savings for the rent vs. buy scenarios, and another showing the cumulative equity saved in the house, but she had been too rushed to add them together. Another problem worried her. Thomas was bound to ask what would happen if real estate prices dropped over the next five years? There had to be a way to use her spreadsheet to figure out the breakeven between the two scenarios that would lead to the same wealth if real estate prices fell. Her clock showed it was time to go. Her cozy one-bedroom would not stay on the market long, so they needed to have this conversation tonight. They would just have to figure out the last few questions together just like any other team assignment from their university days.

Summary of the task:

1) Fill all the above tables and answer the following questions:

2) What is their combined net disposable income excluding rent?

3) What are cumulative savings, at the end of the five years, under the Rent scenario?

4) Under the Buy scenario, what are the cumulative savings after five years?

5) How much principal do they still owe on the mortgage after five years?

6) How much wealth they have in each scenario? (Wealth=Cumulative Savings + House Equity)

7) Same question as 6, but if the condo value drops by 15%.

8) At what percentage drop in condo value would they be indifferent between the two choices, Rent or Buy?

Each team has slightly different numbers, so please find your team # first.

TEAM	8
ASSUMPTIONS
Julianne monthly net income ($)	3,811
Thomas monthly net income ($)	3,606
Household expenses ($)	2,170
Monthly Rent ($)	1,668
Condo Price ($)	491,000
Down payment ($)	20%
Monthly Strata Fee ($)	195
Monthly Taxes and Insurance ($)	302
Julianne Student Loan ($)	12,000
Thomas Student Loan ($)	15,000
Thomas Car Loan ($)	7,500
Julianne Student Loan (APR %)	5.10%
Thomas Student Loan (APR %)	4.90%
Thomas Car Loan (APR %)	6.30%
Mortgage (APR %)	3.60%
Loan from Parents (APR %)	2.10%
Return on ETF (%)	8.00%
Expected change in real estate (%)	-15%