Question

Alicia (first time home buyer) is looking to buy one bed-room condo, and she needs your advice on the maximum price she can afford to offer for her condo purchase when she buys one. She plans to use her savings to pay for the down payment at 20% of purchase amount, and she will get a mortgage for the remaining.

The following info is available: • Mortgage interest rate: 2.40% compounded semi-annually (25-year mortgage amortization with fixed rate for 5 years with same monthly mortgage payment) • Alicia’s annual income is CAD 90,000. • Alicia qualifies for Gross Debt Ratio (GDS) of 35%, and with this GDS ratio she can afford CAD 2,250 for her monthly mortgage payment. •

Financial institutions use stress test rate of 4.94% to qualify for maximum mortgage loan one can borrow.

1. What maximum price Alicia can afford to offer for her condo purchase, assuming there is no stress test.

2. If Alicia buys a condo with her maximum amount calculated in 1, what would be the total interest for the first year?

3. Do you think stress test is helpful for Alicia? Explain.

Answer 1

Annual interest rate of 2.4% compounded semi annually is equivalent to monthly rate of 0.199007% a follows:

Part 1:

Given, maximum affordable monthly mortgage payment as per GDS ratio is CAD 2,250. With this, maximum mortgage eligible is $507,898.93 calculated using PV function of Excel.

Accordingly, maximum price together with down payment is CAD 634,873.66

Calculations as follows:

Part 2:

Total interest for year 1, with the loan amount as in part 1= CAD 11,965.22 calculated using CUMIPMT function of Excel as follows:

Part 3:

Stress test rate indicates the upper interest rate that might be expected in future and accordingly, the mortgage to be reduced so that the same can be serviced. As a result, if the stress test rate is applied, Alicia’s mortgage will have to be reduced.

In case the given stress test rate of 4.94% is compounded monthly, maximum eligible mortgage with monthly payments of CAD 2,250 will be CAD 387,196.95 only. As a result, maximum price affordable will be lower at CAD 483,996.19. This shows that Stress Test is not helpful for the purchase transaction. But it will be helpful in the planning for debt servicing in future.

Calculation as follows: