Question

Jane wishes to buy a house for 150,000 and arrange for the maximum possible conventional loan (hint: what is the LVR?). The lending value assessed by the lender is the same as the purchase price. Jane wants the loan to be amortized over 25 years with monthly payments. Mortgage contract rate j2=4.56% and Bank of Canada 5-year posted fixed rate j2 =8%. Property taxes for the house are 1200/year and heating costs are estimated 60/month. Jane and her husband make a combined income of 60,000 a year. For the couple, they have to make a car loan payment of 350/month and credit card loan payment of 250/month.

(a) For qualification purpose, what mortgage rate to use? Why?

(b) What are the GDS and TDS ratios for the couple?

(c) Based on (a), will the couple qualify for the mortgage?

(d) What is the maximum size of the loan they qualify for using GDS? and using TDS?

(e) Suppose they’ve saved 60,000 for down payment, what is their affordable house purchase price using GDS? and using TD

Answer 1

(a) For qualification purpose, what mortgage rate to use? Why?

For the qualification purpose, the bank uses "Benchmark Qualifying Rate" which is the posted 5-year fixed rate, published by the Bank of Canada. In this question, for qualification purpose, the mortgage rate to use = Bank of Canada 5-year posted fixed rate = 8%

(b) What are the GDS and TDS ratios for the couple?

For debt service ratios, we will have to first estimate the house mortgage servicing amount at the qualifying rate.

For the purpose of debt ratios calculations,

Assessed value = Purchase price = $ 150,000

Maximum LVR under conventional mortgage = 80%

Hence, loan amount = 80% x $ 150,000 = $ 120,000

Frequency = monthly

Interest rate per annum = Qualifying rate = 8%

Interest rate per period = interest rate per month = 8%/12 = 0.667%

Period of loan = nos. of month in 25 years = 12 x 25 = 300

Hence, monthly house mortgage payment required: We will calculate this using the PMT function of excel. Inputs for PMT function are : PMT(Rate, Period, PV) = PMT(0.667%, 300, -120000) = $926.18

GDS ratio = the percentage of income needed to pay monthly housing costs (this includes principal, interest, taxes, and heat)

Combined annual income =  $ 60,000

Hence, combined monthly income = 60,000 / 12 = $ 5,000

Property tax = 1,200 / year = 1,200 / 12 = $ 100 / month

Heat expenses = $ 60 / month

Hence, total expenses towards monthly housing cost = monthly house mortgage expense + property tax + heat = 926.18 + 100 + 60 = $1,086.18

GDS ratio = the percentage of income needed to pay monthly housing costs (this includes principal, interest, taxes, and heat) = 1,086.18 / combined monthly income = 1,086.18 / 5,000 = 21.72%

TDS ratio = percentage of income needed to cover all debts = (Monthly payment towards house + Credit card + car loan) / combined monthly income = (1,086.18 + 250 + 350) / 5,000 = 33.72%

(c) Based on (a), will the couple qualify for the mortgage?

Standard criteria for qualification:

GDS < 35% and TDS < 42%

Since both the criteria are met, the couple do qualify for the loan upto 80% of assessed value.

(d) What is the maximum size of the loan they qualify for using GDS? and using TDS?

Maximum housing expenses per month permissible under GDS of 35% = Monthly income x 35% = 5,000 x 35% =  1,750.00

Maximum house mortgage amount per month permissible = 1,750 - property tax - heat expenses= 1,750 - 100 - 60 = $ 1,590

Maximum size of loan they qualify for using GDS = PV of an annuity of $ 1,590 = PV(rate, period, payment) = PV(0.667%, 300, 1590) = $ 206,008

Using TDS, maximum debt expense permissible = 42% x monthly income = 42% x 5,000 = $ 2,100

Maximum house mortgage payment per month permissible = $ 2,100 - property tax of 100 - heat expense of 60 - credit card loan of 250 - car loan of 350 = $ 1,340

Maximum size of loan they qualify for using TDS = PV of an annuity of $ 1,340 = PV(rate, period, payment) = PV(0.667%, 300, 1340) = $  173,616

(e) Suppose they’ve saved 60,000 for down payment, what is their affordable house purchase price using GDS? and using TDS

Using GDS, maximum loan permissible = $ 206,008

Down payment = $ 60,000

Affordable house price= down payment + loan permissible = 60,000 + 206,008 = $ 266,008

Using TDS, maximum loan permissible = $ 173,616

Down payment = $ 60,000

Affordable house price= down payment + loan permissible = 60,000 + 173,616 = $  233,616