chapter 13 gross debt Flashcards
Jordon Liu has just been hired for a new job, which pays an annual salary of $50,000. Jordon would like to purchase a home closer to the new workplace, and requires a loan of $200,000 over a 25-year amortization period with monthly payments. Property taxes are $1,500 per annum and the market interest rate is 5.45% per annum, compounded semi-annually. What is the gross debt service ratio?
- 32.16%
- 29.59%
- 39.42%
- 26.35%
Correct Answer: 1
Option (1) is correct because the GDSR is 32.16%. This question solves for the GDSR, given the loan amount, property taxes, and borrower’s income. First, the monthly loan payment must be calculated. The monthly loan payment is then multiplied by 12 to determine the annual mortgage payments. Then add the property taxes to this amount and divide the total by the borrower’s annual salary in order to derive the GDSR.
PRESS
DISPLAY
5.45 ⬛ NOM%
5.45
2 ⬛ P/YR
2
⬛ EFF%
5.524256
12 ⬛ P/YR
12
⬛ NOM%
5.389131
200000 PV
200,000
25 × 12 = N
300
0 FV
0
PMT
−1,214.968222
1214.97 × 12 =
14,579.64
+ 1500 =
16,079.64
÷ 50000 =
0.321593
A lender is reviewing a borrower’s mortgage loan application. The borrower has an annual income of $75,000, first mortgage payments of $1,500 per month, car payments of $500 per month, and annual property taxes of $3,000. Which one of the following provides the correct gross debt service ratio (GDSR) and total debt service ratio (TDSR) for this borrower?
- GDSR = 25%; TDSR = 33%
- GDSR = 26%; TDSR = 34%
- GDSR = 27%; TDSR = 35%
- GDSR = 28%; TDSR = 36%
Correct Answer: 4
Option (4) is correct because the GDSR is 28% and the TDSR is 36%.
GDSR = PIT ÷ Gross Income
GDSR = [($1,500 × 12) + $3,000] ÷ $75,000
GDSR = 28%
TDSR = (PIT + Other Debt)¸ Gross Income
TDSR = [(($1,500 + $500) × 12) + $3,000] ÷ $75,000
TDSR = 36%
Which one of the following statements regarding lending constraints is TRUE?
- For insured mortgage loans, the maximum loan-to-value ratio is set by statute at 80% for federally chartered financial institutions.
- The total debt service ratio does not consider other debt obligations of the borrower.
- A lender’s primary concern is ensuring they receive an above-market yield.
- The gross debt service ratio is usually defined as the ratio of the sum of the annual mortgage payments (principal and interest) and annual real property taxes to annual gross income.
Correct Answer: 4
Option (4) is correct because the gross debt service ratio is usually defined as the ratio of the sum of the annual mortgage payments (principal and interest) and annual real property taxes to annual gross income. Option (1) is incorrect because the maximum loan-to-value ratio is set by statute at 80% for uninsured mortgage loans. With mortgage loan insurance, borrowers may obtain up to 95% as the maximum loan-to-value ratio. Option (2) is incorrect because the total debt service ratio includes other debt obligations of the borrower, e.g., additional financing, car payments, maintenance fees, and credit card payments. Option (3) is incorrect because a lender’s primary concern is default. In order to obtain protection against default, lenders can restrict the loan so that only a specified portion of the borrower’s income will be needed to repay the mortgage debt.
A ballet dancer has recently moved to Vancouver to work for the BC Ballet Company and has applied to a local bank for a mortgage loan to finance a $400,000 condominium purchase in Vancouver. The borrower’s income is $65,000 per year. The bank will apply a 39% gross debt service ratio when calculating the maximum loan. Current mortgage rates are 4.25% per annum, compounded semi-annually for 25-year amortization mortgages and the government-specified qualifying rate is 5.25% per annum, compounded semi-annually. Annual property taxes are $3,990 and mortgage payments are to be made monthly. What is the maximum mortgage loan the bank will grant, given the stress test borrower qualification rules for uninsured mortgages? Round your final answer to the nearest dollar.
- $298,699
- $201,534
- $329,877
- $271,863
Correct Answer: 4
Option (4) is correct because the maximum mortgage is $271,863. The maximum loan under the GDSR constraint must be determined. To determine the allowable annual mortgage payments, multiply the borrower’s annual income ($65,000) by the GDSR (0.39) and deduct the annual property taxes for the year ($3,990). This yields total allowable mortgage payments for the year of $21,360, or monthly payments of $1,780. The minimum qualifying rate is based on the greater of the government-specified qualifying rate of j2 = 5.25% or the contract rate plus 2%. In this case, apply a rate of j2 = 6.25% (2% + 4.25%), which is greater than the government-specified rate of j2 = 5.25%.
P + I = (GDSR × Gross Income) – Property Taxes
P + I = (0.39 × $65,000) – $3,990
P + I = $21,360 per year = $1,780 per month
PRESS
DISPLAY
6.25 ⬛ NOM%
6.25
2 ⬛ P/YR
2
⬛ EFF%
6.347656
12 ⬛ P/YR
12
⬛ NOM%
6.17014
1780 +/– PMT
–1,780
25 × 12 = N
300
0 FV
0
PV
271,862.958902
Monthly payments of $1,780 over 25 years at an interest rate of j2 = 6.25% will repay a loan of $271,863, rounded.
A prospective home buyer has applied for a mortgage loan to finance the purchase of a townhouse listed at $485,000. The market value of the townhouse is $475,000 and the lender has assigned a $472,000 lending value to it. The lender demands a 35% gross debt service ratio and an 80% loan-to-value ratio. The purchaser’s annual income is $90,000, property taxes are $2,200 per annum and, if approved, the loan is to be repaid with monthly payments over 20 years. The interest rate is 5.75% per annum, compounded semi-annually (j2 = 5.75%).
Calculate the maximum loan allowable under the lender’s loan-to-value criterion. Round your final answer to the nearest $100.
- $377,600
- $388,400
- $300,200
- $355,500
Correct Answer: 1
Option (1) is correct because the maximum loan allowable under the loan-to-value ratio is $377,600. The maximum loan under the loan-to-value ratio is 80% of the lending value. With a loan-to-value ratio of 80% and a lending value of $472,000, the maximum loan is $377,600.
0.8 × $472,000 = $377,600
A prospective home buyer has applied for a mortgage loan to finance the purchase of a townhouse listed at $485,000. The market value of the townhouse is $475,000 and the lender has assigned a $472,000 lending value to it. The lender demands a 35% gross debt service ratio and an 80% loan-to-value ratio. The purchaser’s annual income is $90,000, property taxes are $2,200 per annum and, if approved, the loan is to be repaid with monthly payments over 20 years. The interest rate is 5.75% per annum, compounded semi-annually (j2 = 5.75%).
Calculate the size of the monthly payment necessary to fully amortize the maximum loan amount based on the loan-to-value ratio (from the previous question).
- $2,935.51
- $2,636.50
- $2,381.02
- $2,464.22
Correct Answer: 2
Option (2) is correct because the monthly payment is $2,636.50. With a lending value of $377,600, the monthly payment is calculated as follows:
PRESS
DISPLAY
5.75 ⬛ NOM%
5.75
2 ⬛ P/YR
2
⬛ EFF%
5.832656
12 ⬛ P/YR
12
⬛ NOM%
5.682306
377600 PV
377,600
20 × 12 = N
240
0 FV
0
PMT
−2,636.495693
A prospective home buyer has applied for a mortgage loan to finance the purchase of a townhouse listed at $485,000. The market value of the townhouse is $475,000 and the lender has assigned a $472,000 lending value to it. The lender demands a 35% gross debt service ratio and an 80% loan-to-value ratio. The purchaser’s annual income is $90,000, property taxes are $2,200 per annum and, if approved, the loan is to be repaid with monthly payments over 20 years. The interest rate is 5.75% per annum, compounded semi-annually (j2 = 5.75%).
Assume that the monthly payments on the borrower’s loan are agreed to be $2,500. Calculate the minimum level of borrower’s income necessary to support these monthly payments based on the lender’s gross debt service ratio of 35%.
- $92,000
- $75,200
- $85,100
- $95,000
Correct Answer: 1
Option (1) is correct because the minimum income required is $92,000. Find the minimum borrower’s income necessary given the monthly payments of $2,500 and annual property taxes of $2,200.
Minimum income = PIT ÷ GDSR
Minimum income = [($2,500 × 12) + $2,200] ÷ 0.35
Minimum income = $32,200 ÷ 0.35
Minimum income = $92,000
A borrower has applied to XYZ Bank for a mortgage loan to finance the purchase of a $1,200,000 home in Vancouver. The bank has supplied the following information:
Lending Value:
$1,200,000
Loan-to-Value Ratio:
80%
Gross Debt Service Ratio:
39%
Amortization Period:
20 years
Payment Terms:
Monthly
Property Taxes:
$5,000 per year
Current mortgage rates are 5% per annum, compounded semi-annually and the government-specified qualifying rate is 5.25% per annum, compounded semi-annually. If the borrower’s annual gross income is $185,000 per year, what is the maximum loan, given the stress test borrower qualification rules for uninsured mortgages. Round your final answer to the nearest dollar.
- $601,730
- $960,000
- $727,382
- $892,116
Correct Answer: 3
Option (3) is correct because the maximum loan is $727,382 under the GDSR.
Loan-to-Value Ratio Constraint
Maximum Loan = Loan-to-Value Ratio × Lending Value
Maximum Loan = 0.80 × $1,200,000 = $960,000
Gross Debt Service Ratio Constraint
→
P + I = (0.39 × $185,000) − $5,000
P + I = $67,150 (annual mortgage payment)
Since the loan states that monthly payments are required:
Maximum monthly mortgage payment = $67,150 ÷ 12 = $5,595.83
The minimum qualifying rate is based on the greater of (1) the government-specified qualifying rate of j2 = 5.25% OR (2) an additional 2% above the mortgage’s negotiated contract rate. In this case, you would apply a rate of j2 = 7% (2% + 5%), which is greater than the government-specified rate of j2 = 5.25%. Monthly payments of $5,595.83 over 20 years at an interest rate of j2 = 7% will repay a loan of $727,382, rounded.
PRESS
DISPLAY
7 ⬛ NOM%
7
2 ⬛ P/YR
2
⬛ EFF%
7.1225
12 ⬛ P/YR
12
⬛ NOM%
6.900047
5595.83 +/− PMT
−5,595.82
20 × 12 = N
240
0 FV
0
PV
727,382.378337
Maximum loan amount using loan-to-value ratio constraint = $960,000
Maximum loan amount using gross debt service ratio constraint = $727,382
The maximum loan is the lesser of the amounts calculated under the loan-to value ratio and the gross debt service ratio, which is $727,382 under the GDSR constraint.
A private lender is initiating a mortgage loan using an interest rate of 6.5% per annum, compounded semi-annually, over a 25-year amortization period, calling for monthly payments. The lender applies a 70% loan-to-value ratio and a 32% gross debt service ratio. A lending value of $275,000 has been assigned to the property. The borrower has an annual gross income of $55,000 and property taxes are $2,000 per annum. Given the above information, determine the down payment required if the purchase price is $275,000 and maximum financing is obtained.
- $75,000
- $193,081
- $154,000
- $82,500
Correct Answer: 4
Option (4) is correct because the down payment required is $82,500. Under the loan-to-value constraint, the maximum loan is $192,500 (0.70 × $275,000). Given a GDSR of 32%, the total allowable annual mortgage and tax payments are $17,600 ($55,000 × 0.32). Subtracting the property taxes gives maximum annual payments of principal and interest of $15,600, or $1,300 per month. Using a monthly payment of $1,300 and an interest rate of j2 = 6.5%, the maximum loan under GDSR is calculated as follows:
PRESS
DISPLAY
6.5 ⬛ NOM%
6.5
2 ⬛ P/YR
2
⬛ EFF%
6.605625
12 ⬛ P/YR
12
⬛ NOM%
6.413688
1300 +/– PMT
–1,300
25 × 12 = N
300
0 FV
0
PV
194,080.895181
The maximum allowable loan is $192,500 (the lesser of the loan-to-value and GDSR constraint). The down payment is determined by subtracting the maximum allowable loan from the required purchase price. The down payment required is $82,500 ($275,000 – $192,500).
