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Strategic Financial Planning over the LifecycleChapter #5: Debts, Loans and Mortgages

Narat Charupat, Huaxiong Huang and Moshe A. Milevsky

Ch. #5: Lecture Notes

CHM (Cambridge 2012) Strategic FP over L Ch. #5: Lecture Notes 1 / 24

Agenda for Today

Main theme: Working with and understanding debt.

How much can you "save" by not-diversifying debts, and insteadconsolidating?

When does borrowing (even more) money to invest make sense?

How do mortgages work in practice vs. in theory?


Question #1: How much will you save?

You have the following debts: (1.) a car loan of $10,000 at 7%effective, plus (2.) bank credit card debt of $3,000 at 19% effective,plus (3.) department store debt of $2,000 at 30% effective, andfinally (4.) student-loan debt of $30,000 at 6% effective.

Question: How much can you save in first-year interest costs, if youconsolidate your debts at a (secured) 4% interest rate?Answer: Compute the total interest paid in year one.

10, 000(0.07) + 3, 000(0.19) + 2, 000(0.30) + 30, 000(0.06) = $3, 670

Compare this with the lower interest if consolidated.

45000(0.04) = $1, 800

So, you would save approximately (3670− 1800) = $1, 870 (in thefirst year) by consolidating debt. Be warned that we have made anumber of assumptions about amortization and payment periods.



You have the following debts: (1.) a car loan of $10,000 at 7%effective, plus (2.) bank credit card debt of $3,000 at 19% effective,plus (3.) department store debt of $2,000 at 30% effective, andfinally (4.) student-loan debt of $30,000 at 6% effective.Question: How much can you save in first-year interest costs, if youconsolidate your debts at a (secured) 4% interest rate?

Answer: Compute the total interest paid in year one.

10, 000(0.07) + 3, 000(0.19) + 2, 000(0.30) + 30, 000(0.06) = $3, 670


45000(0.04) = $1, 800




You have the following debts: (1.) a car loan of $10,000 at 7%effective, plus (2.) bank credit card debt of $3,000 at 19% effective,plus (3.) department store debt of $2,000 at 30% effective, andfinally (4.) student-loan debt of $30,000 at 6% effective.Question: How much can you save in first-year interest costs, if youconsolidate your debts at a (secured) 4% interest rate?Answer: Compute the total interest paid in year one.

10, 000(0.07) + 3, 000(0.19) + 2, 000(0.30) + 30, 000(0.06) = $3, 670


45000(0.04) = $1, 800



Debt Consolidation in Practice

http://www2.manulifeone.ca/en/home/


Question #2: Leverage

You have $10,000 saved-up which you would finally like to "invest" inthe stock market.

The stock/investment you are buying costs $30,000, so you plan toborrow the other $20,000 from the bank (or the brokerage) at aninterest rate of 8% (effective) per year.

At the end of the year, the stock/investment grows by 10% and yousell the stock/investment.

Question: How much money did you make and what was your rateof return on equity (RoE)?


Answer #2:

The value of your financial assets is $30,000 with $20,000 inliabilities. You have $10,000 of equity and a debt-to-equity ratioof $20, 000/$10, 000 = 2.

At the end of the year the assets "grow" to 30000(1+ 0.10) =$33, 000 and the liabilities "grow" to 20, 000(1+ 0.08) = $21, 600.So, the value of your equity is now $33, 000− $21, 600 = $11, 400,which is a gain of $1,400 on your $10,000 investment and a return onequity (RoE) of 14%.

You can also use the shortcut (LiG ) formula:

(1+ L)(1+ G )− L(1+ i)− 1 = G + L(G − i) =0.10+ 2(0.10− 0.08) = 14%

where L is your debt-to-equity ratio, i is the interest rate on debt andG is the growth rate of assets.


Answer #2:

The value of your financial assets is $30,000 with $20,000 inliabilities. You have $10,000 of equity and a debt-to-equity ratioof $20, 000/$10, 000 = 2.At the end of the year the assets "grow" to 30000(1+ 0.10) =$33, 000 and the liabilities "grow" to 20, 000(1+ 0.08) = $21, 600.

So, the value of your equity is now $33, 000− $21, 600 = $11, 400,which is a gain of $1,400 on your $10,000 investment and a return onequity (RoE) of 14%.


(1+ L)(1+ G )− L(1+ i)− 1 = G + L(G − i) =0.10+ 2(0.10− 0.08) = 14%



Answer #2:

The value of your financial assets is $30,000 with $20,000 inliabilities. You have $10,000 of equity and a debt-to-equity ratioof $20, 000/$10, 000 = 2.At the end of the year the assets "grow" to 30000(1+ 0.10) =$33, 000 and the liabilities "grow" to 20, 000(1+ 0.08) = $21, 600.So, the value of your equity is now $33, 000− $21, 600 = $11, 400,which is a gain of $1,400 on your $10,000 investment and a return onequity (RoE) of 14%.


(1+ L)(1+ G )− L(1+ i)− 1 = G + L(G − i) =0.10+ 2(0.10− 0.08) = 14%



Question #3

You have $100,000 saved-up which you would like to invest.

You (somehow manage to) convince a bank to lend you $900,000 atan interest rate of 6% to purchase a (i.) rental property, or (ii.) stockportfolio, or (iii.) units of a hedge fund.

You invest the million dollars and it grows 7% by year end.

Question: What was your rate of return in equity?


Answer #3

Go straight to the leverage equation. The value of L = 9, and thevalue of i = 0.06 and the value of G = 0.07.

Plug into the (LiG ) formula and you get:

G + L(G − i) = 0.07+ 9(0.07− 0.06) = 16%

Your $100,000 grows to $116,000, which is a return on equity of16%, even though the return on assets (RoA) was 7% and thespread between the RoA and the interest rate your were paying wasonly 1%.

This is the impact of leverage!


Summary Table: How Does Leverage Impact Returns?

Here is a summary table, where you can clearly see the impact of leverage.

Impact of Leverage (Debt to Equity Ratio):D-to-E: L Interest: i Growth: G RoE

0 0.05 0.06 0.06+ 0(0.06− 0.05) = 6%1 0.05 0.06 0.06+ 1(0.06− 0.05) = 7%2 0.05 0.06 0.06+ 2(0.06− 0.05) = 8%5 0.05 0.06 0.06+ 5(0.06− 0.05) = 11%20 0.05 0.06 0.06+ 20(0.06− 0.05) = 26%100 0.05 0.06 0.06+ 100(0.06− 0.05) = 106%


Question #4: When things don’t go well.

You have saved $50,000 towards the down-payment on a house.

The house itself costs $500,000 so you must borrow $450,000(mortgage). The 10% down-payment is equivalent to a debt toequity (D-to-E) ratio of 450, 000/50, 000 = 9.0, which was L in ourformula.Assume the bank charges you interest (i = 5%), and lets keep thingssimple and assume you pay back (or renegotiate) the loan at the endof the year.Question: Assume the house appreciates by G = 1% during the year.What is the value of the equity in your house and what was yourreturn on equity (RoE)?Answer: Using the formula

0.01+ 9(0.01− 0.05) = −35%,so your $50, 000 down-payment is now worth 50000(1− 0.35) =$32, 500 and you lost (50000− 32500) = $17, 500 over the year(although you probably did save on rent.)



You have saved $50,000 towards the down-payment on a house.The house itself costs $500,000 so you must borrow $450,000(mortgage). The 10% down-payment is equivalent to a debt toequity (D-to-E) ratio of 450, 000/50, 000 = 9.0, which was L in ourformula.

Assume the bank charges you interest (i = 5%), and lets keep thingssimple and assume you pay back (or renegotiate) the loan at the endof the year.Question: Assume the house appreciates by G = 1% during the year.What is the value of the equity in your house and what was yourreturn on equity (RoE)?Answer: Using the formula




You have saved $50,000 towards the down-payment on a house.The house itself costs $500,000 so you must borrow $450,000(mortgage). The 10% down-payment is equivalent to a debt toequity (D-to-E) ratio of 450, 000/50, 000 = 9.0, which was L in ourformula.Assume the bank charges you interest (i = 5%), and lets keep thingssimple and assume you pay back (or renegotiate) the loan at the endof the year.

Question: Assume the house appreciates by G = 1% during the year.What is the value of the equity in your house and what was yourreturn on equity (RoE)?Answer: Using the formula




You have saved $50,000 towards the down-payment on a house.The house itself costs $500,000 so you must borrow $450,000(mortgage). The 10% down-payment is equivalent to a debt toequity (D-to-E) ratio of 450, 000/50, 000 = 9.0, which was L in ourformula.Assume the bank charges you interest (i = 5%), and lets keep thingssimple and assume you pay back (or renegotiate) the loan at the endof the year.Question: Assume the house appreciates by G = 1% during the year.What is the value of the equity in your house and what was yourreturn on equity (RoE)?

Answer: Using the formula




You have saved $50,000 towards the down-payment on a house.The house itself costs $500,000 so you must borrow $450,000(mortgage). The 10% down-payment is equivalent to a debt toequity (D-to-E) ratio of 450, 000/50, 000 = 9.0, which was L in ourformula.Assume the bank charges you interest (i = 5%), and lets keep thingssimple and assume you pay back (or renegotiate) the loan at the endof the year.Question: Assume the house appreciates by G = 1% during the year.What is the value of the equity in your house and what was yourreturn on equity (RoE)?Answer: Using the formula



Question #5: When things go badly

You have saved $50,000 towards the down-payment on a house thatcosts $500,000 and you borrow $450,000 (mortgage).

The bank charges you interest (i = 5%) and assume you pay back (orrenegotiate) the loan at the end of the year.Question: Assume the house declines by G = −10% during the year.What is the value of the equity in your house and what was your rateof return on equity (RoE)?Answer: Using the formula

−0.10+ 9(−0.10− 0.05) = −145%,

which means that you have negative equity in the house. You lost145% of your down-payment. You owe an additional(0.45)(50000) = $22, 500 to the bank.Here is another way to think about it. The house is worth500000(0.90) = $450, 000 and you owe 450000(1.05) = $472, 500 tothe bank.



You have saved $50,000 towards the down-payment on a house thatcosts $500,000 and you borrow $450,000 (mortgage).The bank charges you interest (i = 5%) and assume you pay back (orrenegotiate) the loan at the end of the year.

Question: Assume the house declines by G = −10% during the year.What is the value of the equity in your house and what was your rateof return on equity (RoE)?Answer: Using the formula

−0.10+ 9(−0.10− 0.05) = −145%,




You have saved $50,000 towards the down-payment on a house thatcosts $500,000 and you borrow $450,000 (mortgage).The bank charges you interest (i = 5%) and assume you pay back (orrenegotiate) the loan at the end of the year.Question: Assume the house declines by G = −10% during the year.What is the value of the equity in your house and what was your rateof return on equity (RoE)?

Answer: Using the formula

−0.10+ 9(−0.10− 0.05) = −145%,




You have saved $50,000 towards the down-payment on a house thatcosts $500,000 and you borrow $450,000 (mortgage).The bank charges you interest (i = 5%) and assume you pay back (orrenegotiate) the loan at the end of the year.Question: Assume the house declines by G = −10% during the year.What is the value of the equity in your house and what was your rateof return on equity (RoE)?Answer: Using the formula

−0.10+ 9(−0.10− 0.05) = −145%,

which means that you have negative equity in the house. You lost145% of your down-payment. You owe an additional(0.45)(50000) = $22, 500 to the bank.

Here is another way to think about it. The house is worth500000(0.90) = $450, 000 and you owe 450000(1.05) = $472, 500 tothe bank.



You have saved $50,000 towards the down-payment on a house thatcosts $500,000 and you borrow $450,000 (mortgage).The bank charges you interest (i = 5%) and assume you pay back (orrenegotiate) the loan at the end of the year.Question: Assume the house declines by G = −10% during the year.What is the value of the equity in your house and what was your rateof return on equity (RoE)?Answer: Using the formula

−0.10+ 9(−0.10− 0.05) = −145%,



Can this happen?

Some observers are doubtful housing prices can decline by (any) suchamounts in Canada. I personally can’t forecast these things any betterthan you, but here is an example of some recent price movements.

New Housing Price Index (1997 = 100)City 2005 2009 4-year Annual Change 12-yearVictoria

Toronto

Regina

Canada

Source: CANSIM 327-0005 Catalogue 62-007-X

There are many statistical "issues" with such indices and one has to bevery careful when comparing them to equivalent stock and bond numbers.


Can this happen?

Some observers are doubtful housing prices can decline by (any) suchamounts in Canada. I personally can’t forecast these things any betterthan you, but here is an example of some recent price movements.

New Housing Price Index (1997 = 100)City 2005 2009 4-year Annual Change 12-yearVictoria 113.3 108.9 ( 108.9113.3 )

1/4 − 1 = −0.98% +0.71%Toronto 132.3 145.8 ( 145.8132.3 )

1/4 − 1 = +2. 45% +3.19%Regina 142.2 251.6 ( 251.6142.2 )

1/4 − 1 = +15.3% +8.00%Canada 129.4 154.6 ( 154.6129.4 )

1/4 − 1 = +4.5% +3.66%Source: CANSIM 327-0005 Catalogue 62-007-X

There are many statistical "issues" with such indices and one has to bevery careful when comparing them to equivalent stock and bond numbers.


Question #6: Mortgage Details:

You have $50,000 for a down-payment on a house that costs$500,000 and so you must borrow $450,000.

You select a 5 year term, fixed-rate mortgage, amortized over 15years, at a rate of 4.5% per year (compounded monthly.)Question: What is your monthly mortgage payment and how muchof that payment is interest vs. principal?Answer:

450000PVA(0, 0.045/12, 180)

=450000130.720

= $3, 442.47

In the first month you are paying (0.045/12)450000 = $1, 687. 5 ininterest and (3442.47− 1687.5) = $1, 754. 97 in principal.Note: If you select a 25 year amortization, the payment is:

450000PVA(0, 0.045/12, 300)

=450000179.910

= $2, 501.25



You have $50,000 for a down-payment on a house that costs$500,000 and so you must borrow $450,000.You select a 5 year term, fixed-rate mortgage, amortized over 15years, at a rate of 4.5% per year (compounded monthly.)

Question: What is your monthly mortgage payment and how muchof that payment is interest vs. principal?Answer:

450000PVA(0, 0.045/12, 180)

=450000130.720

= $3, 442.47


450000PVA(0, 0.045/12, 300)

=450000179.910

= $2, 501.25



You have $50,000 for a down-payment on a house that costs$500,000 and so you must borrow $450,000.You select a 5 year term, fixed-rate mortgage, amortized over 15years, at a rate of 4.5% per year (compounded monthly.)Question: What is your monthly mortgage payment and how muchof that payment is interest vs. principal?

Answer:450000

PVA(0, 0.045/12, 180)=450000130.720

= $3, 442.47


450000PVA(0, 0.045/12, 300)

=450000179.910

= $2, 501.25



You have $50,000 for a down-payment on a house that costs$500,000 and so you must borrow $450,000.You select a 5 year term, fixed-rate mortgage, amortized over 15years, at a rate of 4.5% per year (compounded monthly.)Question: What is your monthly mortgage payment and how muchof that payment is interest vs. principal?Answer:

450000PVA(0, 0.045/12, 180)

=450000130.720

= $3, 442.47


450000PVA(0, 0.045/12, 300)

=450000179.910

= $2, 501.25




450000PVA(0, 0.045/12, 180)

=450000130.720

= $3, 442.47

In the first month you are paying (0.045/12)450000 = $1, 687. 5 ininterest and (3442.47− 1687.5) = $1, 754. 97 in principal.

Note: If you select a 25 year amortization, the payment is:

450000PVA(0, 0.045/12, 300)

=450000179.910

= $2, 501.25




450000PVA(0, 0.045/12, 180)

=450000130.720

= $3, 442.47


450000PVA(0, 0.045/12, 300)

=450000179.910

= $2, 501.25


Question #7: More Mortgage Details:

Assume the $50,000 down-payment, 5-year term, 4.5% mortgagerate and 25 year amortization.

Question: At the end of five years, how much do you (still) owe?What percent of your payments went to the house vs. interest?Answer: You made 60 payments of $2, 501.25. The future valueannuity factor FVA(0, 0.045/12, 60) is 67.1456, so the future value ofyour payments are:

(2501.25)(67.1456) = $167, 947.9

The future value of the original $450,000 loan is:

450000(1+ 0.045/12)60 = $563, 308.1

So, you still owe ($563, 308.1− $167, 947.9) = $395, 360. 2.Alternatively, compute the PVA of the remaining 240 payments.Notice: You made payments totaling (60)($2, 501.25) = $150, 075of which only ($450, 000− $395, 360.2) = $54, 639. 8 (=36.4%) paiddown principal. The remaining $95, 435 went to interest/bank.



Assume the $50,000 down-payment, 5-year term, 4.5% mortgagerate and 25 year amortization.Question: At the end of five years, how much do you (still) owe?What percent of your payments went to the house vs. interest?

Answer: You made 60 payments of $2, 501.25. The future valueannuity factor FVA(0, 0.045/12, 60) is 67.1456, so the future value ofyour payments are:

(2501.25)(67.1456) = $167, 947.9


450000(1+ 0.045/12)60 = $563, 308.1




Assume the $50,000 down-payment, 5-year term, 4.5% mortgagerate and 25 year amortization.Question: At the end of five years, how much do you (still) owe?What percent of your payments went to the house vs. interest?Answer: You made 60 payments of $2, 501.25. The future valueannuity factor FVA(0, 0.045/12, 60) is 67.1456, so the future value ofyour payments are:

(2501.25)(67.1456) = $167, 947.9


450000(1+ 0.045/12)60 = $563, 308.1





(2501.25)(67.1456) = $167, 947.9


450000(1+ 0.045/12)60 = $563, 308.1

So, you still owe ($563, 308.1− $167, 947.9) = $395, 360. 2.Alternatively, compute the PVA of the remaining 240 payments.

Notice: You made payments totaling (60)($2, 501.25) = $150, 075of which only ($450, 000− $395, 360.2) = $54, 639. 8 (=36.4%) paiddown principal. The remaining $95, 435 went to interest/bank.




(2501.25)(67.1456) = $167, 947.9


450000(1+ 0.045/12)60 = $563, 308.1



Mortgage Schedule

Here is the "mortgage schedule" over the entire 60-month term:

Month Owed BoM Interest Payment Owed EoM#1 $450,000.00 $1,687.50 $2,501.25 $449,186.25

#2 $449,186.25 $1,684.45 $2,501.25 $448,369.46

#3 $448,369.46 $1,681.39 $2,501.25 $447,549.60

... ... ... ... ...

#59 $397,386.45 $1,490.20 $2,501.25 $396,375.40

#60 $396,375.40 $1,486.41 $2,501.25 $395,360.57

TOTAL: TOTAL:$95,435 $150,075


Mortgage Penalties

The amount owed at the end of the month, is not necessarily whatyou would have to pay to "get rid" of the debt. There is a penatly forbreaking a mortgage.

For most closed mortgages, you would have to pay a penalty which isthe greater of three months interest and the so-called interest ratedifferential (IRD.)The IRD is computed by multiplying the amount you are pre-payingby an interest rate factor that equals the difference between youroriginal mortgage interest rate and the interest rate that the lendercan charge today when re-lending the funds for the remaining term ofthe mortgage.The Interest Act prohibits IRD penalties on terms over 5 years, afterfive years has elapsed. In such cases, a maximum 3-month interestpenalty may apply. For example, someone who has been in a 6-yearmortgage for 60 months or more would pay a 3-month interestpenalty (maximum) to break it before maturity.


Mortgage Penalties

The amount owed at the end of the month, is not necessarily whatyou would have to pay to "get rid" of the debt. There is a penatly forbreaking a mortgage.For most closed mortgages, you would have to pay a penalty which isthe greater of three months interest and the so-called interest ratedifferential (IRD.)

The IRD is computed by multiplying the amount you are pre-payingby an interest rate factor that equals the difference between youroriginal mortgage interest rate and the interest rate that the lendercan charge today when re-lending the funds for the remaining term ofthe mortgage.The Interest Act prohibits IRD penalties on terms over 5 years, afterfive years has elapsed. In such cases, a maximum 3-month interestpenalty may apply. For example, someone who has been in a 6-yearmortgage for 60 months or more would pay a 3-month interestpenalty (maximum) to break it before maturity.


Mortgage Penalties

The amount owed at the end of the month, is not necessarily whatyou would have to pay to "get rid" of the debt. There is a penatly forbreaking a mortgage.For most closed mortgages, you would have to pay a penalty which isthe greater of three months interest and the so-called interest ratedifferential (IRD.)The IRD is computed by multiplying the amount you are pre-payingby an interest rate factor that equals the difference between youroriginal mortgage interest rate and the interest rate that the lendercan charge today when re-lending the funds for the remaining term ofthe mortgage.

The Interest Act prohibits IRD penalties on terms over 5 years, afterfive years has elapsed. In such cases, a maximum 3-month interestpenalty may apply. For example, someone who has been in a 6-yearmortgage for 60 months or more would pay a 3-month interestpenalty (maximum) to break it before maturity.


Mortgage Penalties

The amount owed at the end of the month, is not necessarily whatyou would have to pay to "get rid" of the debt. There is a penatly forbreaking a mortgage.For most closed mortgages, you would have to pay a penalty which isthe greater of three months interest and the so-called interest ratedifferential (IRD.)The IRD is computed by multiplying the amount you are pre-payingby an interest rate factor that equals the difference between youroriginal mortgage interest rate and the interest rate that the lendercan charge today when re-lending the funds for the remaining term ofthe mortgage.The Interest Act prohibits IRD penalties on terms over 5 years, afterfive years has elapsed. In such cases, a maximum 3-month interestpenalty may apply. For example, someone who has been in a 6-yearmortgage for 60 months or more would pay a 3-month interestpenalty (maximum) to break it before maturity.


How Much is Paid?

Here is a table that summarized the total amount paid, depending on theamortization period. Assuming the rate is fixed over the entire term.

You Borrowed $450,000: How Much Paid?Interest Rate Over 25 years Over 40 years

4.5%

5.5%

6.5%

7.5%


How Much is Paid?

Here is a table that summarized the total amount paid, depending on theamortization period. Assuming the rate is fixed over the entire term.

You Borrowed $450,000: How Much Paid?Interest Rate Over 25 years Over 40 years

4.5% $750,374 $971,0556

5.5% $829,018 $1,114,064

6.5% $911,530 $1,264,587

7.5% $997,638 $1,421,433


What do people select?

In practice here are the terms that Canadians have been selecting over thelast few years:

Amortization Periods for Canadian MortgagesPeriod < 25 years 30 years 35 years 40 yearsFall 2007Fall 2008Fall 2009Fall 2010

Source: Globe and Mail, 22 January 2011 (pageB6)

Note that CMHC no longer offers (insurance on) 40 year mortgages, andrecently restricted 35 year mortgages as well.


What do people select?

In practice here are the terms that Canadians have been selecting over thelast few years:

Amortization Periods for Canadian MortgagesPeriod < 25 years 30 years 35 years 40 yearsFall 2007 63% 11% 11% 15%

Fall 2008 50% 5% 13% 32%

Fall 2009 53% 19% 23% 6%

Fall 2010 58% 12% 30% 0%

Source: Globe and Mail, 22 January 2011 (pageB6)

Note that CMHC no longer offers (insurance on) 40 year mortgages, andrecently restricted 35 year mortgages as well.


Canada Mortgage Housing Corporation (CMHC) Insurance:

www.cmhc-schl.gc.ca/en/co/moloin/moloin_005.cfm


Question #8: Final Details

You have a $50,000 down-payment. The house costs $500,000. Youborrow $450,000 and must pay CMHC (default) insurance.

Question: What is your monthly payment assuming the 5-yearmortgage rate is quoted as 5% with semi-annual compounding andamortized over 25 years?Answer: Since you have a loan to value ratio of 90%, you must addanother 2% to the $450,000.The total amount borrowed is: 450000(1.02) = $459, 000. Note theextra $9,000 paid for (default) CMHC insurance.The monthly mortgage rate is:(

(1+0.052)2)1/12

− 1 = 0.0041239.

The monthly mortgage payment is:459000

PVA(0, 0.0041239, 300)=459, 000171.9380

= $2, 669.57



You have a $50,000 down-payment. The house costs $500,000. Youborrow $450,000 and must pay CMHC (default) insurance.Question: What is your monthly payment assuming the 5-yearmortgage rate is quoted as 5% with semi-annual compounding andamortized over 25 years?

Answer: Since you have a loan to value ratio of 90%, you must addanother 2% to the $450,000.The total amount borrowed is: 450000(1.02) = $459, 000. Note theextra $9,000 paid for (default) CMHC insurance.The monthly mortgage rate is:(

(1+0.052)2)1/12

− 1 = 0.0041239.


PVA(0, 0.0041239, 300)=459, 000171.9380

= $2, 669.57



You have a $50,000 down-payment. The house costs $500,000. Youborrow $450,000 and must pay CMHC (default) insurance.Question: What is your monthly payment assuming the 5-yearmortgage rate is quoted as 5% with semi-annual compounding andamortized over 25 years?Answer: Since you have a loan to value ratio of 90%, you must addanother 2% to the $450,000.

The total amount borrowed is: 450000(1.02) = $459, 000. Note theextra $9,000 paid for (default) CMHC insurance.The monthly mortgage rate is:(

(1+0.052)2)1/12

− 1 = 0.0041239.


PVA(0, 0.0041239, 300)=459, 000171.9380

= $2, 669.57



You have a $50,000 down-payment. The house costs $500,000. Youborrow $450,000 and must pay CMHC (default) insurance.Question: What is your monthly payment assuming the 5-yearmortgage rate is quoted as 5% with semi-annual compounding andamortized over 25 years?Answer: Since you have a loan to value ratio of 90%, you must addanother 2% to the $450,000.The total amount borrowed is: 450000(1.02) = $459, 000. Note theextra $9,000 paid for (default) CMHC insurance.

The monthly mortgage rate is:((1+

0.052)2)1/12

− 1 = 0.0041239.


PVA(0, 0.0041239, 300)=459, 000171.9380

= $2, 669.57



You have a $50,000 down-payment. The house costs $500,000. Youborrow $450,000 and must pay CMHC (default) insurance.Question: What is your monthly payment assuming the 5-yearmortgage rate is quoted as 5% with semi-annual compounding andamortized over 25 years?Answer: Since you have a loan to value ratio of 90%, you must addanother 2% to the $450,000.The total amount borrowed is: 450000(1.02) = $459, 000. Note theextra $9,000 paid for (default) CMHC insurance.The monthly mortgage rate is:(

(1+0.052)2)1/12

− 1 = 0.0041239.


PVA(0, 0.0041239, 300)=459, 000171.9380

= $2, 669.57


Final Comments

The bank will appraise the property and may not agree with yourvaluation. So, you might think that the loan to value ratio is 90%,and they might think it is 95%. This is rather subjective.

Generally speaking, the bank (lender) would like to ensure that yourmortgage payments (plus any other debts you have) does not exceed30% to 40% of your pre-tax income. This is called the gross debtservice (GDS) and total debt service (TDS) ratio.

We have not discussed variable rate mortgages (in detail) and therelative benefits of fixed vs. floating-rate borrowing...

This is a topic for another lecture.


strategic financial planning over the lifecyclemyweb.fsu.edu/pborn/rmi4115/sfpl_chapter5.pdf ·...

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