Buy it right now or wait until having enough down payment?

It is an interesting question for me. Should I buy a house if I don't have enough down payment (20% of the price) for it? Or, is it better for me to wait until I accumulate enough money?

In mortgage-wise, if I have 20% down payment at hand, I should be able to get 80% from mortgage provided that I have a reasonable gross debt ratio and satisfactory credit. If I don't have enough down payment, say only 10% down payment, I can still get 90% from mortgage by paying CMHC mortgage insurance premium to the lender (by adding insurance premium to the mortgage principle). Again, this is based on the fact that I have a reasonable gross debt ratio and satisfactory credit. So, there is no big obstacle preventing me from buying a home with low down payment. The only concern is: will I end up paying more if I choose to pay less down payment?

The best way to figure it out is simply do some calculation. I will compare two scenarios. In scenario 1, I buy right now. In scenario 2, I buy the house after m months when I save enough money. However, the house price increases after m months. To simplify the calculation, several assumptions are made: the house price is assumed to increase monotonically 5% annually, based on historical housing price in Canada; I have to pay rent during the period that I try to save enough down payment; the mortgage interest rate is assumed to be constant throughout the years; I will sell the house in n years from now, regardless of when I buy the house; I can save 25000 CAD annually. The calculation compares the total amount of money spent n years from now.



nomenclature:
alfa:           the ratio of my down payment to the listing price
HPrice:      price of the house
beta:          ratio of ( annual mortgage payment/total mortgage amount) at a given mortgage term (ref 1)
n:               I am going to sell the house n years from now
CMHC:     CMHC mortgage insurance rate, as a function of total mortgage amount (ref 2)
Rent:          the monthly rent that I have to pay while saving money
m:              I have to wait for m months until I have 20% down payment

Scenario 1: Buy right now
 I have alfa*HPrice as down payment. The rest will be paid through mortgage plus the mortgage insurance premium.

Cost = alfa*HPrice + beta*n*[ (1-alfa)*HPrice + CMHC* (1-alfa)*HPrice ]
 
Scenario 2: Buy until having enough money
I wait for m months until I have 20% down payment. However, the house price increases by (1.05)^(m/12) over this period. I also have to pay m*Rent while saving money.

Cost = 0.2*HPrice*(1.05)^(m/12) + beta*(n- m/12 )*0.8*HPrice*(1.05)^(m/12) + m*Rent

Cost difference (Scenario 1 - Scenario 2)
= HPrice*[ alfa - 0.2*(1.05)^(m/12) ] + beta*HPrice*n*[ 1 - alfa + CMHC*(1-alfa) - ( 0.8 - m/(15*n) )*(1.05)^(m/12) ] - m* Rent

Case study 1:
alfa = 0.1; HPrice = 500,000 CAD; beta = 0.0621504 (based on a 5-year term at 3.85% with 25 year amortization); n = 10 year; CMHC = 0.02;   m= 24 months; Rent = 1100.

 If I buy right now, I will save 20646 CAD.

Case Study 2:
alfa = 0.05; HPrice = 500,000 CAD; beta = 0.0621504 (based on a 5-year term at 3.85% with 25 year amortization); n = 10 year; CMHC = 0.0275;   m= 36 months; Rent = 1100.

 If I buy right now, I will save 28480 CAD.

Case Study 3:
alfa = 0.1; HPrice = 500,000 CAD; beta = 0.0621504 (based on a 5-year term at 3.85% with 25 year amortization); n = 20 year; CMHC = 0.02;   m= 24 months; Rent = 1100.


 If I buy right now, I will save 9459 CAD.

 Case Study 4:
alfa = 0.1; HPrice = 400,000 CAD; beta = 0.0621504 (based on a 5-year term at 3.85% with 25 year amortization); n = 10 year; CMHC = 0.02;   m= 24 months; Rent = 1100.


 If I buy right now, I will save 21797 CAD.

 Case Study 5:
alfa = 0.15; HPrice = 500,000 CAD; beta = 0.0621504 (based on a 5-year term at 3.85% with 25 year amortization); n = 10 year; CMHC = 0.0175;   m= 12 months; Rent = 1100.


 If I buy right now, I will save 9367 CAD.

Case Study 6:
alfa = 0.1; HPrice = 500,000 CAD; beta = 0.0757101 (based on a 5-year term at 5.85% with 25 year amortization); n = 10 year; CMHC = 0.02;   m= 24 months; Rent = 1100.


 If I buy right now, I will save 6246 CAD.

Case Study 7:
alfa = 0.1; HPrice = 500,000 CAD; beta = 0.0621504 (based on a 5-year term at 3.85% with 25 year amortization); n = 10 year; CMHC = 0.02;   m= 24 months; Rent = 0.


 If I buy right now, I will pay 5754 CAD more.

Case Study 8:
alfa = 0.1; HPrice = 500,000 CAD; beta = 0.0621504 (based on a 5-year term at 3.85% with 25 year amortization); n = 15 year; CMHC = 0.02;   m= 24 months; Rent = 0.


 If I buy right now, I will have to pay 11347 CAD more.

Case Study 9:
alfa = 0.1; HPrice = 500,000 CAD; beta = 0.0757101 (based on a 5-year term at 5.85% with 25 year amortization); n = 15 year; CMHC = 0.02;   m= 24 months; Rent = 0.


 If I buy right now, I will have to pay 26968 CAD more.

Surprisingly, I found that I actually save money if I buy right now for most of the cases. It is better to buy a house with less than 20% down payment plus mortgage insurance rather than to wait until having 20% down payment, if (1) the interest rate is low; (2) I am sure that I am going to sell the house long before amortization; and (3) I have to pay high rent before having enough money.

Note the amount of money saved may be exaggerated in the above calculation. Although the house price increases 5% annually, as a long term trend, the actual house price, depending on macro economics, may fluctuate randomly in a short term, say within 2 or 3 years. I might end up getting the house at a lower price 2 years from now. Who knows. The interest rate is assumed to be constant for simplicity. In reality, it changes from time to time, which also affects the calculation. Also, I assumed that I can get same mortgage rate regardless of percentage of down payment. The actual mortgage rate may differ. The most significant factor is found to be "rent." The major reason that I can save by buying right now is the high rent. If the rent is very low, or if I am staying at my parents' home, the results will be totally different. In most of the cases, the money I can save mostly attributes to the "rent saving."

The above finding is meant to be for reference only. Do not use it as a general guide. After all, I am not a financial professional...:p But at least I can say, waiting until having enough down payment may not always be a better idea..

Reference website:
1. Mortgage calculation: http://www.canequity.com/mortgage-calculator/
2. CMHC mortgage insurance premium: http://www.cmhc-schl.gc.ca/en/co/moloin/moloin_005.cfm
3. Another website for mortgage insurance premium calculation: http://www.canadian-mortgage-information.com/cmhc-calculator.html