Mila is moving to a new location for work. Based on her revised employment contract, she will be working at the new location for the next 5 years. She is deciding whether she should rent or buy a house. From her research, she can rent an apartment for a cost of $1,800 per month. The house she is considering purchasing will cost $625,000. Mila has just signed a contract to sell her current home and would use some the proceeds from this sale for the down payment. The amount for a down payment for her next property would be $125,000. Mila prefers to purchase a home as she enjoys gardening. She also has many ideas of how to decorate her new space.

Her financial institution is currently offering a mortgage rate of 4.25% for 5 years. Mila would amortize the mortgage over a period of 25 years with monthly payments.

Other costs associated with owning the home are as follows:

• $5,100 p.a. for property taxes.
• $100 monthly for insurance.
• New roof in 3 years, estimated cost in 3 years is $23,000.
• $525 per month for utilities (electricity, water, heat) and landscaping costs (Mila would hire a company to cut grass in the summer and do snow removal in the winter).

All expenses are expected to increase at a rate of 2% p.a. Due to the demand for homes in the new location, the home value is expected to increase 3.25% p.a. Mila can earn a return of 4.5% p.a.

a. Is it a good time for Mila to buy a home or rent in the new location? Ignore expenses such as moving and legal and ignore taxes.

Example / Format of how the question above should be answered ...

Question #4 (19 marks)

Anna and Bob are deciding if it is the right time to purchase a condo. They are currently renting the main floor of a home in High Park at a cost of $1,950 a month. The condo they are considering purchasing will cost $320,000. They will only live there for 5 years before upgrading to a home. The current mortgage rate is 4.15% that is offered by their financial institution. They would amortize the mortgage for a period of 20 years. Annas net income is $43,750 and Bobs net income is $62,550.

Other costs associated with owning the condo are as follows: $2,250 p.a. for property taxes; $1,500 p.a. for insurance and a monthly maintenance fee of $950.

All expenses as well as home values are expected to increase at a rate of 2% p.a.. They can earn a return of 6% p.a.. Annas marginal tax rate is 30% and Bobs is 40%.

1. Assume they qualify for a conventional mortgage. What is their down payment? (1 mark)

Conventional mortgage = 20% down payment

320,000 x 20% = 64,000

2. Calculate the monthly payment based on this down payment amount. (3 marks)

Rate has to be converted to equate with payment schedule.

(1+m)^12 = [1+ (k/2)]^2

(1+m)^12 = (1.02075)^2

(1+m)^12 = 1.041930562

M = 0.3428807%

PV = 320,000 64,000 = 256,000

N = 20 x 12 = 240

I/Y = 0.3429%

PMT = 1,566.84

3. Will the bank provide them with the mortgage based on normal rules? (3 marks)

Gross income Anna = 43,750 / (1 - 0.3) = 62,500

Gross income Bob = 62,550 / (1 0.4) = 104,250

GDS = (1,566.84 x 12) + 2,250 / (62,500 + 104,250)

= 21,052.08 / 166,750

=12.625%

Yes, the bank will give them the mortgage since the GDS < 30%.

4. Is it a good time for them to buy or should they continue to rent? Use the information from the calculations above. Ignore moving and legal expenses. (10 marks)

If they continue to rent they can invest the down payment of 64,000.

PV = 64,000

N = 5

I/Y = 6%

FV = 85,646.44

If they buy the condo:

Cost = 320,000 less down payment of 20% (64,000) = 256,000 mortgage principal.

PMT calculated in part (b) as $1,566.84.

Annual Cost	Year 1	Year 2	Year 3	Year 4	Year 5
Mortgage Payment	18,804	18,804	18,804	18,804	18,804
Property Tax	2,250	2,295	2,341	2,388	2,435
Insurance	1,500	1,530	1,561	1,592	1,624
Condo Fees	11,400	11,628	11,861	12,098	12,340
Gross Home Ownership Cost	33,954	34,257	34,566	34,881	35,203
Rent Expense	23,400	23,868	24,345	24,832	25,329
Net Cost	10,554	10,389	10,221	10,049	9,874

They can invest the net cost they save by renting:

(10,554 x 1.06^4) + (10,389 x 1.06^3) + (10,221 x 1.06^2) + (10,049 x 106^1) + 9,874 = 13,324.18+12,373.47+11,484.32+10,651.94+9,874 = 57,707.91

Total they would have if they rent and invest the difference = 57,707.91 + 85,646.44 = 143,354.35

Value of the condo after 5 years is: 320,000 x 1.02^5 = 353,305.86

Outstanding mortgage after 5 years:

PMT =1,566.84

I/Y = 0.3429%

N = (15 x 12) = 180

PV = 210,186

Home equity = 353,305.86 210,186 =143,119.86

Since the value of renting is greater they should rent. However, we must consider that each year they own the net cost decreases in relation to rental expense and will provide greater equity in the longer term.