**Terminology: **

Lease a contract for purchasing the use of property, such as a building or vehicle, from another, the lessor, for a specified period of time.

If you lease something, you have no equity in the item.

Equity the difference between the value of an item and the amount still owing on it.

Ex. For a $20,000 down payment made on a $230,000 home, the $20,000 is the equity or the portion owned.

Appreciation the increase in value of an asset over time. (1 + percentage in decimal form)

Depreciation the decrease in the value of an asset over time. (1 - percentage in decimal form)

Appreciation and depreciation affect the value of a piece of property and should be considered when making decisions about renting, buying, or leasing.

Each situation is unique, so it is impossible to generalize whether renting, leasing, or buying is best. A cost and benefit analysis can help make this decision.

Ex (1) Josh is a chiropractor and works 6-month contracts in Nunavut. He has two options for housing:

i) He can rent a room with a kitchenette at a hotel for $85 per day, which includes cleaning service, utilities, and a phone.

ii) He can take a 6-month lease of a furnished apartment for $1800 per month. This requires the first and last month's rent up front, along with a refundable damage deposit of $1800. As well, Josh would need to pay utilities and phone at about $150 per month.

a) Analyze the costs and benefits of leasing versus renting.

**Benefits: **

b) Which option do you recommend? Explain.

Ex (2) A company requires 5 computers, a server, and 2 printers. The company's technology policy requires upgrades and renewals every 4 years because the value of computer equipment depreciates at an annual rate of 40%. The costs of purchasing and leasing are shown in the chart below.

a) Analyze the costs and benefits of leasing versus purchasing.

b) Would it be better for the company to purchase or lease? Explain.
**Equipment ** **Lease ($) ** **Purchase ($) **

5 computers 1115 per year 4875

1 server 2000 per year 6500

3. Samantha is a landscaper and needs a rototiller for her next couple of jobs. She has three options:

i) Rent a rototiller for $600 per month. ii) Buy a new one for $1150.

iii) Buy a used rototiller at 65% of the purchase price when new.

a) What is the cost of each option?

b) If the jobs will take 5 weeks to complete, which option is better?

4. The equipment at a fitness centre needs to be replaced. The cost of new equipment is $13 500. The owner of the centre does not have enough cash to pay for it. She has two options:

i) Use a line of credit with an interest rate of 8.7%, compounded monthly.

ii) Lease the equipment for 3 years, for $900 down and $300 each month.

a) What is the cost of buying with a line of credit if the owner pays off the loan at the end of 3 years?

b) What is the cost of leasing for 3 years?

c) The equipment depreciated at 25% per year. What is its value after 3 years?

Ex (1) Greg is looking for a place to live. Greg buys a house for $198,900 with a down payment of 5%. The bank has offered Greg a 25-year mortgage for the

remainder of the cost at 4.15% compounded semi-annually, with payments every two weeks.

a) Calculate the down payment.

b) Calculate his mortgage payment.

N = I = PV = PMT = FV = P/Y = C/Y =

c) After 6 years in his home, Greg decides to move. How much is still owing on his mortgage after 6 years?

(Remember he has only made mortgage payments for 6 years.)

N = I = PV = PMT = FV = P/Y = C/Y =

d) Over the six years, his house has appreciated by 1.5% per year. Calculate the resale value of his home.

e) How much equity does he have in the house?

f) Calculate the total cost of owning the house for 6 years. Total cost = buying cost – equity

g) Brad decides to rent a house for $1100 per month.

Compare Brad's housing cost for 6 years to Greg's housing costs.

Ex(2) A company has spent $45,000 for car rentals over 2 years. The company wants to determine if it should continue to rent or if it should buy or lease two vehicles instead.

a) A new car costs $21,000. A 5% down payment is required. The rest can be financed at 2.9%, compounded monthly, for 2 years. Calculate the monthly payment for one car.

N = I = PV = PMT = FV = P/Y = C/Y =

b) Calculate the resale value of one car after two years. The car depreciates by 40% each year.

d) A 2-year lease for a car requires a down payment of $2500 and monthly payments of $520. Calculate the cost of leasing two cars for two years.

e) Based on the cost, which would you recommend: renting, buying, or leasing?

**Extra Mortgage Question **

Let's see what the payments will be on a mortgage of a home currently on the real estate market.

You go to the bank and are given an interest rate of 3.95%, compounded semi-annually for a 5-year term. You are opting to pay back the mortgage using bi-weekly payments for 25 years. You also have $20 000 for a down-payment.

a) What will be your bi-weekly payment?

N = I = PV = PMT = FV = P/Y = C/Y =

b) What will be the total cost of the house after it is paid off?