1. Chapter 3: Consumer Math
Section 3.4: Leases
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

2. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Terminology
Lease: An agreement that allows for one party to use the property of another party for an extended period of time.
Also referred to as the contract.
Lessee: The party or individual wanting to utilize the property.
Referred to as the tenant in real estate leases.
Lessor: The owner of the property.
Referred to as the landlord in real estate leases.
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

3. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Terminology
In a fixed-term tenancy, either the landlord or the tenant may terminate a rental agreement when the specified term is nearing completion (to be effective at the end of the term), but neither party may terminate the lease early without a penalty based on the remaining period of the lease – unless there is a sufficient reason to do so. An at-will tenancy is a tenancy in which either the landlord or the tenant may terminate at any time by giving reasonable notice. The security deposit is an initial payment paid by the tenant and held by the landlord until the property is returned or vacated.
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

4. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Office Spaces
Class A office spaces are found in the best quality buildings and the most desirable locations. They are in newer, well-constructed, large buildings with convenient access, and are professionally managed. Thus, they are the most expensive to rent. Class B office spaces are found in buildings are well-maintained, but also a little older. They still attract good tenants and provided at more affordable rents than their Class A counterparts. Some Class B buildings were originally Class A facilities and, hence, with renovations, they can be returned to Class A status. Older buildings in need of extensive repairs and are found in less desirable areas are Class C office spaces. Although offering the lowest rental rates, these buildings often need expensive infrastructure and technology upgrades to be suitable for many newer companies.
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

5. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Office Spaces
Example: A company owns a Class B building and charges $3500 per month to rent it. If the company spends $30,000 to upgrade the facility to Class A, by how much would they have to increase the monthly rent to recover the cost of the upgrade within 5 years?
 5 years = 60 months
$30,000/60 months = $500/month
The rent in the upgraded facility would need to be increased by $500/month.
Although it wasn’t asked, the new rent $4000/month.
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

6. Property Management Companies
A property management company provide services ranging from tenant screening to lawn care maintenance to fiscal management, and usually charge between 5-10% of the monthly rent.
Example: ABC Management charges 8.5% of the rental price for their fee. If a home rents for $1250/month, how much does the company earn in a year?
(0.085)($1250)(12) = $1275
Example: Max manages an apartment complex and for his pay, he keeps 30% of the monthly rent. If there are 15 units that each pay $850/month, how much does Max make in a year?
(0.30)($850)(15)(12) = $45,900
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

7. Auto/Equipment Leases
Leasing cars or equipment is an attractive option for many people or companies. Due to depreciation and wear and tear, some large items lose a significant portion of their value over extended periods. Furthermore, as the ages of these things increase, annual maintenance costs escalate, as well. Be sure to consider:
The Up-Front Payment
The Monthly Payment
The Length of the Lease
Possible Additional Charges at the End of the Lease
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

8. Auto/Equipment Leases
Benefits of Leasing:
In the short term, the monthly costs of leasing are lower than the monthly costs of buying.
A new car/equipment every few years.
No long-term commitment.
Benefits of Buying:
In the long term, the cost of buying is less than leasing, because the buyer can continue to drive the car/use the equipment after all the payments have been made.
No limit on mileage/excess wear.
Flexibility to customize your vehicle/equipment.
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

9. Auto/Equipment Leases
Example: A new car can be leased for 36 months for $159/month with $1299 due at signing, or purchased over the same three-year period with $5000 down and monthly payments of $ At the end of the three years, the leased vehicle is returned with no extra charges and the purchased car can be traded in to the dealer for $11,000. What is the total cost of each option?
Lease: 36($159) + $1299 = $7023
Purchase: 36($350) + $ $11,000 = $6,600 Keep in mind, the $11,000 trade-in can be used for a new vehicle.
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates