A company handles an apartment building with 50 units. Experience has shown that if the rent...

A company handles an apartment building with 50 units. Experience has shown that if the rent for each of the units is $800 per month, all of the units will be filled, but 1 unit will become vacant for each $20 increase in this monthly rate. If the monthly cost of maintaining the apartment building is $12 per rented unit, what rent should be charged per month to maximize the profit?

Expert Solution

Let the number of units vacant be x

Number of buildings occupied = (50-x)

Monthly rate = (800+20x)

Cost of maintenance = 12(50-x)

Profit = Revenue - Cost = (50-x)(800+20x) - 12(50-x) = 40000 + 1000x - 800x - 20x^2 - 600 + 12x = -20x^2 + 212x + 39400

d/dx(Profit) = -40x + 212

Equating it to zero, we get x = 212/40 = 5.3

P(5) = -20(5)^2 + 212(5) + 39400 = 39960

P(6) = -20(6)^2 + 212(6)+ 39400 = 39952

Hence the maxima occurs for profit, when integer value is 5.

Monthly rent will be 800 + 5(20) = 900$

If decimal value is accepted, then try 800 + 5.3(20) = 906$

Note - Post any doubts/queries in comments section.

milcah answered 1 year ago

Residential Apartment Building 138 units Apartment Breakdown Monthly Rent (36) Studios ...

Residential Apartment Building 138 units Apartment Breakdown Monthly Rent (36) Studios $ 750.00 (48) 1 Bedrooms 1,500.00 (42) 2 Bedrooms 2,200.00 (12) 3 Bedrooms 2,700.00 Closing Costs: 2.5% of Purchase Price Vacancy: 3% of Gross Potential Rent Loan Constant: 6.5% Ordinary Income Tax Rate: 28% Capital Improvements: $ 213,000 Real Estate Taxes 187,000...

You are considering buying an apartment complex with 50 units. The units rent for $1000 per...

You are considering buying an apartment complex with 50 units. The units rent for $1000 per month each. Usually, there is a 10% vacancy. You want a 7.5% percent total annual after-tax return on the funds you invest. You do not expect any appreciation of the property value. You also expect the property to not have any economic or real depreciation in value, since the maintenance expenses will keep the property in equal condition year after year. When fully occupied,...

Part1) Bob's Apartment Building has 100 units that rent for $1,110 per month each. What is...

Part1) Bob's Apartment Building has 100 units that rent for $1,110 per month each. What is the Gross Potential Income for Bob's Apartment Building? Part2) Bob's Apartment Building has gross potential income of $1,000,000. The expected vacancy rate is 13%. Collection losses are 5% (after allowing for vacancies). Incidental income is $50,000 per year. What is the Effective Gross Income for Bob's Apartment Building? Part3) Bob's Apartment Building has effective gross income of $500,000. Operating expenses are 38% of revenue....

An entrepreneur is considering a new project consisting of an apartment building with 50 units. Each...

An entrepreneur is considering a new project consisting of an apartment building with 50 units. Each unit can be rented for $950/month. It is expected to have an average vacancy rate of 8%. Net operating expenses are budgeted as 30% of the project's gross annual income. What would be the economic value of this project using a cap rate of 8.3%?

1. Graph the market for apartment units that has a binding price ceiling (rent control) and...

1. Graph the market for apartment units that has a binding price ceiling (rent control) and a consumer subsidy. 2. Graph the market for tobacco that has both a consumer tax, and a producer subsidy. For each, always indicate any surplus or shortage, and under- or over-allocation.

A real estate office handles a 60-unit apartment complex. When the rent is $530 per month,...

A real estate office handles a 60-unit apartment complex. When the rent is $530 per month, all units are occupied. For each $25 increase in rent, however, an average of one unit becomes vacant. Each occupied unit requires an average of $30 per month for service and repairs. What rent should be charged to obtain a maximum profit?

The business manager of a 90 unit apartment building is trying to determine the rent to...

The business manager of a 90 unit apartment building is trying to determine the rent to be charged. From past experience with similar buildings, when rent is set at $400, all the units are full. For every $20 increase in rent, one additional unit remains vacant. What rent should be charged for maximum total revenue? What is that maximum total revenue? To help solve the above scenario, perform an internet search for Profit Parabola or Applications of Quadratic Functions. List...

The business manager of a 90 unit apartment building is trying to determine the rent to be charged.

The business manager of a 90 unit apartment building is trying to determine the rent to be charged. From past experience with similar buildings, when rent is set at $400, all the units are full. For every $20 increase in rent, one additional unit remains vacant. What rent should be charged for maximum total revenue? What is that maximum total revenue? To help solve the above scenario, perform an internet search for Profit Parabola or Applications of Quadratic Functions. List...

The manager of a large apartment complex knows from experience that 90 units will be occupied...

The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 468 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 9 dollar increase in rent. Similarly, one additional unit will be occupied for each 9 dollar decrease in rent. What rent should the manager charge to maximize revenue?

The Canadian Government is considering building apartment units for its employees working in a foreign country....

The Canadian Government is considering building apartment units for its employees working in a foreign country. These employees are currently living in rental houses owned by local landlords. Currently, the government reimburses the employees their housing and transportation expenses. Two mutually exclusive locations for building the apartments, are shown in the following data: LOCATION A LOCATION B Original Investment by the Government $8,000,000 $10,000,000 Estimated Annual Maintenance Expenses $360,000 $350,000 Government Savings in annual Reimbursements $1,960,000 $2,100,000 Assume the...

Question