Cost Benefit Analysis is a decision-making tool in economics that takes into consideration the net present value of costs and benefits. But as discussed above, it is applicable to many industries and cases. For example, you can use it while deciding to purchase a real estate property or undertake a new project. But, what is the purpose of making a CBA for an investment?

Basically, Cost Benefit Analysis serves two purposes ;

To verify that an investment's (or a project's) benefits are more than its costs.

To select an investment (or a project) by comparing their benefits over cost ratios.

In order to make a comparison between the positive and negative aspects of the alternatives, a common unit is required. Money is the common unit used for comparison of alternatives. In a CBA calculation, costs and benefits are represented as monetary values. Time value of money is an important concept in CBA. While performing a CBA calculation future costs and benefits are converted into present value by using a discount rate. Note that CBA is used for both long term and short term decisions.

Conducting the cost benefit analysis provides many benefits to decision makers while deciding to purchase a new home or expanding sales in a new region. It can be conducted by big companies as well as individuals while selecting the most effective alternative.

Let's assume that a board chairman of a construction company claims his team to make a comparison between two potential real estate development projects to be constructed. He also reminds them that the company's financial health is getting poor so he has to select one of them.

The team works and lists below the potential incomes and costs of each project.

Assumptions

Note: In order to simplify the cost benefit analysis example, we will not make a net present value calculation for each cost and income.

Project 1

- 500 housing units will be constructed.

- 400 of them will be sold and 100 of them will be rented for 20 years.

- Rental Price of each unit is 4,000 USD per year

- Rented 100 units will be sold 70,000 USD after 20 years.

- Construction Cost of each unit is 100,000 USD.

- The sale price of each unit is 120,000 USD.

- The project needs a luxury sales office with a price of 2,000,000 USD.

- The sales personnel cost is 300,000 USD per year.

- The project duration is 3 years.

- Project financing cost is 3,000,000 USD per year

Project 2

- 400 housing units will be constructed.

- 350 of them will be sold and 50 of them will be rented for 15 years.

- Rented 50 units will be sold 80,000 USD after 15 years.

- Rental Price of each unit is 4,500 USD per year

- Construction Cost of each unit is 90,000 USD.

- The sale price of each unit is 135,000 USD.

- The project needs a luxury sales office with a price of 3,000,000 USD.

- The sales personnel cost is 250,000 USD per year.

- The project duration is 2 years.

- Project financing cost is 2,500,000 USD per year

All the project parameters are summarized in the table below :

\fFall 2020 1. CES Production Consider the following production function: y = [aK-P + (1 - a) L-PJP 0 0, 0 -1. Use the method of Lagrange multipliers to maximize the CES production function Q =50 0.2 K 1/5 + 0.81-1/5 subject to the constraint 5K + 4L = 135 The CES function is maximized with approximately units of capital and units of labor. Round your answers to two decimal places