Financial Applications of Linear Programs for Portfolio Selection, Financial Planning & Financial Mix Strategy

Instructor: Brendan Verma

Brendan was a Financial Advisor for 10 years and has completed all 3 levels of the CFA Program.

In the world of corporate finance, companies are constantly choosing among available courses of action. These decisions are often subject to a variety of constraints. Let's explore how linear programming can help!

How Corporate Finance Decisions are Made

Superstore, Inc., is a global retail company with significant presence in the mid-sized grocery stores segment. With over 2,000 stores across the country, it is a well-recognized brand with stable operations. In its most recent executive meeting the company's management team has proposed two projects:

  • Expanding into new distribution channels by setting up an online grocery store
  • Extending Superstore's physical presence through a franchise model

The management team of Superstore, Inc., faces some of the following questions: Which project will provide an acceptable rate of return and risk? How will company cash flows be impacted? What's the optimum mix of borrowing to pay for the project and how would this impact the company's cost of capital? If both projects are undertaken, in what proportion should that happen? What impact would these projects have on existing operations? What would be the most appropriate investment in the project to minimize changes in personnel/technology resources?

These questions give rise to several constraints that need to be considered. Constraints such as cost of capital, personnel and technology availability, existing debt covenants, cash flow variance, hurdle rates, and maximum break-even periods will shape the ultimate decision of which project to invest in.

Using Linear Programming in Corporate Finance Decisions

In general, corporate finance executives face two important decisions: How best to spend their company's money (portfolio selection) and where to get that money from (financing mix). This ensures that a company undertakes activities that maximize its value, through the best combination of return and risk. However, as seen from the example above, the decision is usually subject to a variety of constraints.

Linear programming can be used to:

  • Choose the most suitable mix of financing, such that the overall cost of capital is kept to a minimum, and/or specific constraints on types of borrowing are maintained.
  • Choose between a variety of available projects, such that risk and return are optimized, while respecting constraints like maximum break-even period or hurdle rates.

Mathematically speaking, the goal of linear programming is to optimize the value of the objective function given the constraints placed on the variables that define it.

What is the objective function? maximize X = a * A + b * B

What are the constraints? a < specified value, b > specified value

Portfolio Selection

Portfolio theory suggests that when taking on new projects, a company should not just consider the individual project but how it would affect the overall return and riskiness of the company's portfolio of projects.

Continuing from the previous example, while Superstore's management will evaluate the individual merit of the proposed projects, it must also consider the impact on existing operations. How will franchising the brand impact sales at company-owned stores? What is the likelihood that the new projects may fail, and how will that affect the overall risk in the company's current operations? Will these projects help to reduce the company's operational risk? Will new competencies be added that could be leveraged down the line? Here, the company is taking a portfolio perspective and evaluating the impact of the new project on the existing and future operations. Through portfolio selection, it is deciding how to spend money.

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