Modeling Discrete Choice: Categorical Dependent Variables, Logistic Regression, and Maximum Likelihood Estimation Net Present Value (NPV) / MBA Resources

Introduction to Net Present Value (NPV) - What is Net Present Value (NPV) ? How it impacts financial decisions regarding project management?

NPV solution for Modeling Discrete Choice: Categorical Dependent Variables, Logistic Regression, and Maximum Likelihood Estimation case study

At Oak Spring University, we provide corporate level professional Net Present Value (NPV) case study solution. Modeling Discrete Choice: Categorical Dependent Variables, Logistic Regression, and Maximum Likelihood Estimation case study is a Harvard Business School (HBR) case study written by Anton Ovchinnikov. The Modeling Discrete Choice: Categorical Dependent Variables, Logistic Regression, and Maximum Likelihood Estimation (referred as “Regression Choice” from here on) case study provides evaluation & decision scenario in field of Technology & Operations. It also touches upon business topics such as - Value proposition, Business models, Customers, Financial analysis, Operations management.

The net present value (NPV) of an investment proposal is the present value of the proposal’s net cash flows less the proposal’s initial cash outflow. If a project’s NPV is greater than or equal to zero, the project should be accepted.

NPV = Present Value of Future Cash Flows LESS Project’s Initial Investment

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Case Description of Modeling Discrete Choice: Categorical Dependent Variables, Logistic Regression, and Maximum Likelihood Estimation Case Study

This technical note introduces business students to the concepts of modeling discrete choice (e.g., a consumer purchasing brand A versus brand B) using logistic regression and maximum-likelihood estimation. It draws the analogy between modeling discrete choice and building a regression model with a dummy dependent variable and on an example illustrates the need for estimating the probability of a choice rather than the choice itself, which leads to a special kind of regression - logistic regression. The note presents the concepts of utility and a random utility choice model, of which the logistic regression model is the most commonly used. It shows how choice probabilities can be constructed from utilities leading to the logit model. It then presents the maximum-likelihood estimation (MLE) method of fitting the logit model to the choice data. Working through a detailed example using Solver and accompanying spreadsheet model, the note gives students deep understanding for how MLE works and how it is similar and different to the standard least-squared estimation in linear regression. The note concludes by presenting the results of estimation using StatTools, a commercial statistical software. The note avoids the use of heavy mathematical machinery but still requires rudimentary knowledge of exponent and logarithmic functions, probability, and optimization with Solver, as well as familiarity with the "standard" linear regression. Applications include building of models for consumer choice, estimating price elasticity, price optimization, product versioning, product line design, and conjoint analysis.

Case Authors : Anton Ovchinnikov

Topic : Technology & Operations

Related Areas : Business models, Customers, Financial analysis, Operations management

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Calculating Net Present Value (NPV) at 6% for Modeling Discrete Choice: Categorical Dependent Variables, Logistic Regression, and Maximum Likelihood Estimation Case Study

Years	Cash Flow	Net Cash Flow	Cumulative     Cash Flow	Discount Rate @ 6 %	Discounted Cash Flows
Year 0	(10029657)	-10029657	-	-
Year 1	3456905	-6572752	3456905	0.9434	3261231
Year 2	3963541	-2609211	7420446	0.89	3527537
Year 3	3961841	1352630	11382287	0.8396	3326438
Year 4	3238273	4590903	14620560	0.7921	2565016
TOTAL			14620560		12680222

The Net Present Value at 6% discount rate is 2650565

In isolation the NPV number doesn't mean much but put in right context then it is one of the best method to evaluate project returns. In this article we will cover -

Different methods of capital budgeting

What is NPV & Formula of NPV,
How it is calculated,
How to use NPV number for project evaluation, and
Scenario Planning given risks and management priorities.

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Capital Budgeting Approaches

Methods of Capital Budgeting

There are four types of capital budgeting techniques that are widely used in the corporate world –

1. Profitability Index
2. Payback Period
3. Internal Rate of Return
4. Net Present Value

Apart from the Payback period method which is an additive method, rest of the methods are based on Discounted Cash Flow technique. Even though cash flow can be calculated based on the nature of the project, for the simplicity of the article we are assuming that all the expected cash flows are realized at the end of the year.

Discounted Cash Flow approaches provide a more objective basis for evaluating and selecting investment projects. They take into consideration both –

1. Magnitude of both incoming and outgoing cash flows – Projects can be capital intensive, time intensive, or both. Regression Choice shareholders have preference for diversified projects investment rather than prospective high income from a single capital intensive project.
2. Timing of the expected cash flows – stockholders of Regression Choice have higher preference for cash returns over 4-5 years rather than 10-15 years given the nature of the volatility in the industry.

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Formula and Steps to Calculate Net Present Value (NPV) of Modeling Discrete Choice: Categorical Dependent Variables, Logistic Regression, and Maximum Likelihood Estimation

NPV = Net Cash In Flowt1 / (1+r)t1 + Net Cash In Flowt2 / (1+r)t2 + … Net Cash In Flowtn / (1+r)tn
Less Net Cash Out Flowt0 / (1+r)t0

Where t = time period, in this case year 1, year 2 and so on.
r = discount rate or return that could be earned using other safe proposition such as fixed deposit or treasury bond rate. Net Cash In Flow – What the firm will get each year.
Net Cash Out Flow – What the firm needs to invest initially in the project.

Step 1 – Understand the nature of the project and calculate cash flow for each year.
Step 2 – Discount those cash flow based on the discount rate.
Step 3 – Add all the discounted cash flow.
Step 4 – Selection of the project

Why Technology & Operations Managers need to know Financial Tools such as Net Present Value (NPV)?

In our daily workplace we often come across people and colleagues who are just focused on their core competency and targets they have to deliver. For example marketing managers at Regression Choice often design programs whose objective is to drive brand awareness and customer reach. But how that 30 point increase in brand awareness or 10 point increase in customer touch points will result into shareholders’ value is not specified.

To overcome such scenarios managers at Regression Choice needs to not only know the financial aspect of project management but also needs to have tools to integrate them into part of the project development and monitoring plan.

Calculating Net Present Value (NPV) at 15%

After working through various assumptions we reached a conclusion that risk is far higher than 6%. In a reasonably stable industry with weak competition - 15% discount rate can be a good benchmark.

Years	Cash Flow	Net Cash Flow	Cumulative     Cash Flow	Discount Rate @ 15 %	Discounted Cash Flows
Year 0	(10029657)	-10029657	-	-
Year 1	3456905	-6572752	3456905	0.8696	3006004
Year 2	3963541	-2609211	7420446	0.7561	2997006
Year 3	3961841	1352630	11382287	0.6575	2604975
Year 4	3238273	4590903	14620560	0.5718	1851493
TOTAL					10459479

The Net NPV after 4 years is 429822

(10459479 - 10029657 )

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Calculating Net Present Value (NPV) at 20%

If the risk component is high in the industry then we should go for a higher hurdle rate / discount rate of 20%.

Years	Cash Flow	Net Cash Flow	Cumulative     Cash Flow	Discount Rate @ 20 %	Discounted Cash Flows
Year 0	(10029657)	-10029657	-	-
Year 1	3456905	-6572752	3456905	0.8333	2880754
Year 2	3963541	-2609211	7420446	0.6944	2752459
Year 3	3961841	1352630	11382287	0.5787	2292732
Year 4	3238273	4590903	14620560	0.4823	1561667
TOTAL					9487612

The Net NPV after 4 years is -542045

At 20% discount rate the NPV is negative (9487612 - 10029657 ) so ideally we can't select the project if macro and micro factors don't allow financial managers of Regression Choice to discount cash flow at lower discount rates such as 15%.

Acceptance Criteria of a Project based on NPV

Simplest Approach – If the investment project of Regression Choice has a NPV value higher than Zero then finance managers at Regression Choice can ACCEPT the project, otherwise they can reject the project. This means that project will deliver higher returns over the period of time than any alternate investment strategy.

In theory if the required rate of return or discount rate is chosen correctly by finance managers at Regression Choice, then the stock price of the Regression Choice should change by same amount of the NPV. In real world we know that share price also reflects various other factors that can be related to both macro and micro environment.

In the same vein – accepting the project with zero NPV should result in stagnant share price. Finance managers use discount rates as a measure of risk components in the project execution process.

Sensitivity Analysis

Project selection is often a far more complex decision than just choosing it based on the NPV number. Finance managers at Regression Choice should conduct a sensitivity analysis to better understand not only the inherent risk of the projects but also how those risks can be either factored in or mitigated during the project execution. Sensitivity analysis helps in –

What are the key aspects of the projects that need to be monitored, refined, and retuned for continuous delivery of projected cash flows.

What are the uncertainties surrounding the project Initial Cash Outlay (ICO’s). ICO’s often have several different components such as land, machinery, building, and other equipment.

What can impact the cash flow of the project.

Understanding of risks involved in the project.

What will be a multi year spillover effect of various taxation regulations.

Some of the assumptions while using the Discounted Cash Flow Methods –

Projects are assumed to be Mutually Exclusive – This is seldom the came in modern day giant organizations where projects are often inter-related and rejecting a project solely based on NPV can result in sunk cost from a related project.

Independent projects have independent cash flows – As explained in the marketing project – though the project may look independent but in reality it is not as the brand awareness project can be closely associated with the spending on sales promotions and product specific advertising.

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Negotiation Strategy of Modeling Discrete Choice: Categorical Dependent Variables, Logistic Regression, and Maximum Likelihood Estimation

References & Further Readings

Anton Ovchinnikov (2018), "Modeling Discrete Choice: Categorical Dependent Variables, Logistic Regression, and Maximum Likelihood Estimation Harvard Business Review Case Study. Published by HBR Publications.