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Using Regression Analysis to Estimate Time Equations 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 Using Regression Analysis to Estimate Time Equations case study


At Oak Spring University, we provide corporate level professional Net Present Value (NPV) case study solution. Using Regression Analysis to Estimate Time Equations case study is a Harvard Business School (HBR) case study written by F. Asis Martinez-Jerez, Ariel Andres Blumenkranc. The Using Regression Analysis to Estimate Time Equations (referred as “Equations Regression” from here on) case study provides evaluation & decision scenario in field of Finance & Accounting. It also touches upon business topics such as - Value proposition, Costs, Financial analysis.

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




Case Description of Using Regression Analysis to Estimate Time Equations Case Study


This note presents a simple way to estimate time equations using regression analysis in Excel. The note quickly outlines regression analysis, then presents a real-life case example from the natural gas industry that students can use to gain experience developing and interpreting the results of time equations.


Case Authors : F. Asis Martinez-Jerez, Ariel Andres Blumenkranc

Topic : Finance & Accounting

Related Areas : Costs, Financial analysis




Calculating Net Present Value (NPV) at 6% for Using Regression Analysis to Estimate Time Equations Case Study


Years              Cash Flow     Net Cash Flow     Cumulative    
Cash Flow
Discount Rate
@ 6 %
Discounted
Cash Flows
Year 0 (10016715) -10016715 - -
Year 1 3446489 -6570226 3446489 0.9434 3251405
Year 2 3972661 -2597565 7419150 0.89 3535654
Year 3 3952093 1354528 11371243 0.8396 3318253
Year 4 3231501 4586029 14602744 0.7921 2559651
TOTAL 14602744 12664964


The Net Present Value at 6% discount rate is 2648249

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.




Capital Budgeting Approaches

Methods of Capital Budgeting


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

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

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. Equations Regression 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 Equations Regression have higher preference for cash returns over 4-5 years rather than 10-15 years given the nature of the volatility in the industry.




Formula and Steps to Calculate Net Present Value (NPV) of Using Regression Analysis to Estimate Time Equations

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 Finance & Accounting 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 Equations Regression 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 Equations Regression 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 (10016715) -10016715 - -
Year 1 3446489 -6570226 3446489 0.8696 2996947
Year 2 3972661 -2597565 7419150 0.7561 3003902
Year 3 3952093 1354528 11371243 0.6575 2598565
Year 4 3231501 4586029 14602744 0.5718 1847621
TOTAL 10447036


The Net NPV after 4 years is 430321

(10447036 - 10016715 )






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 (10016715) -10016715 - -
Year 1 3446489 -6570226 3446489 0.8333 2872074
Year 2 3972661 -2597565 7419150 0.6944 2758792
Year 3 3952093 1354528 11371243 0.5787 2287091
Year 4 3231501 4586029 14602744 0.4823 1558401
TOTAL 9476359


The Net NPV after 4 years is -540356

At 20% discount rate the NPV is negative (9476359 - 10016715 ) so ideally we can't select the project if macro and micro factors don't allow financial managers of Equations Regression 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 Equations Regression has a NPV value higher than Zero then finance managers at Equations Regression 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 Equations Regression, then the stock price of the Equations Regression 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 Equations Regression 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 –

Understanding of risks involved in the project.

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.

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

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.




References & Further Readings

F. Asis Martinez-Jerez, Ariel Andres Blumenkranc (2018), "Using Regression Analysis to Estimate Time Equations Harvard Business Review Case Study. Published by HBR Publications.