Simple Regression Mathematics 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 Simple Regression Mathematics case study

At Oak Spring University, we provide corporate level professional Net Present Value (NPV) case study solution. Simple Regression Mathematics case study is a Harvard Business School (HBR) case study written by Frances X. Frei, Dennis Campbell. The Simple Regression Mathematics (referred as “Mathematics Regression” from here on) case study provides evaluation & decision scenario in field of Technology & Operations. It also touches upon business topics such as - Value proposition, Financial analysis, Technology.

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 Simple Regression Mathematics Case Study

A student technical note used in the third module of a Harvard Business School course on Managing Service Operations, which addresses how service managers can inform their decisions with customer data (606-097).Describes the underlying mathematics of regression.

Case Authors : Frances X. Frei, Dennis Campbell

Topic : Technology & Operations

Related Areas : Financial analysis, Technology

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Calculating Net Present Value (NPV) at 6% for Simple Regression Mathematics Case Study

Years	Cash Flow	Net Cash Flow	Cumulative     Cash Flow	Discount Rate @ 6 %	Discounted Cash Flows
Year 0	(10017625)	-10017625	-	-
Year 1	3458437	-6559188	3458437	0.9434	3262676
Year 2	3964349	-2594839	7422786	0.89	3528256
Year 3	3947966	1353127	11370752	0.8396	3314788
Year 4	3243948	4597075	14614700	0.7921	2569511
TOTAL			14614700		12675232

The Net Present Value at 6% discount rate is 2657607

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. Payback Period
2. Profitability Index
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. Timing of the expected cash flows – stockholders of Mathematics 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.
2. Magnitude of both incoming and outgoing cash flows – Projects can be capital intensive, time intensive, or both. Mathematics Regression shareholders have preference for diversified projects investment rather than prospective high income from a single capital intensive project.

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Formula and Steps to Calculate Net Present Value (NPV) of Simple Regression Mathematics

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 Mathematics 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 Mathematics 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	(10017625)	-10017625	-	-
Year 1	3458437	-6559188	3458437	0.8696	3007337
Year 2	3964349	-2594839	7422786	0.7561	2997617
Year 3	3947966	1353127	11370752	0.6575	2595852
Year 4	3243948	4597075	14614700	0.5718	1854738
TOTAL					10455543

The Net NPV after 4 years is 437918

(10455543 - 10017625 )

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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	(10017625)	-10017625	-	-
Year 1	3458437	-6559188	3458437	0.8333	2882031
Year 2	3964349	-2594839	7422786	0.6944	2753020
Year 3	3947966	1353127	11370752	0.5787	2284703
Year 4	3243948	4597075	14614700	0.4823	1564404
TOTAL					9484157

The Net NPV after 4 years is -533468

At 20% discount rate the NPV is negative (9484157 - 10017625 ) so ideally we can't select the project if macro and micro factors don't allow financial managers of Mathematics 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 Mathematics Regression has a NPV value higher than Zero then finance managers at Mathematics 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 Mathematics Regression, then the stock price of the Mathematics 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 Mathematics 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 –

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

Understanding of risks involved in the project.

What can impact the cash flow of 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 Simple Regression Mathematics

References & Further Readings

Frances X. Frei, Dennis Campbell (2018), "Simple Regression Mathematics Harvard Business Review Case Study. Published by HBR Publications.