Chi-Square Goodness-of-Fit Test 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 Chi-Square Goodness-of-Fit Test case study

At Oak Spring University, we provide corporate level professional Net Present Value (NPV) case study solution. Chi-Square Goodness-of-Fit Test case study is a Harvard Business School (HBR) case study written by Phillip E. Pfeifer. The Chi-Square Goodness-of-Fit Test (referred as “Goodness Chi” from here on) case study provides evaluation & decision scenario in field of Global Business. It also touches upon business topics such as - Value proposition, .

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 Chi-Square Goodness-of-Fit Test Case Study

This note describes the chi-square statistic as applied to goodness-of-fit tests. Goodness-of-fit tests check to see how closely a sample matches a particular probability distribution (e.g., normal, Poisson, binomial).

Case Authors : Phillip E. Pfeifer

Topic : Global Business

Related Areas :

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Calculating Net Present Value (NPV) at 6% for Chi-Square Goodness-of-Fit Test Case Study

Years	Cash Flow	Net Cash Flow	Cumulative     Cash Flow	Discount Rate @ 6 %	Discounted Cash Flows
Year 0	(10011705)	-10011705	-	-
Year 1	3443968	-6567737	3443968	0.9434	3249026
Year 2	3979176	-2588561	7423144	0.89	3541452
Year 3	3944854	1356293	11367998	0.8396	3312175
Year 4	3224875	4581168	14592873	0.7921	2554403
TOTAL			14592873		12657057

The Net Present Value at 6% discount rate is 2645352

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. Net Present Value
2. Payback Period
3. Internal Rate of Return
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. Goodness Chi 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 Goodness Chi 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 Chi-Square Goodness-of-Fit Test

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 Global Business 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 Goodness Chi 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 Goodness Chi 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	(10011705)	-10011705	-	-
Year 1	3443968	-6567737	3443968	0.8696	2994755
Year 2	3979176	-2588561	7423144	0.7561	3008829
Year 3	3944854	1356293	11367998	0.6575	2593806
Year 4	3224875	4581168	14592873	0.5718	1843833
TOTAL					10441222

The Net NPV after 4 years is 429517

(10441222 - 10011705 )

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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	(10011705)	-10011705	-	-
Year 1	3443968	-6567737	3443968	0.8333	2869973
Year 2	3979176	-2588561	7423144	0.6944	2763317
Year 3	3944854	1356293	11367998	0.5787	2282902
Year 4	3224875	4581168	14592873	0.4823	1555206
TOTAL					9471398

The Net NPV after 4 years is -540307

At 20% discount rate the NPV is negative (9471398 - 10011705 ) so ideally we can't select the project if macro and micro factors don't allow financial managers of Goodness Chi 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 Goodness Chi has a NPV value higher than Zero then finance managers at Goodness Chi 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 Goodness Chi, then the stock price of the Goodness Chi 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 Goodness Chi 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 can impact the cash flow of the project.

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

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.

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 Chi-Square Goodness-of-Fit Test

References & Further Readings

Phillip E. Pfeifer (2018), "Chi-Square Goodness-of-Fit Test Harvard Business Review Case Study. Published by HBR Publications.