Introduction to Net Present Value (NPV) - What is Net Present Value (NPV) ? How it impacts financial decisions regarding project management?
At Oak Spring University, we provide corporate level professional Net Present Value (NPV) case study solution. A Note on Statistics and the Law case study is a Harvard Business School (HBR) case study written by Gregory S. Zaric, lleana Funez. The A Note on Statistics and the Law (referred as “Conditional Statistical” from here on) case study provides evaluation & decision scenario in field of Strategy & Execution. It also touches upon business topics such as - Value proposition, Business law, 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.
This note presents an overview of ways in which statistical arguments are used in court cases. Topics covered include linear regression, significance, independence, bias, conditional probability, Baye's Theorem and inversion of conditional probabilities. In addition to these topics, the note contains a number of true examples where statistical reasoning has been used or misused as part of a legal argument.
| Years | Cash Flow | Net Cash Flow | Cumulative Cash Flow |
Discount Rate @ 6 % |
Discounted Cash Flows |
|---|---|---|---|---|---|
| Year 0 | (10025786) | -10025786 | - | - | |
| Year 1 | 3466359 | -6559427 | 3466359 | 0.9434 | 3270150 |
| Year 2 | 3975829 | -2583598 | 7442188 | 0.89 | 3538474 |
| Year 3 | 3944535 | 1360937 | 11386723 | 0.8396 | 3311908 |
| Year 4 | 3237206 | 4598143 | 14623929 | 0.7921 | 2564170 |
| TOTAL | 14623929 | 12684702 |
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 -
Capital Budgeting Approaches
There are four types of capital budgeting techniques that are widely used in the corporate world –
1. Net Present Value
2. Internal Rate of Return
3. Payback Period
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. Timing of the expected cash flows – stockholders of Conditional Statistical 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. Conditional Statistical shareholders have preference for diversified projects investment rather than prospective high income from a single capital intensive project.
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
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 Conditional Statistical 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 Conditional Statistical 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.
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 | (10025786) | -10025786 | - | - | |
| Year 1 | 3466359 | -6559427 | 3466359 | 0.8696 | 3014225 |
| Year 2 | 3975829 | -2583598 | 7442188 | 0.7561 | 3006298 |
| Year 3 | 3944535 | 1360937 | 11386723 | 0.6575 | 2593596 |
| Year 4 | 3237206 | 4598143 | 14623929 | 0.5718 | 1850883 |
| TOTAL | 10465002 |
(10465002 - 10025786 )
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 | (10025786) | -10025786 | - | - | |
| Year 1 | 3466359 | -6559427 | 3466359 | 0.8333 | 2888633 |
| Year 2 | 3975829 | -2583598 | 7442188 | 0.6944 | 2760992 |
| Year 3 | 3944535 | 1360937 | 11386723 | 0.5787 | 2282717 |
| Year 4 | 3237206 | 4598143 | 14623929 | 0.4823 | 1561153 |
| TOTAL | 9493494 |
At 20% discount rate the NPV is negative (9493494 - 10025786 ) so ideally we can't select the project if macro and micro factors don't allow financial managers of Conditional Statistical to discount cash flow at lower discount rates such as 15%.
Simplest Approach – If the investment project of Conditional Statistical has a NPV value higher than Zero then finance managers at Conditional Statistical 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 Conditional Statistical, then the stock price of the Conditional Statistical 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.
Project selection is often a far more complex decision than just choosing it based on the NPV number. Finance managers at Conditional Statistical 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 key aspects of the projects that need to be monitored, refined, and retuned for continuous delivery of projected cash flows.
What can impact the cash flow of 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 will be a multi year spillover effect of various taxation regulations.
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.
Gregory S. Zaric, lleana Funez (2018), "A Note on Statistics and the Law Harvard Business Review Case Study. Published by HBR Publications.
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