Bayesian Estimation & Black-Litterman 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 Bayesian Estimation & Black-Litterman case study

At Oak Spring University, we provide corporate level professional Net Present Value (NPV) case study solution. Bayesian Estimation & Black-Litterman case study is a Harvard Business School (HBR) case study written by Erik Stafford, Joshua D Coval. The Bayesian Estimation & Black-Litterman (referred as “Bayesian Litterman” from here on) case study provides evaluation & decision scenario in field of Finance & Accounting. It also touches upon business topics such as - Value proposition, Risk 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

Case Description of Bayesian Estimation & Black-Litterman Case Study

Describes a practical method for asset allocation that is more robust to estimation errors than the traditional implementation of mean-variance optimization with sample means and covariances. The Bayesian inspired Black-Litterman model is described after introducing the intuition of the Bayesian approach to inference in a univariate setting.

Case Authors : Erik Stafford, Joshua D Coval

Topic : Finance & Accounting

Related Areas : Risk management

Calculating Net Present Value (NPV) at 6% for Bayesian Estimation & Black-Litterman Case Study

Years              Cash Flow     Net Cash Flow     Cumulative    
Cash Flow
Discount Rate
@ 6 %
Cash Flows
Year 0 (10010249) -10010249 - -
Year 1 3464449 -6545800 3464449 0.9434 3268348
Year 2 3971518 -2574282 7435967 0.89 3534637
Year 3 3969231 1394949 11405198 0.8396 3332643
Year 4 3221989 4616938 14627187 0.7921 2552117
TOTAL 14627187 12687745

The Net Present Value at 6% discount rate is 2677496

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. Payback Period
2. Internal Rate of Return
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. Bayesian Litterman 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 Bayesian Litterman 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 Bayesian Estimation & Black-Litterman

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 Bayesian Litterman 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 Bayesian Litterman 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 %
Cash Flows
Year 0 (10010249) -10010249 - -
Year 1 3464449 -6545800 3464449 0.8696 3012564
Year 2 3971518 -2574282 7435967 0.7561 3003038
Year 3 3969231 1394949 11405198 0.6575 2609834
Year 4 3221989 4616938 14627187 0.5718 1842183
TOTAL 10467619

The Net NPV after 4 years is 457370

(10467619 - 10010249 )

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 %
Cash Flows
Year 0 (10010249) -10010249 - -
Year 1 3464449 -6545800 3464449 0.8333 2887041
Year 2 3971518 -2574282 7435967 0.6944 2757999
Year 3 3969231 1394949 11405198 0.5787 2297009
Year 4 3221989 4616938 14627187 0.4823 1553814
TOTAL 9495862

The Net NPV after 4 years is -514387

At 20% discount rate the NPV is negative (9495862 - 10010249 ) so ideally we can't select the project if macro and micro factors don't allow financial managers of Bayesian Litterman 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 Bayesian Litterman has a NPV value higher than Zero then finance managers at Bayesian Litterman 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 Bayesian Litterman, then the stock price of the Bayesian Litterman 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 Bayesian Litterman 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.

Understanding of risks involved in the project.

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

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.

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.

Negotiation Strategy of Bayesian Estimation & Black-Litterman

References & Further Readings

Erik Stafford, Joshua D Coval (2018), "Bayesian Estimation & Black-Litterman Harvard Business Review Case Study. Published by HBR Publications.

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