When to use NPV, IRR or MIRR

By | May 26, 2010

What is Capital Budgeting?

Capital budgeting is the process of allocating capital after determining project feasibility. Determining project feasibility is a 3 part process:

Step 1] Qualitative Analysis – Relationship/Branding feasibility, Socio-Cultural & Political feasibility
Step 2] Forecasting Performance – Financial Modeling & Structural analysis (Most critical!)
Step 3] Quantitative Analysis –IRR (or MIRR), NPV, Payback period and other quantitative analysis

Note: Step 1 & 2 are far more critical & demanding, however, the focus of this article is Step 3

What’s all the fuss about?

In real world situations, a company may have a choice of investing in several competing projects at the same time while resources may be sufficient for just one. This is where it may have to make a choice as to which project must be selected based on feasibility measured on different dimensions (at times one conflicting with the other). By dimensions we mean Qualitative & Quantitative factors the weights of which may change based on circumstances and priorities. E.g. for building a stronger/long-term relationship with a large prospective client a manager may choose to overlook quantitative factors in anticipation of securing future projects. However, as mentioned earlier Qualitative factors are beyond the purview of this article. Now, when choosing between quantitative methods one might come across conflicting results. E.g. Project A may have a superior IRR while Project B may have a better NPV.

Which metric should one choose and what are the pitfalls involved in calculating them? This article delves into popular quantitative project analysis techniques with a view to cut through the haze and get to the most appropriate/robust method suited to real world situations.

What is IRR & how does it work?

IRR is one of the most popular return analysis tool used in Project Appraisal, Private Equity Deals, LBO analysis & calculating Bond YTMs too! Put simply, Internal Rate of Return measures the return generated by an asset assuming that the reinvestment rate of cash flows thus generated, is the same as the IRR itself. In Short: IRR is an iterative process where reinvestment rate is the same as the IRR itself!

Note: When measured correctly, IRR equals the Compounded Annual Growth Rate (CAGR)

What is MIRR and why is it considered better than IRR?

The biggest problem with IRR, as cited by popular academicians, is that the Reinvestment Rate of interim cash flows is same as the IRR itself. In real world situations however, a company may not have the opportunity to get the same IRR as before. Put simply, IRRs of each new project will differ and hence the manager must find a way to incorporate that change instead of just assuming the same RR (Reinvestment
Rate) as IRR.

MIRR to the rescue: The Modified Internal Rate of Return provides the flexibility of modifying the RR as desired. Managers may find it difficult to forecast RRs down the investment horizon and hence a safe assumption would be to set it equal to the Cost of Capital, below which, incremental projects will result in ‘Value Destruction’ (The concept of EVA™).

In Short: MIRR delinks the Reinvestment Rate from IRR thereby giving the manager an option to choose a different/more realistic rate (usually Cost of Capital) thereby giving a more reliable conclusion.

Does that mean MIRR is the best?

No. Both IRR & MIRR fail to capture the Present Value of money and are hence called ‘Internal’ Rates! The best method must factor Internal Return as well as the Cost of Capital to determine Present Value. The Net Present Value (NPV) method aims to capture both and hence is the preferred choice by managers the world over.

What is NPV?

The NPV method ‘discounts’ operating cash flows at a rate that captures the cost of capital (i.e. the capital used/contributed to generate cash flows). The NPV method aims to capture the amount available after meeting the cost of all capital contributors (all claimholders). In fact, the NPV method is what leads to the concept of value creation through Economic Profit. Thus even if the IRR of Project A is better than Project B, a relatively lower Cost of Capital may swing the decision in favor of Project B.

In Short: A positive NPV is a must and the higher the better. The relationship between NPV and IRR is that “IRR is the rate at which NPV = Zero” When Cost of Capital is more than IRR the NPV will be Negative

Note: Discounting/Compounding is beyond the scope of this article

Now what’s Cost of Capital?

Suppose you were to setup a business you would start by estimating the asset requirement based on the market you want to cater (Local, National or International) and then determine how it must be funded. E.g. If Assets worth Rs.10,000 must be bought you may be able to invest just Rs.3000 while the balance Rs.7000 may have to be borrowed (i.e. Raising Debt). Now, you will have a certain opportunity cost of the money invested (popularly measured by CAPM) say 15% while the lender of Rs.7000 debt may ask for a fixed return of 7.86%. This implies that you will have to generate a minimum return of (15% x 3000) + (7.86% x 7000) = Rs.1,000. Implying a minimum return of 1,000/10,000 = 10%, also called the Weighted Average Cost of Capital (WACC) or simply Cost of Capital.

Note: The explanation was an oversimplification of the process and real world calculations are far more complicated

How does NPV work?

From the example above if we assume that the business generates Cash flows of Rs. 4,000…3,500…1,500…2,000…2,500 over a 5 year horizon. The NPV would be calculated as under:

Finally what do I choose?

NPV will always rule above all, as the Return on Funds deployed must always exceed their cost (i.e. IRR must always be > WACC). Between IRR & MIRR, IRR will always result in more ‘noise’ as compared to MIRR and will hence result in an incorrect feasibility study. What may appear to be just a 1-2% difference would result in huge difference when measured in monetary terms rather than percentages!

In Short: The order of preference must be NPV, MIRR & IRR. However, the answer is not that simple, read on…

What’s the larger picture?

It should be noted that the Structural Analysis (i.e. Revenue Stream, Payment Schedules etc.) and Financial Modeling (i.e. actual framework of the Income Statement, Balance Sheet & Cash Flow Statement that will be used to create the forecast) of the projected cash flows is the most critical, the results of which are used as an input for any kind of quantitative analysis (i.e. IRR, MIRR or NPV analysis!)

What’s the bottom-line?

Now that you have understood that quantitative analysis is just a small part of a much larger framework. It should now be obvious that blindly choosing one metric over the other would be naïve! Although NPV is a superior metric it does not by itself disclose scope for improvement. This is the very reason why we recommend that a project should not be rejected simply because it has a lower NPV, unless there is no way to improve it. Let’s see how…

IRR = Max Potential Return: IRR reveals the maximum return potential of a project assuming no interference from external factors like funding constraints and the ‘funding mix’. Put simply, if two projects have identical Funding Costs the one having a higher IRR will have a higher NPV and hence should be selected. This also implies that NPV should be first ‘tested for improvement’.

Testing NPV for improvement: NPV is affected by two components – IRR of cash flows and Cost of Funding. IRR of projects is far tougher to improve as compared to the ‘Funding mix’ (which in turn determines the Cost of Capital i.e. WACC). Theoretically, IRR can be improved by improving efficiency, but that’s a different story altogether! In most cases, it is more or less controlled by external factors, typically industry specific. Comparatively, WACC is more elastic and some critical steps may help reduce it!

The role of Capital Structure in managing WACC: Optimum Capital Structure, by many, is believed to be a theoretical concept as practitioners believe that following a ‘Target Structure’ is nearly impossible as market conditions will not allow one to keep it stable unless the firm is at a ‘Matured stage’, where expansion needs are limited and capital management becomes far simpler! High growth companies are driven by Capex and the funding mix is not as important as getting the right amount while for matured companies the priority reverses!

Many practitioners believe “Raise money when you can, and not when you should” However, if debt is raised without really being required at a certain time it will increase the risk and hence the Cost of Equity. Modern theory suggests that Optimum Capital Structure should be based not on interest tax shields but rather the risk specific to the firm and industry on a long term basis.

Risk-Expected Return relationship: Incremental risk increases the cost of equity, irrespective of whether cash rewards (dividends) are paid or not. If there are senior claimholders over Equity the Cost of Equity is bound to increase and the higher the claim of seniors higher the Cost of Equity. Put simply, it is this risk that can and must be tested for improvement.

Basically, risk can be broken into two broad categories – firm specific (fairly elastic) and industry specific (mostly inelastic). Firm specific risk can be further broken down into Operating & Financial Risk.

– Operating risk results from fixed operating costs such as Fixed Assets, Rent, Lease etc. One way to curb operating costs is to control excess capacity additions in good times – Easier said than done! This is the most common cause of risk, typical in cyclical sectors where ‘bad timing’ of capex can increase risk by under utilization of capacity.

– Financial risk is an outcome of fixed financial costs i.e. Interest. As mentioned before this is difficult to control and is dependent on too many factors (mostly external) only few of which can be controlled by a company. Put simply, if a company has superior operating risk managing capabilities it will be perceived as less risky by the debt issuer and will thus reduce interest cost as well.

In Short: Companies with poor operational performance will always have higher financial costs/risk.
From the above discussion it should be clear that operating risk is easier to control and will help reduce overall risk thereby reducing the cost of capital and increasing NPV!

Bottom-Line: IRR (or more correctly MIRR) should be used to judge maximum potential of a project based on which a firm must try to reduce risk to maximize NPV. Easier said than done but the right way out!

3 thoughts on “When to use NPV, IRR or MIRR

  1. Dr Kannapiran Arjunan

    IRR is the best criterion: Neither NPV nor MIRR is useful

    1. NPV is nothing more than the unutilised or unallocated NCF and if fully allocated it will become zero and the IRR will be the maximum at Zero NPV (see papers in the link attached).

    2. MIRR should not be used as the results might lead to wrong advice to the investors and potentially law suit for the wrong advice, because:

    a. MIRR assume reinvestment but in reality there is no reinvestment as discussed in the papers …Link attached).

    b.MIRR can be misleading in the case of multiple IRR situation. In those situations the non-normal cash flow will indicate the net cash flow before discounting is either zero or negative and that being the case how come MIRR manipulate to get a higher rate of return. MIRR is dubious manipulation.

    c. If you keep on increasing the reinvestment rate the MIRR limitlessly will increase without any relationship to the capacity of the NCF to support such a higher return. Again a dubious return by MIRR.

    1. “A New Method to Estimate NPV from the Capital Amortization Schedule and an
    Insight into Why NPV is Not the Appropriate Criterion for Capital Investment
    Decision”. paper link: https://ssrn.com/abstract=2899648.

    This paper introduces a new method to estimate the NPV based on Capital Amortization Schedule (CAS) and not the conventional DCF method. The new method is more transparent. This paper questions the validity of the NPV as a preferred criterion than IRR. The results also clarify that there is no reinvestment of intermediate income, as CAS does not involve reinvestment. When there is no reinvestment, the MIRR estimate is also redundant.

    2. IRR Performs Better than NPV: A Critical Analysis of Cases of Multiple IRR and
    Mutually Exclusive and Independent Investment Projects. https://ssrn.com/abstract=2913905

    3. The Controversial Reinvestment Assumption in IRR and NPV Estimates: New Evidence Against Reinvestment Assumption (February 16, 2017). https://ssrn.com/abstract=2918744

    These papers present evidence to identify the most appropriate investment criterion (IRR vs NPV) with emphasis on the controversial multiple, negative and no IRR, mutually exclusive investment and
    independent projects. The analysis is based on the estimated return on capital (ROC), return on invested capital (ROIC) and capital amortization schedule (CAS). Numerical evidence is furnished to recommend IRR as the best criterion and not the NPV.

    The analytical results presented in these papers question some of the conventional wisdoms advocated by most finance and economic texts or project analysis guide or publications or teaching materials and therefore the contents will enable the respective authors or organization to revise or update their publications accordingly. The current practice is to prefer NPV but the evidence does not support such preference.

    Dr Kannapiran c. Arjunan, PhD, MBA ckannapiran@yahoo.com

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