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Joachim Kuczynski, 05 March 2021

Baldwin rate definition

The modified internal rate of return (MIRR), or Baldwin rate of return respectively, is an advancement of the internal rate of return (IRR). But also the MIRR can be misleading and can generate false investment decisions. The MIRR is defined as:

   

FV means the final value at the last considered period, PV stands for the present value.

Pitfalls of the Badwin rate

These points have to be considered carefully when applying the MIRR:

• Cash flows in different countries, with different currencies, equity betas, tax rates, capital structure, etc. should be evaluated with specific risk-adjusted discount rates. In MIRR the project is profitable, if the rate of return is higher than the required WACC. But which WACC do we mean in projects with various differing cash flows ? No diversification of cash flows can be taken into account in MIRR. But that is crucial in evaluating international projects.
• You need premises about the reinvestment rate of the contribution cash flows that affect the profitability of the project. These premises are not required in the (e)NPV concept. Hence you add an additional element of uncertainty in your calculation when using the MIRR, without any need.
• Reinvesting contribution cash flows (numerator of the root) with the risk adjusted WACC means that the return of the project increases when the project risks and WACC increases. That cannot be true. In pinciple you should not use key figures that require assumptions about reinvestment return rates. You are evaluating a certain project and not of other unknown investment sources. In general you can discount all cash flows with its appropriate discount rate and capitalize it to the last period.
• Does capitalizing (or rediscounting) a cash flow with a risk-adjusted discount rate to a future period make sense in general? I do not think so. To rediscount cash flows with a risk adjusted discount rate including a risk premium means that you are increasing the risk of the project. The project does not remain the same, because its risk increases. Only taking a riskless discount rate for reinvestments would not increase the risk of the project. The MIRR comes from a classical perspective with no risk adjustment of the discount rates. If you are using risk-adjusted discount rates, you are mixing two concepts that do not fit.
• An additional positive cash flow must improve the profitability of the project. If you add an additional, small cash flow in an additional period , the Baldwin rate can decrease. This is because the number of periods increases and the value of the root decreases. Cases that lead to wrong results are not acceptable for decision key figure.
• If you have e.g. an after sales market with small positive cash flows, the Baldwin rate decreases by considering these cash flows in your calculation. This is because the number of periods increases and the -th root decreases. Thus an after sales market cannot be implemented in your calculation.
• You have to define clearly, which cash flow is in the numerator and which is in the denominator of the root. There is no clear and logic distinction. Thus you can find different definitions in literature. Anyway avoid to take balance sheet definitions of “investment”. Note that besides investments also fixed costs and leasing payments have to be discounted with a default free discount rate in general.
• You cannot compare mutual exclusive investment projects, if the investments or the project periods are different.
• You can also not evaluate investment projects with negative value contribution to the firm. But anyway such projects exist and have to be decided.
• All cash flows should be considered as expected value of a probability distributions. The expected value of the Baldwin rate is not the Baldwin rate of the expected values of the cash flows.

Conclusion

The (e)NPV concept is much better than the MIRR or Baldwin Rate of Return. The (e)NPV does not have all the pitfalls mentioned above. Further you can also evaluate and compare value-loosing investment alternatives and do not need any premises about reinvestment rates. There are only disadvantage of the MIRR / Baldwin rate compared to the (e)NPV, try to avoid the application of MIRR / Baldwin rate.

Operating leverage is the sensitivity of an asset’s value on the market development caused by the operational cost structure, fixed and variable costs. The asset can be a company, a project or another economic unit. A production facility with high fixed costs is said to have high operating leverage. High operating leverage means a high asset beta caused by high fixed costs. The cash flows of an asset mainly consists of revenues, fixed and variable expenses:

cash flow = revenues – fixed expenses – variable expenses

Costs are variable if they depend on the output rate. Fixed costs do not depend on the output rate. The present value (PV) of the asset is the present value of its cash flows. Present values are linear, we obtain for the asset’s PV:

PV(asset) = PV(revenues) – PV(fixed expenses) – PV(variable expenses)

Rearranging leads us to:

PV(revenues) = PV(fixed expenses) + PV(variable expenses) + PV(asset)

Those who receive the fixed expenses are like debtholders in the project. They get fixed payments. Those who receive the net cash flows of the asset are like shareholders. They get whatever is left after payment of the fixed expenses. Now we analyze how the beta of the asset is related to the betas of revenues and expenses. The beta of PV(revenue) is a weighted average of the betas of its component parts:

   

   

The fixed expense beta is close to zero, because the fixed expenses do not depend on the market development. The receivers of the fixed expenses get a fixed stream of cash flows however the market develops. That means . The betas of revenues and variable expenses are more or less the same, because they are both related to the output. Therefore we can substitute for .

   

Setting PV(revenue) – PV(var.exp.) = PV(asset) + PV(fixed exp.) we obtain:

   

This is the relationship of asset beta to the beta of turnover. The asset beta increases with increasing fixed costs. As an accounting measure we define the degree of operating leverage (DOL) as:

   

The degree of operating leverage measures the change in profits when revenues change.

Valuing the equity beta is a standard issue in DCF analysis. In many cases you take an industry segment beta and adjust it to your company or project. The adjustment of the industry beta also includes the adjustment of operating leverage. We assume that is the same for all companies in the industry segment. is the beta of the segment without operating leverage. The is the average asset beta of the industry segment, which has an average ratio of fixed expenses to profits. is provided by public databases.

For detailed information see: Brealey/Myers/Allen: Principles of Corporate Finance, 13th edition, p. 238, McGraw Hill Education, 2020)

In this post I want do derive the after-tax discount rate from the before-tax discount rate. “Before tax” means that the tax shield is not considered in the discount rate. It does not mean that the tax expenses (without tax shield) are not considered in the free cash flow. The tax expenses (without tax shield) are a part of the free cash flow in the before-tax and in the after-tax discount rate. For further information have a look at my other post WACC with Tax Shield. Abbreviations:

… before-tax discount rate
… after-tax discount rate
… rate of debt to sum of equity and debt ,
… debt interest rate
… equity interest rate
… marginal corporate tax rate

We assume that the values of , and are known. Then the before-tax discount rate is:

   

Rearranging the above to solve for we have:

   

The after-tax discount rate at a constant leverage rate is:

   

This is the famous equation most financial analysts might know. The factor “-t” comes from the tax shield and decreases the discount rate. Hence the discount rate after taxes is lower than the return rate before taxes. But you have to take care. This after-tax formula is only valid if the leverage rate remains constant. Additionally it assumes that the total amount of tax expenses can be deducted by tax shield. If these two premises are not true, the previous formula does not work and you have to an analyze the topic with the adjusted present value (APV) approach. For a general view see this post. By substituting we get:

   

This formula can be useful, because you do not have to know the equity return rate to calculate the after-tax return rate. But have in mind that this is only valid, if the leverage ratio is constant and the total tax shield amount can really be deducted from the tax expenses.

Correctly appraising capital projects with DCF analysis methods requires knowledge, practice and acute awareness of potentially serious pitfalls. I want to point out some common errors in project appraisal and suggest ways of avoiding them. For many people DCF analysis seems to be quite easy but it is not for complex projects. Here are some crucial issues from my point of view:

• Decision focus: The calculation is focused on making the right decision concerning a project or an investment. That can be different from a calculation including all expenditures of the project or investment, e.g. sunk costs. For further comments concering this topic see Incremental Free Cash Flows.
• Point of view: It has to be defined clearly from which perspective you are doing the decision and calculation. For example, the calculation can be different from the view of a business area and from the view of the overall company. The right perspective determines the relevant incremental cash flows.
• Investment: Define clearly what you mean when talking about “investment”. Avoid the balance sheet view, look at investment as initial expenditures reqired for later contribution cash flows. In my point of view the term “investment” is best defined as commitments of resources made in the hope of realizing benefits that are expected to occur over a reasonably long period of time in the future.
• Cash flows: A clear view of cash flow is important, avoid views from accounting and cost accounting, e.g. depreciation. And take into account tax effects.
• Incremental cash flows: The correct definition of incremental cash flow is crucial. It is the difference between the relevant expected after-tax cash flows associated with two mutually exclusive scenarios: (1) the project goes ahead, and (2) the project does not go ahead (zero scenario). Sunk costs must not considered. For further comments see Incremental Free Cash Flows.
• Comparing scenarios: Alway be aware of having a relative sight between the cash flow scenarios. Sometimes it is not so easy to define what would happen in the future without the project (zero scenario).
• Risk-adjusted discount rates: Risk adjustment of discount rates has to be done for all (!) cash flows of the investment project that have significant risk differences: Fixed costs, investment expenses, one time expenses and payments, expenses for working capital, leasing, tax shields and contribution cash flows (turnover and variable costs) in various markets. For more infos concerning risk adjusted discount rates see Component Cash Flow Procedure.
• Key figures: The only key figure that is valid for all types of projects and investment decision is the famous NPV. All other well-known figures like IRR, Baldwin rate, … are leading to false decisions in some cases. NPV also allows to build the bridge to financial calculation approaches like option valuation. Payback and liquidity requirements have to be considered carefully additionally to NPV.
• Expected versus most likely cash flows: Quite often analysts take most likely cash flows. The right way is to consider the expected value of the cash flows.
• Limited capacity: Do not forget internal capacity limitation when regarding market figures. Limited capacity has also to be considered when constructing the event tree in real options analysis. Besides that the temporal project value development with contribution cash flow’s WACC has to be ensured in the binomial tree.
• Hurlde rates: Avoid hurlde rates for project decisions, because the can also lead to false decisions. Especially when you take one hurdle rate for different projects.
• Cash flow forecasting: Forecasts are often untruthful. Try to verify and countermeasure cash flows from different sources.
• Inflation: Be careful considering inflation. In multinational project it might influence the foreign currency location’s required return. You can also consider a relationship between inflation rate and expected future exchange rates according to the purchasing power parity (PPP).
• Real and nominal discount rates and cash flows: The procedure should be consistent for cash flows and discount rates. Usually we take nominal values for the calculation.
• Real Options: A DCF analysis should always be linked to a real options analysis. The more flexibility is in the project the more important is a real options analysis. Risk adds value to real options.
• Precise cash flow timing: The influence of timing intervals can be significant. You can choose smaller time intervals in crucial time periods to increase accuracy.