A Scorecard to Detect Financial Leverage Profitability

This study investigates how balancing internal and external financing sources can create economic value. We set a financial scorecard, consisting of the Cost of Debt (COD), Return on Investment (ROI), and the Cost of Equity (COE). We show that COE should be a cap for COD and a floor for ROI in order to increase the Net Present Value at Weighted Average Cost of Capital and the Adjusted Present Value of the levered investment. However, leverage should be carefully monitored if COD and ROI go off the grid. Situations where leverage has the opposite effect on value creation and the Equity Internal Rate of Return are also discussed. Illustrative examples are given. The proposed model aims to help corporate management in financial decisions.


Introduction
A long-standing question in corporate management is how to balance internal and external financing sources in levered industrial investments in order to increase creation of added value (see Brealey et al., 2016 among others).
By setting up a Key Perfomance Index (KPI) dashboard consisting of the Cost of Debt (COD), the unlevered Cost of Equity (COE) and Return on Investment (ROI), we formalize the intuitive condition that debt cost should be sufficiently cheap and investment should be sufficiently profitable.We show that COE shoud be a cap for COD and a floor for ROI.If KPIs go off this grid, external funding sources require careful monitoring.In fact, leverage may destroy added value, which is measured by the Net Present Value at Weighted Average Cost of Capital (NPV at WACC) and the Adjusted Present Value (APV).Secondly, we discuss the impact of leverage on Equity Internal Rate of Return (Equity IRR).We show that situations may exist where leverage pushes Equity IRR up and destroys economic value at the same time.These findings are illustrated by didactic examples.
In light of this evidence, this study proposes a test to signal project financial leverage profitability, able to support the Chief Financial Officers in making fast decisions.This paper is organized as follows.Section 2 describes the framework and collects basic notations.In Section 3 sufficient and necessary conditions for leverage to generate positive and increasing value are examined.Linkages with Equity IRR are also discussed.In Section 4 the findings are illustrated using didactic examples.Section 5 concludes.

The Framework
Financing is an essential part of operating any business, in fact a firm's potential for growth is limited without adequate access to financing (Rahaman, 2011).
By using the terminology (Note 1) introduced by Lutz and Lutz (1951), we restrict our analysis to PICO projects characterized by a unique cash outflow (point input) at and providing distributed cash in-flows (continuous outputs) at future dates.The investment will be supported with a POCI loan, providing a single cash inflow (point output) at requiring a number of future repayments for principal and interests (continuous output).
Here is the notation that will be used throughout the document.Let's consider an economic agent (i.e. a firm) facing the opportunity of investing in an industrial project A that promises at time , with , free , with the usual convention that means that at time there is a money outflow, while a money inflow and no cash movement.
For simplicity but without loss of generality, we can assume that: a single project generates free operating cash-flow at times where ; -initial project outlay ; -initial time ; -initial unitary borrowing at time asks for payments at subsequent epochs s t where .
At the beginning, the project is debt financed and equity financed with .If the project is all-equity financed; whereas if it is all-debt financed.
The debt financing stream reads .The equity financing at initial time is .
The equity cash flow (ECF) generated by the project at time is given by the difference between free operating inflow and the debt repayment outflow , for .
And we can assume that , so that no further capital is required during the project's life-time (Note 2).For all-equity financed projects, the most conceptually best analysis tool from the stockholders' perspective is the Net Present Value (NPV) method (see Brealey et al., 2016 among others).
The created economic value of an all-equity financed project A corresponding to , is calculated by discounting free operating project cash-flow A, given by where i is the discount rate.This definition highlights the crucial role played by the discount rate in profitability valuation.The proper discount rate is COE, meant as shareholders' required rate of return on an equity investment for the period from 0 to .

Levered Investment Valuation
NPV has to be corrected for debt reimbursement costs if the project is partially supported by external funding.The prevailing methods are based on calculating NPV at WACC, labelled WACC method and calculating NPV of net equity cash-flow, labelled Adjusted Present Value (APV) method.Here we demonstrate that the profitability tracking rule is just the same for both the methods.Let's consider the following KPIs: -ROI defined as Internal Rate of Return (IRR) of the free operating project cash-flow A; and -COD defined as IRR of the debt cash-flow D.
ROI and COD exist and are unique for PICO projects and POCI financing.

WACC method
The most common method used by executives is NPV at WACC (see for example Copeland et. al. 1996).WACC α rate for a debt financed project is defined as ( ) where .
That can be rewritten as ( ) The following is true for PICO projects: -For cheap loan condition, i.e. , discounting factors in (1) increase in leverage .It means that ( ) NPV WACC α value increases in leverage , so debt should be taken at the maximum value permitted; ( ) NPV WACC α is equal to the ( ) NPV COE generated by all-equity financed project.
Discounting free operating cash-flow with , at WACC α implicitly assumes that the levered investment maintains the debt percentage invariant over time.However, severe distortions in valuation of the present value may occur if capital structure changes.

APV method
Following the seminal ideas of Myers (1974) the APV approach has been independently formalized and extended by Grubbstrom et al. (1991) and Peccati (1989) (see Myers, 2015).APV is defined as NPV of net equity cash-flow (ECF) at the discount rate i: with .By re-writing the above formula we get where is the net present value of free operating project cash-flow A at the discount rate i if the project is all-equity financed; and stands for the net present value of a unitary debt cash stream D at the discount rate i.
Since formula (2) involves the net equity stream, the appropriate discount rate is COE.Discounting at WACC rate would be conceptually incorrect because the debt cost is already incorporated in free operating project cash-flow (see Krüger et al., 2015).From here on, we will use the short notation and . We can prove (see Appendix A) that this is valid for PICO projects: -

COD COE
The double condition (3) simply formalizes the intuitive guideline that leverage creates positive and increasing value if loan is cheap and project is profitable.It is worthwhile noting that profitability is detected by the same balanced scoreboard track (3) even though the WACC and APV methods are grounded on different assumptions (see Cigola and Peccati, 2005).
External financing has to be handled with care if the double condition (3) is weakened.Specifically: -For cheap loan and unprofitable project, i.e. and : leverage creates positive or null value and the project destroys value.These two opposite effects may partially compensate each other and final value may be either positive or negative; -For expensive loan and profitable project, i.e. and : leverage destroys value and the project creates a positive or null value.Again, final value may turn positive or negative according to the leverage level.

Equity IRR Criterium
A popular KPI for gauging equity profitability is the return on equity defined as the interest rate earned by equity in one period.Recently, this KPI has been extended to multi-period investments (see Beal, 2000).Equity IRR α is defined as the IRR of net equity cash flow of a debt financed project.The double condition (3) implies , and that implies that leverage increases Equity IRR α (see Farinelli et al., 2017).Then the double condition (3) implies that leverage increases A NPV at WACC, APV and Equity IRR α .However, the simple condition that guarantees that leverage increases Equity IRR α , is not sufficient to ensure the double condition (3).For expensive loans (i.e.
) leverage has an opposite effect on value creation and Equity IRR α .In fact, leverage increases Equity IRR α thanks to the project profitability (i.e. ), but at the same time, it decreases

Numerical Illustrations
To ascertain the impact of leverage on and Equity IRR α we discuss a didactic case.Let the project A be structured as in Table 1.At the start, project A requires an outflow of €1000; and promises €600 a year later and €700 two years later.The results 18.88% ROI = . Let A be debt financed and ( ) Debt is reimbursed in one year.Let compute NPV at WACC and APV as defined in ( 1) and ( 2 Case I: Cheap loan and profitable project.Let , and 18.88% ROI = . Double condition (3) applies, so both debt and project create positive value.It follows that the higher the leverage , the higher positive A NPV at WACC α and positive values, for any .Since , the higher , the higher , as well.We can conclude that optimal leverage strategy is to debt financing at maximum level.That is illustrated in Table 1, where as increases, positive A NPV at WACC α , positive and increase, as well.The model informs that optimal leverage is for .That means that at initial time equity should not be invested in the project A. Equity should be invested only a year latter when debt repayment asks for €1080.Since the project revenue is of only €600, the difference should be covered by an equity outflow of €480.Equity is rewarded by €700 a year after.That financing strategy makes Table 3. Case II: Cheap loan and unprofitable project.Let , and 18.88% ROI = .

COD COE
Due to cheap debt conditions (i.e.
) external financing creates value.However equity should not be invested in the project A, because project return is lower than the equity return (i.e.
).The values A NPV at WACC α and may be negative.Due to cheap debt conditions, value creation switches from negative to positive for sufficient high levels of external financing.Loan is expensive (i.e. ) consequently leverage destroys value.Project is profitable (i.e. ) then creates value and all-equity financed project is the most profitable strategy.Because of , then increases with (see Farinelli et al., 2017).In conclusion, an increase in leverage moves

Conclusion
In this paper we have created a scorecard to fast track leverage effects on profitability.The profitability requirement that "debt should be fairly cheap and the project fairly profitable" is formalized by the double condition that COE should be a cap for COD and a floor for ROI., so COE must be a floor for ROI.Analogously, if and only if , so COE must be a cap for COD.Q.E.D.

Notes
Note 1.Such terminology is constructed ''from the viewpoint of the project''.Consequently, when the project asks for money, we say that there is an input (in the project).When the project pays some positive cash-flow, we say that it produces an output.
Note 2. This condition characterizes the so called normal equity cash flow.

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ANPV WACC α value decreases in leverage , so debt should be limited to the minimum value necessary.A NPV WACC α value.

Table 1 .
Project A cash flow

Table 4 .
Leverage increases Equity IRR because .In conclusion, Equity IRR criterium goes hands in hands with NPV at WACC and APV criteria.
ANPV at WACC α , and increase in .A NPV at WACC α

Table 5 .
WACC α and down and, at the mean time, up.So WACC and APV methods identify leverage strategies which are in conflict with Equity IRR criterium.In conclusion, debt should be: (1) limited to the minimum necessary, if you follow WACC and APV methods, but (2) it should be augumented at the maximum level permitted, if you follow Equity IRR criterium.
ANPV at Under these circumstances, leverage increases NPV at WACC, APV and Equity IRR.However, Equity IRR criterium may conflict with WACC and APV methods if this double condition is relaxed and the loan is expensive.Leverage may increase Equity IRR and bring down NPV at WACC and APV at the same time.Brief didactic examples illustrate the results.