The Net Present Value (NPV), the Capital Asset Pricing Model (CAPM), and the Weighted Average Cost of Capital (WACC) are some of the tools which are mostly used for the purpose of capital budgeting. The techniques are widely used for decision-making, especially when a firm wants to find the value of assets. The NPV is a cornerstone in financial economics. As known, the rate of return that is required is among the primary components that constitutes the NPV, the former is often determined from CAPM. The WACC may be used in lieu of CAPM for determining the discount rate to be used in the NPV model. Thus, there are interactions between these three techniques. This paper will delve into an understanding of the NPV, CAPM, and WACC concepts. The paper will then delve at discussing the interaction between the NPV rule, the CAPM, and the concept of WACC. Lastly, the paper will outline the legal context in which these concepts may become relevant.
Concepts of NPV, CAPM, and WACC
The NPV
This technique is widely employed to determine if an investment is profitable. In order to find the NPV, one need to know the initial cost (IC) of the project as well as the cash flows. The present value, denoted as PV, of the cash flows then need to be determined and summed up to find the total PV 1 . The NPV of a project is the total PV minus the IC. The formula used in find NPV is given below 2 ;
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The algebraic formula for determining the Net Present Value is shown below;
It is important to note that the IC is negative since it represents cash outflow.
The NPV is positive if the total PV is greater than the IC of investment. If the IC is greater, then the NPV is negative. During the decision-making process, a firm may use the NPV rule to decide whether to decide if to invest in a project, such as n acquisition. According to the NPV rule, a company should invest in a project with a positive NPV because this reflects positive returns 3 . In case a firm wants to invest in two independent projects, the NPV for both project ought to be positive in order to make the firm the decision of investing in it. However, for mutually exclusive project, a firm ought to choose the alternative with highest NPV. There are cases where the NPV is neutral (=0); this means that investing in the project will neither yield positive or negative returns. In such cases, the management may use other tools for decision-making to decide on whether to invest in the project. For instance, it may non-monetary factors, such as goodwill.
CAPM
Regardless of the way a firm diversifies its investments, some level of risks will always exist. This makes the firm seek a return rate (r) that compensates for that risk. The investment risk, as well as the rate of return that is required can be computed by utilizing the CAPM technique. William Sharpe developed the CAPM model in 1964 4 . The CAPM is a model that provides a relationship between the return that is expected for assets and systematic risk. The model is used to show the return that is expected on a security is equal to sum of the risk premium and the risk-free return 5 . Figure 1 illustrates the CAPM concept.
Figure 1: Capital Asset Pricing Model 6 .
The CAPM formula is shown below;
…………………………………………… .. 7
Where;
Among the components of the CAPM formula, the beta ( ?) is one of the measures that can be used to measure a stock’s risk. It often used to measure the relative volatility of a stock. A stock’s beta of 1 indicates that the share prices move in line with the market 8 . The CAPM formula is employed when determining the expected returns on an asset. This statistical measure shows the amount of compensation, in the form of a risk premium, equity investors need, in order to take additional risk. Basically, the risk premium ought to be greater than the risk-free rate. For a firm to invest in a project that is more risky, it desires a higher risk premium. The CAPM is widely employed in the finance industry. The model is used to calculate the WACC as CAPM computes the cost of equity. The WACC is utilized widely in financial modeling.
The Concept of WACC
The WACC is return a business or company presumes to pay off all its different investors. A company’s financing is categorized into two components; debt and equity. The WACC is the average cost of raising firms financing. The formula for WACC is;
…………………………… . 9
The WACC formula is composed of two components, the equity, and the debt component. The CAPM can be used to calculate the cost of equity as it equates rates of return to volatility. The concept of WACC can be used to determine the NPV of a business, which can, in turn, used to calculate its enterprise value as well as its equity value. When evaluating mergers and acquisitions, companies tend to use their WACC as a hurdle rate. If the Internal Rate of Return (IRR) for investment is higher than its WACC, a firm should buy back its own shares. Alternatively, the company can payout a dividend as an alternative to investing in the project.
Interaction between the NPV rule, the CAPM, and the concept of WACC
One of the components in the NPV formula is the discount rate, which is the minimum required rate of return to convince an investing company to secure the target. The deduction rate is utilized to discount the returns as well as the terminal values of investment to present value. The key parameter in the NPV method is the required rate of return on equity. This parameter provides an interaction between the NPV rule, the CAPM, and the concept of WACC. The required rate (r) on equity used in the NPV formula can be determined using the CAPM 10 . Other than the CAPM, the WACC and the Arbitrage Pricing Theory (APT) are two other techniques that can be used to determine the discount rate 11 .
The NPV is one of the techniques that is widely used to evaluate projects. NPV is used to determine whether a project can yield returns. When calculating the NPV, the future cash flows are discounted at a given rate. This rate can be determined using WACC. WACC can be utilized to discount all the cash flows as well as the terminal values. In addition, WACC serves as the cost of capital for a firm when determining Economic Value Added. Thus, this technique can be used as a measure of value creation.
WACC offers a way for calculating the cost of a firm’s debt as well as the equity of financing. The technique includes the financing decision when calculating the discount rate and, therefore, the impact of the interest deduction on the debt 12 . Thus, under WACC, the benefit of the interest deduction is reflected in a lower cost of capital. Just like when using the CAPM technique, when using the WACC technique to calculate the cost of capital, the cash flows ought to be projected based on all-equity financing. The cost of equity used in WACC can be determine from the CAPM. Thus there is interaction between CAPM and WACC since the CAPM has a role in the use of WACC
In order to understand the principles behind CAPM, it is very important to have a clear understanding of these three concepts of (I) systematic and unsystematic risk, (II) beta, and (III) the market risk premium 13 . CAPM gives the rate of return that can be used in the NPV formula by taking into account the three variables mentioned above. The expected rate of return can be derived from the algebraic statement of the CAPM.
In 2008, Magni set out to determine the reliability of using the CAPM alongside the NPV 14 . Magni used disequilibrium values to compute an investment’s NPV and checked its consistency with the CAPM. For the purpose of decision-making, the author found that the CAPM formula can be used to logically deduce the disequilibrium NPV. In his derivation, Magni assumed security market exists in his computations in order to meet assumptions of the CAPM. In this scenario, it means that any asset traded in the security market would lie on the characteristic line and the relationship is shown below;
With;
Equation 1 and 2 can be restated in NPV terms;
Magni solved equation 3 and found a well-known certainty equivalent form which as shown below;
………… .(4) 15
Legal Context in which the NPV rule, the CAPM, and the Concept of WACC become Relevant
One of the legal contexts in which the NPV rule, the CAPM, and the concept of WACC become relevant is in the appraisal of proceedings. For instance, in Weinberger v. UOP, the decision made by the Supreme Court of Delaware, emphasize the significance of these valuation models 16 . The court found that the controlling shareholder, who acquired the target in a free-out merger, to have violated its fairness duty to the public shareholders. In Weinberger, the court held that for succeeding accounts, the remedy for complaining shareholders is to dissent from the transaction formally as well as to have their shares appraised 17 . In addition, courts were required to follow a more “liberal approach” in finding the stock value in appraisal proceedings rather than exclusively using the Delaware Block Method (DBM).
The DBM was used to determine the worth of a company by taking the weighted average of the trading value, target’s shares, net asset value, and past dividend stream 18 . However, this formula was rejected as it gave “no weight” to asset value as well as the market value. Instead, the Discounted Cash Flow technique was used as it was found to be basically sound. The Delaware Court found projected revenues to be objectively based and reasonable, and the CAPM, as well as the WACC, was used to determine the discount rate 19 .
Mergers, tender offer, and leveraged buyouts are other legal contexts in which NPV, CAPM, and WACC techniques are likely to be employed 20 . Investment bankers may use these techniques to issue fairness opinions in the contexts named above. The CAPM and WACC techniques may also be used to find if a fraudulent transfer has transpired in a leveraged buyout (LBO). In such a case, the secured creditors offer new debt to fund the LBO, and the transaction could be regarded as a fraud on the unsecured creditors unless the target’s assets have sufficient value. The main concern is if the leveraged buyout company is solvent after the transaction. If the company is insolvent, it indicates that a fraudulent transfer has occurred 21 . Two valuation standards are employed for determining if a company is a solvent. These two methods include (I) the liquidation method; and (II) the going concern method. The latter is the most appropriate method and can be determined using the DCF, CAPM, and WACC techniques.
CAPM and WACC can be used in other legal contexts; for example, they can be used to determine the division of new securities issued in a bankruptcy reorganization. The techniques can also be used to determine the offering price of shares in an initial public offering. Other legal contexts in which these techniques may be used include utility rate-making cases, in which the techniques can be used to the rate of return a regulated utility should be allowed to earn.
The NPV value, the CAPM, and WACC are widely used by companies to make investment decisions. Corporations use these techniques to evaluate their projects. For instance, WACC can be used to evaluate the project with the same risks as well as a project with different risks. When evaluating projects with similar risk level, it is suitable to use a standard rate in order to make a sound decision on whether to accept or reject the projects. In other words, a firm which wants to invest in projects can realistically undertake a similar risk as well as utilize the WACC as a rate to agree on investing in a project or not. WACC is also appropriate when evaluating two projects with different risks. In summary, the NPV rule, the CAPM, and the concept of WACC have significance in a variety of contexts.
Conclusion
The NPV, CAPM, and WACC are powerful techniques that are used in making capital budgeting decisions. These three techniques are companions, and there are interactions between them. One of the parameters that provide interaction between the NPV rule, CAPM, and WACC is rate required. The rate required is the key parameter in the NPV method, and this parameter can be calculated using CAPM and WACC. In addition, the CAPM formula can be used to logically deduce the disequilibrium NPV. The paper also found that there are numerous legal contexts in which the NPV rule, CAPM, and WACC become relevant. Some of the legal contexts in which these techniques can be used include; the appraisal of proceedings, mergers, tender offer, and leveraged buyouts, they can be used to determine the division of new securities issued in a bankruptcy reorganization, they can be used in utility rate-making cases, and lastly, the can be used by companies to make investment decisions.
Bibliography
Books
Fama, E., & French, The CAPM: Theory and Evidence. Center for Research in Security Prices (CRSP). (University of Chicago 2003). [Page 1].
Journal Articles
Hawaldar, I, Relevance of Capital Asset Pricing Model- A Review. Journal on Banking Financial Services & Insurance Research. Vol. 1 (2); 85-97. [Page 86].
Magni, C, CAPM-Based Capital Budgeting and Nonadditivity. Journal of Property Investment and Finance, Vol 26 (5). 388-398. [Page 390].
Thompson, S, A Lawyer’s Guide to Modern Valuation Techniques in Mergers and Acquisitions. Journal of Corp. Vol. 21. 457-539. [Page 463, 465, 466, 468, 501 & 502].
Case
Case Briefs, Weinberger v. UOP. [Online]. Available at: https://www.casebriefs.com/blog/law/corporations/corporations-keyed-to-klein/mergers-acquisitions-and-takeovers/weinberger-v-uop-inc/ . Accessed 7 th June 2019.
Academic Websites
Corporate Finance Institute, Capital Asset Pricing Model (CAPM). [Online]. Available at: https://corporatefinanceinstitute.com/resources/knowledge/finance/what-is-capm-formula/ . Accessed 7 th June 2019. [Paragraph 1].
Finance Formulas, Net Present Value. [Online]. Available at: http://financeformulas.net/Net_Present_Value.html . (Paragraph 1). Accessed 7 th June 2019.
Jan, I, Net Present Value (NPV). [Online]. Available at: https://xplaind.com/478294/npv . [Paragraph 1]. Accessed 7 th June 2019.
Mcclure, B, Explaining the Capital Asset Pricing Model (CAPM). [Online]. Available at: https://www.investopedia.com/articles/06/capm.asp . Accessed 7 th June 2019. [Page 5 & 6].
Seth, S, What is the Formula for Weighted Average Cost of Capital (WACC)? [Online]. Available at: https://www.investopedia.com/ask/answers/063014/what-formula-calculating-weighted-average-cost-capital-wacc.asp . Accessed 7 th June 2019. [Paragraph 5].
1 Finance Formulas, Net Present Value. [Online]. Available at: http://financeformulas.net/Net_Present_Value.html . Accessed 7 th June 2019. Par. 1.
2 Ibid [Par. 1].
3 Irfanullah Jan, Net Present Value (NPV). [Online]. Available at: https://xplaind.com/478294/npv . Accessed 7 th June 2019. Par. 11.
4 Eugene Fama & Kenneth French, The CAPM: Theory and Evidence. Center for Research in Security Prices (CRSP): University of Chicago. Page 1.
5 Iqbal Hawaldar, Relevance of Capital Asset Pricing Model- A Review. Journal on Banking Financial Services & Insurance Research. Vol. 1 (2); 85-97. Page 86.
6 Corporate Finance Institute, Capital Asset Pricing Model (CAPM). [Online]. Available at: https://corporatefinanceinstitute.com/resources/knowledge/finance/what-is-capm-formula/ . Accessed 7 th June 2019. Par. 1.
7 Ben Mcclure, Explaining the Capital Asset Pricing Model (CAPM). [Online]. Available at: https://www.investopedia.com/articles/06/capm.asp . Accessed 7 th June 2019. Par. 5.
8 Ben Mcclure, Explaining the Capital Asset Pricing Model (CAPM). [Online]. Available at: https://www.investopedia.com/articles/06/capm.asp . Accessed 7 th June 2019. Par. 6.
9 Shobhit Seth, What is the Formula for Weighted Average Cost of Capital (WACC)? [Online]. Available at: https://www.investopedia.com/ask/answers/063014/what-formula-calculating-weighted-average-cost-capital-wacc.asp . Accessed 7 th June 2019. Par. 5.
10 Samuel Thompson, A Lawyer’s Guide to Modern Valuation Techniques in Mergers and Acquisitions. Journal of Corp. Vol. 21. 457-539, page 501.
11 Ibid [501].
12 Ibid [501].
13 Ibid [502].
14 Carlo Magni , CAPM-Based Capital Budgeting and Nonadditivity. Journal of Propoerty Investment and Finance, Vol 26 (5). 388-398. Page 389.
15 Ibid [390].
16 Weinberger v. UOP, (1983) 457 A.2d. 701, 1983 Del. Lexis 371
17 Ibid [N.p].
18 Samuel Thompson, A Lawyer’s Guide to Modern Valuation Techniques in Mergers and Acquisitions. Journal of Corp. Vol. 21. 457-539. Page 463.
19 Ibid, 465.
20 Ibid, 466.
21 Ibid, 468.
