Cost of capital: spot rate or forward rate?

ABSTRACT

In this study, we intend to reveal some problems with the classic valuation method – the weighted average cost of capital (WACC) method. We first address a fundamental question about WACC, that is, should WACC be interpreted as a spot rate, a forward rate or any kind of average of either of them? We show that the nature of WACC is the expected forward rate. We next demonstrate that without understanding this nature, we may misinterpret the famous MM formula and MM Proposition II, as well as develop incorrect valuation framework. Our findings provide insightful implications to academia and practitioners for the proper interpretation and implementation of the WACC method.

KEYWORDS:

• Capital structure
• WACC
• APV
• spot rate
• forward rate

JEL CODES:

• G 31
• G 32

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ The other valuation methods include such as the flows to equity method and the adjusted present value (APV) method. Please refer to Booth (2002) for comparison of the different valuation methods.

² Of course, in reality, there may be some loss of tax shields due to the crowding-out effect of the nondebt tax shields such as lease payments. See for example, Graham (2000) and Qi, Liu and Johnson (2012) for some detailed discussion. In this article, we ignore this secondary tax effect.

³ For example, see Cooper and Nyborg (2006, 2007), Brealey, Myers and Allen (2005), Miles and Ezzell (1980), Sabal (2005, 2007) and Pereiro (2002) for some detailed discussion about the valuation methods and the capital structure decisions and uncertainty in tax shields.

⁴ It is normally believed that the weighted average cost of capital (WACC) method requires constant leverage ratio and constant tax rate, see for example, Brealey, Myers and Allen (2005) and Sabal (2007); and the APV method is better for firms with complicated debt ratio and tax rates, see for example, Sabal (2005, 2007) and Pereiro (2002). However, Qi (2010), by carefully analysing their studies, shows that these understandings about the WACC and the APV methods are not necessarily true given their arguments. In a separate study by Qi and Han (2010), it is illustrated that the APV method may likely be more demanding because it requires knowledge of more variables than the WACC method does.

⁵ What if the firm can borrow at R_D while individuals can only borrow at R_P? Then the present value of the tax shields becomes $R_{D}D{T}_C/R_P<D{T}_C$ because normally $R_D<R_P$. This means that the individual cannot fully replicate the leverage in the personal account because he/she has to pay a higher interest of R_P and therefore, he/she is better off letting the firm do the borrowing and the firm’s discount rate is $R_{TS}=R_D$, resulting in a higher present value of the tax shields.

⁶ There are still open issues regarding the relationship between R_TS and capital structure policy. For more recent studies in this regard, see for example, Fernández (2004, 2005, 2006), Cooper and Nyborg (2006, 2007), Johnson and Qi (2008) and Liu (2009).

⁷ The MM Proposition I states that (1) debt policy is irrelevant without taxes; (2) firms ought to use 100% debt if there are taxes and tax reductions.

⁸ Hamada formula assumes safe debt, that is, r_D = r_f.

⁹ Such a policy typically implies that the firm is operating on the same scale every year to yield constant free cash flows (FCFs) and firm value.

¹⁰ Including geometric and arithmetic averages.

¹¹ This is because in practice, one uses the observed debt/equity ratio at time t = 0 to calculate r_E in Equation 12. This makes one tend to think that r_E given by Equation 12 is $r_{E0}$, the equity return for the period $\left[0,1\right]$, which can be the required, actual or expected return. However, this subtle difference does not have an effect on the conclusion because r_E given by Equation 12 can be none of these three interpretations.

¹² This is because WACC₁ would be the greatest of WACC_t since debt ratio D/V_t decreases with time. A flat rate that satisfy Equation 14 must be somewhere between the largest and lowest WACC_t.

¹³ Suppose this tax shield can be fully realized either through carryforwards or carrybacks, or other means such as merging with a profitable firm with large tax liabilities.

¹⁴ Of course, the firm can pay the existing equity holders some dividend, but that has to be covered by either raising new additional capital or drawing on the firm’s existing assets. These technicalities can be ignored without affecting our analysis at all.