Using a Cost of Capital Where One Really Shouldn't

20 Pages Posted: 1 Jan 2020

See all articles by Minh Phuong Doan

Minh Phuong Doan

Deakin University - School of Accounting, Economics and Finance

Phuong Nguyen Trang Doan

affiliation not provided to SSRN

Piet Sercu

FEB at KU Leuven

Date Written: December 15, 2019

Abstract

Myers (1974---‘M74’) derives the Cost of Capital (CC), including the corporate-tax subsidy on borrowing, for a one-period investment project. From Miles and Ezzell (1980), this CC remains valid in multiperiod projects provided that, during the project's life, debt is continuously re-aligned with ex post GPVs. In contrast, when the debt schedule is static --- i.e. set to stabilise leverage ex ante only --- no CC works outside the Modigliani and Miller (1963---‘MM63’) perpetuities scenario; one generally needs a recursive Adjusted NPV (rANPV).

Real-life leverage being neither fully static nor fully dynamic, two questions arise: (i) do M74's CC and rANPV produce very different valuations in a static/multiperiod problem?, and (ii) is it useful to heuristically adopt a non-linear interpolation between the M74 and MM63 polar CCs? We find, first, that M74's CC is is (mildly) conservative but vastly less biased and more precise than MM63's. Second, two of the heuristic compromise CCs are marginally more correct than even M74, but they remain biased upwards. Remembering that M74 also applies when debt is GPV-indexed ex post, M74 seems the safer procedure.

Highlights:

– With a ‘static’ debt schedule set to stabilise leverage ex ante, a finite-life project’s risk cannot be constant, so no Cost of Capital (CC) can work perfectly.

– When expressed as fractions of gross present value, minor-looking CC-based valuation errors largely reflect the low PV of the true tax shields rather than a precise assessment.

– The Myers (1974) one-period cost of capital (CC) is mildly conservative and works very well for multiperiod NPV-ing even when debt is static.

– The Miller-Modigliani CC for perpetuities, when applied in finite-life problems, is vastly overoptimistic and imprecise, especially when the CC takes into account growth.

– We also propose four heuristic procedures that non-linearly interpolate between the above two CCs. The two that take into account the changing risk do succeed in beating Myers’ CC, but the gains are small and the bias is upward rather than conservative.

Keywords: Capital structure, capital budgeting, NPV, WACC, tax effects

JEL Classification: G31, G32

Suggested Citation

Doan, Minh Phuong and Doan, Phuong Nguyen Trang and Sercu, Piet M. F. A., Using a Cost of Capital Where One Really Shouldn't (December 15, 2019). Available at SSRN: https://ssrn.com/abstract=3504084 or http://dx.doi.org/10.2139/ssrn.3504084

Minh Phuong Doan

Deakin University - School of Accounting, Economics and Finance

221 Burwood Highway
Burwood, Victoria 3215
Australia

Phuong Nguyen Trang Doan

affiliation not provided to SSRN

Piet M. F. A. Sercu (Contact Author)

FEB at KU Leuven ( email )

Naamsestraat 69
Faculty of Economics and Business
Leuven, 3000
Belgium
+32 16 32 67 56 (Phone)
+32 16 32 67 32 (Fax)

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