Post- to Pre-Tax Discount Rates: Not a Simple Conversion
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Fellow of the Institute of Chartered Accountants in England & Wales (FCA), Fellow of the Institute of Directors (FIoD) and Chartered Alternative Investment Analyst (CAIA).
Abstract
It is widely accepted that financial markets tend to make assessments of value on expectations of post-tax cash flows, since that is what equity investors receive. There is however, from time to time, a need to ascertain and apply a pre-tax discount rate to discount pre-tax cashflows. Examples include (i) the assessment of regulatory returns and (ii) impairment testing of cash generating units. This paper highlights the implicit assumptions inherent in the most commonly applied shorthand method of determining pre-tax discount rates before considering modifications to create a more realistic assumption set. The paper concludes with the derivation of a shorthand formula for finite life project cashflows, which often require a pre-tax discount rate. The author agrees that while all the cash flows should be modelled on a post-tax basis and then back solved, using an iterative approach, to find the actual pre-tax rate, where a shorthand is required the formulae discussed in this paper can be applied, provided the limitations are understood.
About the author
Fellow of the Institute of Chartered Accountants in England & Wales (FCA), Fellow of the Institute of Directors (FIoD) and Chartered Alternative Investment Analyst (CAIA).
Acknowledgements
With thanks to James Nicholson, James Church Morely, Miao Gu, Chia Fun Liang and Koa Quan Wei for their comments and suggestions.
Appendix
A Equation 3 derivation
To derive eq. (3) we start with a proof of a geometric progression. This has been set out below for convenience. Then by recognising that pre- and post-tax cash flows that continuously grow at a fixed rate are geometric progressions we can reduce them using the same approach.
Since the value of the cash generating unit should not change, whether we discount pre-tax cash flows using a pre-tax discount rate, or post-tax cash flows using a post-tax discount rate, the reduced pre-tax and post-tax forms should be equal.
Standard Geometric Progression proof:
Progression:
Multiply by “a”:
Deduct both sides:
Factorise:
Rearrange for “y”:
Net Present Value of pre-tax cash flows:
The Net Present Value (“NPV”) of pre-tax cash flows (“CF”), continuously growing at a fixed rate (“g”), for a finite period (“n”) after discounting at a given pre-tax discount rate (“rb”):
Factorise:
Reduce as a geometric progression:
Net Present Value of post-tax cash flows:
The same can be applied for post-tax cash flows assuming the relationship between pre- and post-tax cash flows is one minus the tax rate (“t”):
Equivalence:
Since the NPV should be unchanged we can place the pre-tax and post-tax parts opposite each other, and cancel the “CF” term to give:
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- The Corporate Life Cycle and the Cost of Equity
- Resolving the Reliance on Fixed Estimation Dates in the Implied Cost of Equity Capital Approach
- Restricted Stock Discounts: An Empirical Analysis
- Terminal Value in SMEs: Testing the Multiple EV/EBITDA Approach
- Post- to Pre-Tax Discount Rates: Not a Simple Conversion
Artikel in diesem Heft
- The Corporate Life Cycle and the Cost of Equity
- Resolving the Reliance on Fixed Estimation Dates in the Implied Cost of Equity Capital Approach
- Restricted Stock Discounts: An Empirical Analysis
- Terminal Value in SMEs: Testing the Multiple EV/EBITDA Approach
- Post- to Pre-Tax Discount Rates: Not a Simple Conversion
