Choosing a Discount Rate for Depreciation Tax Shields

Summary

The document asks why corporate finance treatments use different discount rates for tax shields. It contrasts a textbook discussion that treats depreciation tax shields as safe nominal cash flows, discounted at the firm’s after-tax borrowing rate, with an adjusted present value approach that may discount interest tax shields at the pre-tax borrowing rate when debt is fixed.

The response explains the distinction in terms of the cash flow being valued: under the assumption that the firm will not default, equity holders receive the tax benefit as an annuity, while the benefit is realized through profits after tax. This motivates using the after-tax borrowing rate for depreciation tax shields. The explanation is brief and points to a fuller textbook treatment; it does not spell out all assumptions or reconcile every APV convention. The appropriate rate therefore depends on the specific tax shield, its risk, and the financing policy assumed.

Key ideas

• Depreciation tax shields can be treated as safe nominal cash flows when the firm is certain to pay taxes.
• The document associates depreciation tax shields with the firm’s after-tax borrowing rate.
• For a fixed-debt assumption, APV treatments may discount interest tax shields at the pre-tax cost of debt.
• The brief explanation assumes the firm does not default and does not fully cover alternative financing policies.

Tags

# What rate to discount tax shield


# What rate to discount tax shield












On the appendix for Chapter 19 of Principles of Corporate Finance (BMA), it discusses the topic of "Discounting Safe, Nominal Cash Flows", in which case they argue that

> However, suppose we ask what depreciation tax shields are worth by themselves. For a firm that’s sure to pay taxes, depreciation tax shields are a safe, nominal flow. Therefore, they should be discounted at the firm’s after-tax borrowing rate

However, I remember that in the APV method, V_L = V_U + PV(Tax Shield). When we discount the tax shield here, we use the pre-tax borrowing rate (suppose the company keep the debt amount fixed).

I was wondering why is there a difference between the discount rate of tax shields?

> Reference: Brealey, Myers and Allen, Principles of Corporate Finance

## Answer by michaelcarniol (score 1)

https://quant.stackexchange.com/a/37232

Assuming the company does not default, the equity holders receive the benefit of the tax shield as an annuity. That means, as you suggested, one should discount the tax shield at the cost of debt. But, equity holders receive profits after tax, which implies using the after-tax borrowing rate. See the Holthausen and Zmijewski textbook for a more complete discussion.

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