# The Tax-Deductibility of Debt

Whilst tax regimes differ throughout the world, one policy many governments have in common that we need to consider is the treatment of debenture interest as an allowable deduction against a firm's tax liability. Not only does this lower the "true" cost of corporate borrowing but also widens the gap between yields on debt and equity explained earlier.

Providing management can generate sufficient taxable profits to claim the tax relief on debt interest, the higher the rate of corporation tax, the greater the fiscal benefit conferred on the company through issuing debt, rather than equity to finance its investments.

In the preceding valuation models Kd represents the * gross *return received by investors

*satisfying their*

**before***tax liability. What is important to the company, however, is the project discount rate defined by this gross return*

**personal**

**after corporation tax.**To prove the point, let us first consider * irredeemable *debt (i.e. with no redemption value) with a level interest stream in perpetuity. The valuation model

*tax is given by:*

**incorporating**where: P0 = the current market price of debt, I = annual interest payments t = rate of corporation tax Kdt = post-tax cost of debt

So, if we rearrange terms, the "real" cost of debt to the company after tax is

(7) = I(1-t) / Po

And because the investors' * gross *return (Kd) equals the company's cost of debt before tax, it follows that with a tax rate (t) we can also rewrite Equation (7) as follows;

(8) Kdt = Kd (1-t)

In a world of corporate taxation, the capital budgeting implications for management are clear.

(9) Kdt < Kd

To maximise corporate wealth, the post-tax cost of debt should be incorporated into any overall discount rate as a cut-off rate for investment.

Equation (6) onwards might seem strange, since P0 is still the market value of the debentures held by investors represented by the future cash flows which they expect to receive. But it is important to remember that we are now modeling income-value relationships from the * company's *perspective.

The interest cash flows capitalized on the right-hand side of Equation (6) are therefore * net *of corporation tax, which do not concern investors directly. So, if a company pays £100,000 a year interest on irredeemable debentures with a market price of £1 million and the rate of corporation tax is 25 percent, its effective cost of debt defined by Equation (7):

Kdt = [£100,000 (1-0.25)] / £1 million = 7.5%

Turning to * redeemable *debt, the company still receives tax relief on interest but often the redemption payment is not allowable for tax. To calculate the post-tax cost of capital it is necessary to derive an IRR that incorporates tax relief on interest alone by solving for Kdt in the following

*equation:*

**finite**Consider five-year debt with a 15 percent coupon rate, redeemable at £100 par, issued at £90 percent. If the annual rate of corporation tax is 33 percent, we can determine the post-tax cost of debt by solving for Kdt in the following equation.

**Activity 2**

A company's irredeemable debt has a coupon rate of 8 percent and a market value of £76 percent. Corporation tax is 30 percent and the firm's has sufficient tax liability to set off against its interest.

Calculate the investor's gross return and the company's effective cost of debt.

Comment on the disparity between the two and the capital budgeting implications for management.

Investors receive the following gross return before personal taxation: Kd = £8 / £76 = 10.53% d

The post-tax cost to the company for providing this return is;

Kdt = £8(1-0.30) / £76 = 7.36%

Loan interest reduces the corporate tax bill. For every £8 distributed to investors as interest, the company effectively pays:

I(1-t) = £8 (1-0.30) = £5.60

The £2.40 difference represents tax relief contributed by the tax authorities.

Turning to capital budgeting, if management finance new investment by issuing debt, this must reflect current post-tax yields of equivalent risk. Each £100 block will be priced at £76. The post-tax cost of debt capital (Kdt =7.36%) represents the discount rate that equates the amount raised to the PV of future cash flow required to service this new issue (interest less tax relief).

The tax adjusted cost of debt (Kdt) is the IRR that represents the true corporate cost of new debt issues. If the ENPV of a prospective debt-financed project discounted at this IRR is positive, then its return will exceed the cost of servicing that debt and management should accept it.