# Tax Shield

A tax shield represents a reduction in income taxes which occurs when tax laws allow an expense such as depreciation or interest as a deduction from taxable income.

For example, if a company has cash inflows of USD 20 million, cash outflows of USD 12 million, its net cash flows before taxation work out to USD 8 million. If the company has made initial investment in machinery of USD 25 million (which has useful life of 5 years) and the tax code allows deduction of depreciation expense of USD 5 million (USD 25 million divided by 5) from net cash flows, the company’s taxable income each year comes out to USD 3 million (USD 8 million minus $5 million). If the tax rate is 33%, the company’s tax liability works out to USD 1 million (USD 3 million × 33%) which equals after-tax net cash flows of USD 7 million (USD 8 million – USD 1 million).

Had there been no provision in tax laws regarding deduction of depreciation expense, the tax liability and after-tax net cash flows would have been USD 2.64 million (USD 8 million × 33%) and USD 5.36 million (USD 8 million – USD 2.64 million). The allowability of depreciation expense as a deduction from net cash flows for the purpose of calculation of taxable income has reduced the taxes due by USD 1.64 million (USD 7 million – USD 5.36 million or equivalently, USD 2.64 million – USD 1 million). This represents a tax shield.

In capital budgeting, we come across two types of tax shield: depreciation tax shield and interest tax shield.

## Depreciation Tax Shield

Depreciation tax shield is the reduction in tax liability that results from admissibility of depreciation expense as a deduction under tax laws. The example discussed above illustrates a depreciation tax shield.

In capital budgeting calculations, net operating cash flows are reduced by the amount of depreciation tax shield available each year. Net present value and internal rate of return are calculated using the after-tax cash flows which are determined using either of the following formula:

CF = (CI − CO − D) × (1 − t) + D

CF = CI − CO − (CI − CO − D) × t

Where CF is the after-tax operating cash flow, CI is the pre-tax cash inflow, CO is pre-tax cash outflow, t is the tax rate and D is the depreciation expense.

These two equations are essentially the same. The expression (CI – CO – D) in the first equation represents the taxable income which when multiplied with (1 – t) yields after-tax income. Depreciation is added back because it is a non-cash expense and we need to work with after-tax cash flows (instead of income). The second expression in the second equation (CI – CO – D) × t calculates depreciation tax shield separately and subtracts it from pre-tax net cash flows (CI – CO).

## Interest Tax Shield

Interest tax shield refers to the reduction in taxable income which results from allowability of interest expense as a deduction from taxable income. The most significant advantage of debt over equity is that debt capital carries significant tax advantages as compared to equity capital.

In calculation of net present value, interest tax shield is typically not reflected in net cash flows rather it is adjusted by multiplying the cost of debt with (1 – tax rate) in the weighted-average cost of capital. This is why we multiply cost of debt (k_{d}) with (1 – t) when calculating weighted-average cost of capital (WACC) as shown below:

WACC = w_{e} × k_{e} + w_{d} × k_{d} × (1 − t)

Where w_{e} is the weight of equity, k_{e} is the cost of equity, w_{d }is the weight of debt, k_{d} is the pre-tax cost of debt (i.e. its yield to maturity) and t is the tax rate.

The factor of (1-t) reduces the debt component which results in a lower WACC which in turn results in a higher present value of net cash flows. Why is it so? It is because present value is higher when discount rate is lower.

However, we can identify the total present value of interest tax shield as the difference between net present value calculated at pre-tax WACC (NPV_{P}) and net present value calculated at after-tax (traditional) WACC (NPV_{A}).

Interest Tax Shield = NPV_{P} − NPV_{A}

An alternative approach called adjusted present value (APV) discounts interest tax shield separately. Even though the APV method is a bit complex, it is more flexible because it allows us to factor-in the risk inherent in admissibility of interest tax shield. For example, it allows us to adjust the discount rate we use for calculating of present value of interest tax shield up or down depending on our assessment of availability of enough taxable income to avail the tax shield.

by Obaidullah Jan, ACA, CFA and last modified on