# How To Calculate The Tax Percentage

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## How To Calculate The Tax Percentage

This article cites 12 references, which can be found at the bottom of the page.

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Knowing how to calculate percentages will not only help you do well on your math test, but it will help you do well in the real world. You can calculate percentages to calculate the remaining amount for restaurant tips, find out the percentage change in prices, and even determine the statistics of your favorite sports team. While the language may seem confusing at first, calculating percentages is actually quite simple.

We’ll introduce you to the main types of percentage problems you’ll encounter in math homework and work, and give you everyday examples of percentage calculations.

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To calculate a percentage, first write the number you want to convert as a percentage of the total so you get a fraction. Then convert the fraction to a decimal by dividing the top number by the bottom number. Finally, multiply the decimal by 100 to get the percentage. To learn how to calculate discounts using percentages, scroll down! Intrinsic Value Time Value of Money (TVM) Present Value (PV) Future Value (FV) Present Value of Growth Opportunity (PVGO) Adjusted Present Value (APV) Net Present Value (NPV) Compounding Illiquidity Discount

DCF Model Training Terminal Value EBIATNOPATU Unlevered Free Cash Flow NOPLAT Discount Factor Mid-Year Convention Stock-Based Compensation in DCF Inverse DCF Model DCF Leverage Model Common DCF Model Mistakes Evaluating Football Fields

Discount Rate Capital Structure WACC Cost of Equity (ke) Capital Asset Pricing Model (CAPM) Beta (β) Equity Risk Premium (ERP) Cost of Debt (kd) Risk Free Rate (rf) Cost of Equity (kp) Industry Beta Private Equity WACC Firms

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The cost of debt is the minimum rate of return required for a borrower to assume the burden of debt financing for a particular borrower.

Calculating the cost of debt is relatively straightforward compared to the cost of capital because the interest rates on debt obligations such as loans and bonds are readily observable in the market (e.g. via Bloomberg).

The cost of debt is the effective interest rate a company needs to pay on its long-term debt obligations, and it is the minimum that a lender expects to return to a borrower to cover potential losses of capital when lending.

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For example, a bank may lend a company \$1 million of debt capital at 6.0% per annum for a period of 10 years.

The question here is, “Is it correct to use an annual interest rate of 6.0% as the company’s cost of debt?” – the answer is

On the date the original terms of the loan were agreed upon, the price of the debt—that is, the annual interest rate—was the contractual agreement negotiated in the past.

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If companies were trying to borrow in the credit markets now, the price of the debt would likely be different.

Background checks performed by lenders use the borrower’s recent financial performance and credit metrics for a specific period (i.e., the past), rather than the current date.

Note that the discounted cash flow (DCF) method of valuing companies is based on a “forward-looking” basis, with estimates being a function of discounting future free cash flows (FCF) to date.

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That is, the cost of debt must reflect the “current” cost of borrowing, i.e. a function of the current company’s credit profile (e.g. credit ratio, credit agency ratings).

The process of estimating the cost of debt involves finding out the yield on the borrower’s existing debt, which involves two factors:

The cost of debt is the interest rate a company must pay to raise debt capital and can be derived by determining the yield to maturity (YTM).

## Effective Tax Rate

YTM refers to the bond’s internal rate of return (IRR), which is a more accurate approximation of the current update rate if the company is trying to raise debt starting today.

Thus, the price of debt is not a nominal interest rate, but the yield on a company’s long-term debt instrument. The nominal interest rate on debt is historical data, while the yield can be calculated on a current basis.

While using market yields from sources such as Bloomberg is certainly preferred, the pre-tax cost of debt can be calculated manually by dividing the annual interest rate by the total amount of debt (also known as the “real interest rate”).

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The effective interest rate is defined as the compounded average rate a company pays on all its debt, expressed as a percentage.

The yield quoted on the Bloomberg terminal refers to the change in yield to maturity (YTM), known as the “bond equivalent yield” (or BEY).

Effective Annual Yield (EAY) can also be used (arguably more accurate), but the difference is usually small and unlikely to have a significant impact on the analysis.

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EAY is a compounded annual rate of return, while BEY annualizes a bond’s semi-annual rate of return by simply doubling it (e.g. 3.0% x 2 = 6%) – an oft-criticized convention that is still widely practiced use.

The formula uses the “after-tax” cost of debt when calculating the weighted average cost of capital (WACC).

The reason the pre-tax cost of debt must be tax-affected is that interest is tax deductible, effectively creating a “tax shield”—that is, the interest expense reduces the company’s taxable income (earnings before taxes, or EBT).

## How To Calculate Federal Income Tax

Note that the tax benefits of debt financing are factored into the company’s discount rate, including all providers of capital (or WACC), which is why DCF uses Net Operating Profit After Tax (NOPAT) in its calculations to avoid double counting.

The difference between the pre-tax and after-tax costs of debt can be attributed to how the interest expense reduces taxes paid rather than dividends paid to holders of common or preferred stock.

As a prelude to our modeling exercise, we will calculate the cost of debt in Excel using two different approaches but using the same model assumptions.

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With these numbers, we can calculate the interest expense by dividing the annual coupon rate by two (to convert to a semi-annual rate) and then multiplying by the face value of the bond.

Interest rate “RATE” Excel function semiannual interest rate (%) =RATE(Term * 2, semiannual interest expense, semiannual interest rate, – bond current price, bond par value) semiannual interest rate (%) = 2.8%

Since the rate is a semiannual figure, we must multiply it by two to convert to an annual figure.

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To get the after-tax cost of debt, multiply the pre-tax cost of debt by (1 – tax rate).

For the next part of our modeling exercise, we will calculate the cost of debt, but in a more visually illustrated form.

In our table, we listed two cash inflows and outflows from the lender’s perspective because we calculated YTM from their perspective.

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The bond has a face value of \$1,000 and is preceded by a minus sign to indicate that this is a cash outflow.

Using the “IRR” function in Excel, we can calculate a yield to maturity (YTM) of 5.6%, which equates to the pre-tax cost of the debt.

The final step is therefore the impact of the tax on YTM, as shown in our completed model output, which in turn equates to an estimated 4.2% cost of debt.

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