 # Cost of Debt in WACC By Yuriy Smirnov Ph.D.

## Definition

To estimate a company’s cost of debt, we need to determine the debtholders’ required rate of return. At first glance, solving this problem doesn’t appear to be particularly challenging, but in practice we may face some difficulties because debt may have a different nature and features, e.g., a bond or a loan may have a fixed or floating interest rate. In the case of a fixed rate, it is quite simple to assess the cost of debt, but a floating interest rate means that the required rate of return will change over time.

## Long-term and short-term debt

The long-term debt of a company is mainly represented by its bonds, but the company can also use long-term loans.

Short-term debt financing isn’t usually employed on a regular basis. Most often companies use it to cover seasonal needs in capital, and we should not consider it in WACC calculation. Some companies, though, can employ short-term debt on a regular basis, and in such a case it should be included in the capital structure.

## Formula

As interest payments are tax deductible for the company, the cost of debt in WACC is not equal to debtholders’ required rate of return. To calculate its after-tax value, we need to use the following formula

kd = rd × (1 - T)

where rd is a debtholder’s required rate of return or pretax cost of debt, and T is a marginal tax rate.

Because the debt component of capital is mostly represented by bonds, we can use following formula to find the pretax cost of debt or bondholders’ required rate of return for current issues

 P = N C + Face Value Σ (1 + rd)t (1 + rd)N t = 1

where P is the current market price of a bond, N is the number of years to maturity, and C is the annual coupon payment.

If a company performs a new bond issue, it can face flotation costs. In that case, the formula above must be modified as

 P × (1 - F) = N C + Face Value Σ (1 + rd)t (1 + rd)N t = 1

where F represents floatation costs.

Please note that this technique can be applied to bonds that have a fixed coupon rate!

## Historical vs. marginal cost of debt

During the life of a company, it can apply debt financing on an ongoing basis, but interest rates also tend to change over time, which means that every next debt issue will most likely have a different required rate of return from the previous one. So, if a company’s debt consists of at least two issues with different interest rates, we can distinguish historical and marginal cost of debt. Let’s consider a simple example when a company’s debt is represented by two bond issues:

• \$2,000,000 at a 10.5% fixed coupon rate
• \$3,000,000 at a 12.75% fixed coupon rate

The marginal pretax cost of debt is a rate at which the last \$1 was raised. In the example above, the marginal rate is 12.75%.

Historically, the cost of debt is a weighted average of all its components. The total debt of the company is \$5,000,000, so the proportion of the first bond issue is 0.4 (\$2,000,000÷\$5,000,000), and the proportion of the second bond issue is 0.6 (\$3,000,000÷\$5,000,000). The cost of debt then equals 11.85% (0.4×10.5%+0.6×12.75%).

## Examples

### Example 1

Company A has \$10,000,000 in outstanding debt raised by 5-year bonds of 9% annual fixed coupon rate. The current marginal corporate tax rate is 30%.

The after-tax cost of debt for the company will be 6.3%.

kd = 9% × (1 - 0.3) = 6.3%

## Example 2

Company B plans to finance a new \$5,000,000 project by issuing 10-year bonds of \$1,000 par value and 7.5% annual fixed coupon rate. The current market price of the equal risk bond is \$980, floatation costs are 1.5%, and the marginal corporate tax rate is 25%.

As a first step, we need to determine the required rate of return rd by solving the following equation:

 \$980 × (1 - 0.015) = \$75 + \$75 + \$75 + \$75 + \$75 (1 + rd)1 (1 + rd)2 (1 + rd)3 (1 + rd)4 (1 + rd)5

To do it, we can use online calculator or Microsoft Excel function “IRR.” The required rate of return, including floatation costs, is 8.38%. So, the after-tax cost of debt for Company B will be 6.285%.

kd = 8.38 × (1 - 0.25) = 6.285%