The Definitive Guide to the Cost of Debt

Cost of Debt – arguably one of the most simple (yet perceptually complicated) metric in Finance and Investing. Here’s everything you need to know about it, including what it is, why it matters, and how to calculate it.

You might want to grab a tea though – this is the most extensive guide on the Cost of Debt on “the internet”.

If you’re after specific aspects of the cost of debt, feel free to explore individual sections. Each section is designed to stand on its own for the most part. Where sections depend on one another, you’ll be pointed to the appropriate section when it’s relevant.

Table of Contents hide

1 What is Cost of Debt?

1.1 Cost of Raising Debt Finance

1.2 Appropriate Discount Rate for Debt Cash Flows

1.3 Appropriate Rate of Return for Debt Investors

2 Why Does The Cost of Debt Matter?

2.1 Importance for Users

2.2 Importance As a Risk Signal

3 How to Calculate Cost of Debt?

3.1 How to Calculate Cost of Debt using Interest on Debt

3.2 How to Calculate Cost of Debt using the CAPM (Capital Asset Pricing Model)

3.3 How to Calculate Cost of Debt using Modigliani & Miller II

4 Do All Calculations of Cost of Debt Provide The Same Result?

5 How Does Tax Affect The Cost of Debt?

6 What is the Difference Between Cost of Debt and Cost of Capital?

7 What is the Difference Between Cost of Debt and Cost of Equity?

8 Cost of Debt Calculation Example

8.1 Calculate Cost of Debt using Interest on Debt

8.2 Calculate Cost of Debt using the CAPM

8.3 Calculate Cost of Debt using Modigliani & Miller II

8.4 Comparing Estimates Using Different Approaches

9 Wrapping Up

What is Cost of Debt?

Firstly, what is Cost of Debt?

Consistent with most things in Finance, the clue is in the name.

The Cost of Debt is the cost… of debt.

More specifically, it’s the cost of raising debt finance.

It has three main interpretations or use-cases, including:

cost of raising debt finance (i.e., the cost of borrowing),
appropriate discount rate for debt cash flows, and
appropriate rate of return for debt investors

Let’s consider each of these three interpretations / use-cases individually.

Cost of Raising Debt Finance

The cost of debt is expressed in percentage terms. And it represents the amount of money a business would have to pay its debt holder for every $1 of debt financing it obtains from them.

So, if the cost of debt for a company is say, 5%, then it means that the company would essentially pay its lenders $0.05 for every $1 of debt capital it raises from them.

The payments would largely be made in the form of interest payments.

Thus, in the simplest sense, the Cost of Debt is nothing but the interest rate on a loan.

As a result of representing the cost of raising debt finance, the Cost of Debt is also an appropriate “discount rate” for debt-related cash flows.

Appropriate Discount Rate for Debt Cash Flows

A discount rate is a rate at which future cash flows of a business are discounted at.

The process of discounting future cash flows is a focal theme/concept within Finance.

The idea is to put a price on future cash flows as of today. That price is referred to as the Present Value of Future Cash Flows.

Now, the process of discounting is beyond the scope of this particular article. But we have linked to related/sister articles, so if you’re interested, do give those a read.

At this stage, it’s suffice for you to know that the Cost of Debt is the appropriate discount rate to discount debt-related future cash flows back to the present.

And perhaps more importantly, it’s important for you to know that the Cost of Debt is an essential ingredient of the Weighted Average Cost of Capital (WACC).

Appropriate Rate of Return for Debt Investors

Recall that we said that the cost of debt is the cost of raising debt capital.

As a result of this, it also represents the return a debt investor requires in order to invest.

Intuitively, companies raise money from investors (be that equity investors or debt investors).

The “costs” that the company pays to raise finance is the return that investors earn!

Intuitively, when you pay interest on a loan as an individual, the bank or lender makes a return.

The interest that you pay is your cost of borrowing (aka Cost of Debt). And it’s also the rate of return for the bank/lender.

Why Does The Cost of Debt Matter?

The Cost of Debt matters a great deal for many reasons. We can broadly think of in terms of its importance to users (companies and investors), and in terms of a signal for the company’s risk.

Let’s consider both interpretations.

Importance for Users

There are broadly two main user-groups of the cost of debt, including:

companies, and
investors

For companies, the cost of debt represents the cost they can expect to pay in order to raise debt finance.

For investors, on the other hand, cost of debt represents the rate of return they can expect to earn by lending their money to a given company.

Importance As a Risk Signal

The cost of debt can also be seen as a signal for the riskiness of a company.

Note that, over here, we’re not referring to riskiness in the context of the total risk of a stock or idiosyncratic risk.

Here, the “riskiness” is more in the context of default risk.

Given the investment fundamentals of price, risk, and return we know that risk and return maintain a proportional relationship.

Thus, if a firm has a very high default risk, investors will demand a very high rate of return when lending to the firm.

Firms with high cost of debts, therefore, can be reasonably thought of as high risk firms. At least in the context of their ability to pay back investors.

How to Calculate Cost of Debt?

There are 3 main ways of calculating the Cost of Debt, including:

Interest on debt,
The CAPM, and
Modigliani & Miller II

Going forward, we’re going to use the mathematical notation $k_d$ to refer to the Cost of Debt.

Note that some people refer to use $r_d$ to refer to the cost of debt instead of $k_d$ . Either is okay/acceptable.

People who use $r_d$ tend to see it as the required rate of return on debt. We touched on the rationale and intuition behind this idea in the first couple of sections in this article.

We’re choosing to use $k_d$ instead of $r_d$ because $k$ is typically used to reflect costs in financial economics.

How to Calculate Cost of Debt using Interest on Debt

$k_d$ can simply be the interest rate on a loan, estimated as:

$k_d = \frac{\$I}{D}$

Here:

$k_d$ represents the Cost of Debt
$\$I$ refers to the dollar value of interest paid (i.e., the interest expense)
$D$ reflects the market value of debt

This is probably the easiest and simplest way to calculate cost of debt.

Values for $$I$ are easily accessible from the interest expense reported on the income statement of publicly listed companies.

RELATED: Profit and Loss Tutorial

The value for $D$ is a tad bit trickier to obtain, but not impossible by any means.

This method is also the only estimate for $k_d$ which explicitly showcases the interest rate on debt as the appropriate cost of debt.

As you’ll see in just a bit, the other measures for $k_d$ don’t quite explicitly show it as an interest rate.

How to Calculate Cost of Debt using the CAPM (Capital Asset Pricing Model)

$k_d$ can be estimated by using the CAPM (i.e. the Capital Asset Pricing Model) as:

$k_d = r_f + \beta_D (E[r_m] - r_f)$

In this particular Cost of Debt formula:

$k_d$ refers to the Cost of Debt
$r_f$ represents the risk free rate of return
$\beta_D$ reflects the Systematic Risk of the stock’s debt
$E[r_m]$ represents the expected return on the market portfolio (e.g., the return on the S&P500 market index), and
$E[r_m] - r_f$ displays the market risk premium

We talk a great deal about the limitations of the CAPM in our article (linked above). Do give that a read if you’d like to learn more about the CAPM.

You might also want to explore other asset pricing models if you’re looking to better understand this area of finance.

Note that, although there’s no reference to an interest rate explicitly here, the value for $k_d$ is still, essentially, an interest rate on debt.

So, lenders who use the CAPM to calculate $k_d$ will essentially use the value for $k_d$ as the interest rate they charge borrowers.

Similarly, companies that use CAPM to estimate $k_d$ will essentially use that estimate as the value for the interest rate on their borrowings.

Thus, although the CAPM-based estimate for $k_d$ doesn’t explicitly show or display an interest rate, it essentially is the interest rate on debt.

Hopefully, that makes sense.

Let’s now think about another way of calculating $k_d$ .

How to Calculate Cost of Debt using Modigliani & Miller II

The third – and final – formal way of calculating $k_d$ involves using a model created by Modigliani and Miller as part of their second proposition on firm value / capital structure.

Using M&M II, the formula for cost of debt is expressed as:

$k_d = k_a + \frac{E}{D} \left(k_a - k_e \right)$

Note that this particular formula for cost of debt is far from commonly used.

Indeed, it’s somewhat rare to see this form of $k_d$ on “the internet” and in most syllabi in formal education, at least at the time of writing.

Nevertheless, the approach holds mathematically, in that we’re simply rearranging the expression for Cost of Equity (estimated using M&M II) to obtain an expression for $k_d$ .

Here’s the simplified proof.

The Cost of Equity (estimated using M&M II) is calculated as…

$k_e = k_a + \frac{D}{E} \left(k_a - k_d \right)$

This is equivalent to writing…

$k_e = k_a + \frac{D}{E} k_ a - \frac{D}{E} k_d$

Rearranging to get $k_d$ by itself yields…

$k_d = \frac{k_a + \frac{D}{E}k_a - k_e}{\frac{D}{E}}$

This in turn is equivalent to writing…

$k_d = \left(k_a + \frac{D}{E} k_a - k_e \right) \frac{E}{D}$

Simplifying results in the final cost of debt formula as…

$k_d = k_a + \frac{E}{D} \left(k_a - k_e \right)$

As with the CAPM-based estimate for $k_d$ from above, note that, although the M&M II based estimate for $k_d$ doesn’t explicitly show an interest rate, the value for $k_d$ essentially represents the interest rate on borrowings/lending.

Do All Calculations of Cost of Debt Provide The Same Result?

People often wonder – indeed, strongly believe – that the estimate for $k_d$ should be identical, regardless of which approach you use to calculate it.

Sadly, this is simply almost never true.

Estimates for $k_d$ will almost certainly be different if you estimate is using interest on debt vs. the CAPM vs. M&MII.

This is because of a variety of reasons, including (but not limited to):

differences in assumptions across models
differences in variables used to calculate $k_d$
working with different sample timeframes
reliability of the raw data used in the estimate

Anecdotal evidence suggests that many practitioners tend to take a simple average of different estimates.

This, in our opinion, is far from prudent – mainly because of the reasons of differences highlighted above.

Taking simple average of different estimates is akin to taking the average of apples and oranges and concluding it’s the average values for apples alone!

How Does Tax Affect The Cost of Debt?

Tax – strictly, the corporation tax rate – can help decrease the cost of debt financing in most countries.

Since interest expense is tax deductible for companies in most countries, the tax rate can essentially decrease the effective cost of debt.

That’s because interest expense decrease the value for taxable income.

This in turn means companies face a smaller tax bill (compared to a firm with 0 interest expense, or one that operates in a country where interest expense is not tax deductible).

As an example, suppose a company’s cost of debt is equal to 6% and its corporation tax rate is 20%.

Given the fact that any interest payment will be tax deductible, the firm’s effective interest rate is 6%(1 – 20%) = 4.8%.

What is the Difference Between Cost of Debt and Cost of Capital?

The Cost of Debt is the cost of raising debt capital. Cost of Capital on the other hand, is the cost of raising capital (both debt as well as equity).

Generally speaking, a reference to the “Cost of Capital” will typically imply that we’re talking about the Weighted Average Cost of Capital (WACC).

If the firm in question has 0 debt, then a reference to Cost of Capital can also mean Cost of Equity.

Note that, for a firm that has debt and equity capital structure, the cost of debt will always be lower than the cost of capital.

What is the Difference Between Cost of Debt and Cost of Equity?

The Cost of Equity represents the cost of raising equity capital. As highlighted earlier, the Cost of Debt reflects the cost of raising debt finance.

Note that, since equity is riskier than debt (from an investor’s standpoint), the cost of equity will always be greater than the cost of debt.

Equity financing is less risky from a firm’s / entrepreneur’s standpoint, but riskier from an investor’s standpoint.

Okay, how that you know what the Cost of Debt is and how to calculate it, let’s apply the different formulas with an example.

Cost of Debt Calculation Example

Consider Starmont Inc., which recently announced its intention to pay dividends of $2.50 per share every year for the foreseeable future, for each of its 100m shares. Some analysts believe that the company may increase its dividends by up to 5% each year. They base this on the firm’s high amount of available capital, including $800m of debt (based on recent market valuations) and total assets of $3.5bn in current market value terms.

Analysts believe that the 5% growth rate is achievable, even though the firm faces approximately $32 million in interest payment each year.

The firm’s positive exposure to the market, given its (equity) beta of 1.25, means it’s poised for strong performance ahead. The firm’s debt beta equates to 0.85. Analysts expect the overall market return to be 12% per year over the coming years. Yields on risk-free securities are reported at 1.5%.

Analysts from EveningStar Inc. estimate the firm’s cost of capital to be 10% and its cost of equity to be 11.78%.

What is Starmont Inc.’s Cost of Debt?

The question provides sufficient information for you to calculate $k_d$ using all three approaches highlighted above.

So go on! Give it a go and try estimating Starmont Inc.’s $k_d$ on your own.

Hint: we’ve bolded items in the question for a very good reason! 😉

We’re going to assume you did that, so let’s go ahead now and solve it together.

NOTE: if you’ve already read our sister article on the Definitive Guide to Cost of Equity, note that there are minor differences between the example question here vs. the one in that article. We’ve tried to maintain a large level of similarity so you can explore how the Cost of Equity, Cost of Debt, and Cost of Capital interact.

Calculate Cost of Debt using Interest on Debt

Recall that $k_d$ can simply be the rate of interest on the loan as:

$k_d = \frac{\$I}{D}$

Where:

$k_d$ represents the Cost of Debt
$\$I$ refers to the dollar value of interest paid
$D$ reflects the market value of debt

We’re told from the question that the firm’s interest expense is equal to $32m each year. Thus $\$I =$ $\$32m$ .

The market value of debt ( $D$ ) is equal to $800m per the question.

Plugging in the numbers into the cost of debt formula (calculated using the interest on debt approach) we have…

$k_d = \frac{\$32m}{\$800m}$

Solving for that yields…

$k_d = 0.04 = 4\%$

Calculate Cost of Debt using the CAPM

Recall that $k_d$ can be estimated by using the CAPM as:

$k_d = r_f + \beta_D (E[r_m] - r_f)$

From the question, we know that:

$r_f$ is equal to 1.5% (since that’s the yield on risk-free securities)
$\beta_D$ is 0.85 (as stated in the question as the value for the “debt beta”)
$E[r_m]$ is equal to 12% since that’s what the question suggests analysts expect

Plugging in the numbers from the question into the CAPM-based formula for cost of equity, we have…

$k_d = 0.015 + 0.85(0.12 - 0.015)$

Solving for that yields…

$k_d = 0.10425 \equiv 10.425\%$

Calculate Cost of Debt using Modigliani & Miller II

Finally, if we were to use Modigliani & Miller II (M&MII), we can estimate $k_d$ as…

$k_d = k_a + \frac{E}{D} \left(k_a - k_e \right)$

In this case, $k_a$ is essentially the firm’s cost of capital. We’re told that this is equal to 10%.

We’re also told – again, from the question – that the firm’s cost of equity ( $k_e$ ) is equal to 11.78%.

We have a value for $D$ (being $800m per the question). However, a value for $E$ (the market value of Equity) isn’t provided explicitly.

We can calculate $E$ by using the Accounting Equation as our framework. The Accounting Equation can be expressed as:

Assets = Liabilities + Equity

Liabilities is just another term for Debt. Thus, we can write the Accounting Equation as…

Assets = Debt + Equity

Rearranging for Equity, we have…

Equity = Assets – Debt

We’re told that Debt and Total Assets equate to $800m and $3.5bn respectively (from the question).

Thus, Equity must be equal to…

Equity = $3.5bn – $0.8bn = $2.7bn

Plugging in all our numbers into the formula for cost of debt (using M&M II), we have…

$k_d = 0.1 + \frac{\$2.7bn}{\$0.8bn} \left(0.1 - 0.1178 \right)$

Solving for this by applying “BODMAS” yields…

$k_d = 0.1 + 3.375 \times -0.0178$

Finally, solving further, we get…

$k_d \approx 0.039925 \approx 4\%$

Comparing Estimates Using Different Approaches

From our ‘simple’ example alone, we’ve obtained 2 different estimates for $k_d$ using three different approaches, including:

4% when we use the interest on debt approach,
10.425% when we use the CAPM, and
4% when we use M&M II

Note that we designed the question in a way where the answer for $k_d$ is equal to 4% whether one uses the interest on debt approach or M&MII.

It’s not prudent to expect to have identical values for $k_d$ regardless of which approach one uses.

But which one is the “correct” $k_d$ you ask?

In this example instance, it’s more likely that 4% is the appropriate $k_d$ . Mainly because we wrote the question and intended it to be equal to 4% 😉

From a practical, real world standpoint, the honest answer is that no one knows what the “true” or “correct” cost of debt should be.

Seriously.

In the real world, one would likely choose the estimate the “best fits” with the story trying to be sold.

If investors believe Starmont Inc. from above is significantly risky, they’ll perceive the estimate for $k_d$ from the CAPM to be the most appropriate.

If, on the other hand, investors believe Starmont Inc. isn’t all that risky, they might perceive the 4% estimate for $k_d$ to be very much appropriate.

Thus, the answer to what the “correct” cost of debt is, it depends.

Wrapping Up

Alright, hopefully, all of this makes sense, and you now have a strong understanding of the Cost of Debt including what is is, why it matters, and how to calculate it.

In summary, you learned that the Cost of Debt represents the cost of raising debt capital (aka debt financing).

Since debt is raised by companies from investors, $k_d$ is also equivalent to the rate of return for a debt investor, excluding the effects of transaction costs and taxes.

Furthermore, you learned that there are 3 main ways of calculating $k_d$ , including by using:

Interest on Debt
CAPM, and
Modigliani and Miller II (M&M II)

Importantly, remember that the 3 approaches are unique and independent. They will NOT necessarily give you the same result for $k_d$ .

This is because each model has its own set of assumptions, and relies on its own set of variables and data.

It’s not prudent nor constructive to simply take an average across all estimates, because – again – each mode has its own set of assumptions, and relies on its own set of variables and data.

Taking a simple average of all 3 estimates is akin to taking an average of the number of apples and oranges, and describing it as the average number of apples.

If any part of this extensive guide / article on the Cost of Debt is not quite clear, please do give it another read.

You might also want to explore the complement to $k_d$ – the Cost of Equity. That’s as extensive as this particular article; arguably even more extensive since there are a few more complexities when it comes to the Cost of Equity.

The point is, you’ll want to make sure you have a good cup of tea before you start reading about the Cost of Equity.

If you’d like to go further and learn to invest like the pros, do check out our courses on investing that are designed to help you master complex concepts in finance and investing.

That’s a wrap from us for now.

Keep learning, keep growing!

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What is Cost of Debt?

Cost of Raising Debt Finance

Appropriate Discount Rate for Debt Cash Flows

Appropriate Rate of Return for Debt Investors

Why Does The Cost of Debt Matter?

Importance for Users

Importance As a Risk Signal

How to Calculate Cost of Debt?

How to Calculate Cost of Debt using Interest on Debt

How to Calculate Cost of Debt using the CAPM (Capital Asset Pricing Model)

How to Calculate Cost of Debt using Modigliani & Miller II

Do All Calculations of Cost of Debt Provide The Same Result?

How Does Tax Affect The Cost of Debt?

What is the Difference Between Cost of Debt and Cost of Capital?

What is the Difference Between Cost of Debt and Cost of Equity?

Cost of Debt Calculation Example

Calculate Cost of Debt using Interest on Debt

Calculate Cost of Debt using the CAPM

Calculate Cost of Debt using Modigliani & Miller II

Comparing Estimates Using Different Approaches

Wrapping Up

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What is Cost of Debt?

Cost of Raising Debt Finance

Appropriate Discount Rate for Debt Cash Flows

Appropriate Rate of Return for Debt Investors

Why Does The Cost of Debt Matter?

Importance for Users

Importance As a Risk Signal

How to Calculate Cost of Debt?

How to Calculate Cost of Debt using Interest on Debt

How to Calculate Cost of Debt using the CAPM (Capital Asset Pricing Model)

How to Calculate Cost of Debt using Modigliani & Miller II

Do All Calculations of Cost of Debt Provide The Same Result?

How Does Tax Affect The Cost of Debt?

What is the Difference Between Cost of Debt and Cost of Capital?

What is the Difference Between Cost of Debt and Cost of Equity?

Cost of Debt Calculation Example

Calculate Cost of Debt using Interest on Debt

Calculate Cost of Debt using the CAPM

Calculate Cost of Debt using Modigliani & Miller II

Comparing Estimates Using Different Approaches

Wrapping Up

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