# Back to Basics: Calculating the cost of debt ## We explore risks and costs associated with debt as part of your Finance studies in our Back to Basics series with reminders of the key formulae at your disposal.

In a company, debt finance can take a number of forms. For example, money can be borrowed from a bank as a term loan, or money can be borrowed from investors, in the form of debentures.

The cost of debt is the cost that the company needs to pay its debt providers to keep them happy – it is the return that a company needs to provide to its debt holders.

This return rewards the lenders for the risk that they are exposed to, so the cost of debt will vary from one type of debt to another.

## Cheaper cost vs. higher risk

Debt is the cheapest source of finance for companies. It is cheaper than ordinary and preference shares for the following reasons:

• Debt is cheaper to issue than shares;
• Interest payments on debt are tax deductible expenses for companies;
• The risk that debt providers are exposed to is lower, meaning that a lower return is required. The lower risk is due to:
• Debt being secured;
• Debt providers being paid out before shareholders in the event of liquidation; and
• Interest payments having to be made before dividends can be paid out.

However, debt is also a riskier form of finance for companies as interest must be paid and security for debt has been given.

An increase in debt is an increase in gearing, meaning that the financial risk of a company has increased. Companies need to carefully balance the use of cheaper debt funding versus the additional risk that debt brings to a business.

## Calculating the cost of debt

We need to calculate the cost of debt to determine the return that is being offered to lenders. The cost of debt is also included as one of the components in the Weighted Average Cost of Capital (WACC) calculation.

There are two different ways of calculating the cost of debt. The method chosen depends on whether the debt is redeemable or not. If debt is redeemable, it is repaid; irredeemable debt is not repaid.

### If debt is irredeemable (not repaid), the following formula can be used:

#### Kd = I (1 - t) / P

where:

Kd =     cost of debt capital

I =        annual interest payment

t =        corporation tax rate

P =      market price of debt (ex-interest)

If debt is redeemable, the cost of debt is calculated as the redemption yield on the debt. The redemption yield is an Internal Rate of Return (‘IRR’) calculation. It is the discount rate which equates the market value of the debt with the present value of interest and capital cash flows.

However, there is an exception. If debt is redeemable but issued at par, is redeemable at par and is currently trading at its nominal value, the cost of debt can be correctly calculated using the irredeemable formula rather than calculating the redemption yield.

Both methods would give the same answer, but the irredeemable formula is quicker.

### Worked example:

Calculate the cost of debt on:

1. An 8% irredeemable debenture, that is currently trading at £95.52. Tax is currently 20%.

Solution:

Kd = I (1 - t) / P = 8 (0.8) / 95.52 = 6.7%

2. An 8% debenture, which is currently trading at £95.52 and is redeemable in five years at a premium of 5%. Tax is currently at 20%.

Solution:

 Time Cash flows Discount rate (10%) PV Discount rate (5%) PV Y0 (95.52) 1.0000 (95.52) 1.0000 (95.52) Y1 – Y5 6.40 (after tax) 3.791 24.26 4.329 27.71 Y5 105 0.6209 65.19 0.7835 82.27 (6.07) 14.46

Redemption yield = 5% + [(10% – 5%) x (14.46 / 14.46 + 6.07)] = 8.52%

3. An 8% debenture that was issued at par (£100), is redeemable in 5 years’ time at par and is currently trading at par. Tax is currently at 20%.

Solution:

Kd = I (1 - t) / P = 8 (0.8) / 100 = 6.4%

### Tips for calculating the cost of debt:

• The par value of a bond is £100, unless you are told otherwise.
• We remove tax from interest payments, but not from capital repayments.
• In Advanced Finance questions, the cost of debt on term loans is usually the after-tax interest rate.
• In Advanced Finance questions it is important to show your workings.
• Remember that the cost of debt is a percentage (%).
• Check your answer - the cost of debt should be lower than the cost of equity and the cost of preference shares, provided tax is taken into consideration.

## Topics

• CA Student blog