The cost of debt and preference shares

Debt is the cheapest source of long-term finance a company has, for two reasons that stack on top of each other.

• Lenders take less risk than shareholders. They are paid before any dividend, they usually hold security, and they rank ahead in a liquidation — so they require less.
• Interest is deducted before tax. Every kwacha of interest reduces taxable profit, so the government pays part of the bill.

The second point is the one that changes the arithmetic. A company borrowing at 10% with tax at 30% does not really bear 10%. The interest reduces its tax bill by 3%, so the cost to the company is 7%.

Two different numbers are now in play and they answer different questions. The pre-tax cost is what the investor earns; the after-tax cost is what the company bears. WACC is built from what the company bears, so the after-tax figure is the one that goes into it.

The relief only exists if there is taxable profit to relieve. A company making losses is paying the full 10% and getting nothing back, which is one reason lossmaking firms find debt so much heavier than the textbook suggests.

A bank loan is the simplest case. It is not traded, so there is no market price to work from and no yield to calculate — the cost is the interest rate written into the agreement, adjusted for tax.

Preference shares look like debt and are treated like equity. They pay a fixed dividend, they rank ahead of ordinary shares, and where they are irredeemable that dividend is a perpetuity — so the cost is the yield the market is getting on them.

8% preference shares of ZMW100 nominal, quoted at ZMW85, cost 8 ÷ 85 = 9.41%. The dividend is fixed at ZMW8 by the nominal value, not by the price — the price is what an investor pays today to receive it.

That single difference is why preference shares can cost more than a bank loan carrying a higher headline rate. A 15% loan taxed at 30% costs 10.5%; 9.41% preference shares cost 9.41%; but 12% preference shares would cost 12% against a 15% loan’s 10.5%, and the loan would be cheaper despite looking more expensive on the face of it.

An irredeemable bond has a fixed coupon and no maturity date. The interest runs forever, so it is a perpetuity, and its cost is the coupon divided by the market price. Interest is deductible, so this one does carry the tax adjustment.

The nominal value sets the coupon; the market price sets the yield. A ZMW1,000 bond with a 9% coupon pays ZMW90 a year for as long as it exists, whatever the bond changes hands for. If it trades at ZMW1,125 the buyer is getting 90 ÷ 1,125 = 8%, and if it trades at ZMW900 the buyer is getting 10%.

So a bond’s price and its yield always move in opposite directions. That relationship holds for every fixed-income instrument and it is worth carrying forward — it is the whole reason interest rate risk exists.

With tax at 25%, that ZMW1,000 9% bond trading at ZMW1,125 costs the company 90 × 0.75 ÷ 1,125 = 6%, against the 8% its holder receives.

A redeemable bond pays a coupon and then repays its nominal value on a fixed date. Two kinds of cash flow, one of them years away, so there is no dividing one number by another. Its cost is the yield to maturity — the discount rate at which the present value of everything the bond pays equals what it costs today.

That is an IRR, and it is found the same way: two rates, one either side, then interpolate.

TC Co has 9% ZMW100 bonds redeemable at par in three years, trading at ZMW98.25. Lay out the cash flows from the investor’s side: pay ZMW98.25 now, receive ZMW9 a year, and ZMW109 in the final year when the coupon and the redemption arrive together.

The yield is above the 9% coupon, and it has to be: the bond costs ZMW98.25 and repays ZMW100, so the holder collects a ZMW1.75 gain on top of the interest. A bond trading above par works the other way — the holder takes a loss at redemption and the yield falls below the coupon.

9.69% is what the investor earns. To get what the company bears, run the same calculation using the coupon net of tax. Some questions ask for one, some for the other, and the difference is several percentage points — read which is wanted before laying out the table.

Each instrument has one method, and it follows from the shape of the cash flows rather than from anything you need to memorise. A perpetuity divides; a finite stream with a repayment at the end needs an IRR; an untraded loan has no price to divide by, so it uses its stated rate.

When debt has a beta

Where a question supplies a debt beta, the cost of debt is found by CAPM in exactly the way the cost of equity is. Corporate debt is not risk-free — the borrower can default — and a beta puts a number on how much of that risk moves with the market.

With a risk-free rate of 4.6%, a market risk premium of 6% and a debt beta of 0.75, the pre-tax cost of debt is 4.6% + 0.75 × 6% = 9.10%, and at 30% tax the company bears 6.37%.

Debt betas are small — well below any equity beta for the same company, because lenders are exposed to far less of the business’s fortunes than owners are. A debt beta of zero is the special case where the debt is treated as risk-free, and then the cost of debt is simply the risk-free rate.