The first long term source of finance that we consider is the cost of long term debt, which is usually the cheapest of the long-term sources of finance. The majority of long term debt of large corporations is the result of issuing bonds.

### Flotation cost

Companies that issue bonds have to take into account the** flotation cost**, which is the complete cost the company has to incur to issue and sell a security, such as common stock, preferred stock and bonds. This cost reduces the company’s net proceeds from issuing security.

Flotation cost consists of underwriting and administrative costs. Underwriting costs are payment to investment bankers for their services and administrative costs are costs other than the underwriting costs of issuing bonds.

### Finding the before-tax cost of long-term debt (rd)

To find the after-tax cost of long term debt, we first need to find the before-tax cost of long term debt (rd). As mentioned above, the majority of long term debts of large corporations are the result of issuing bonds. By using a financial calculator, we can find the before tax cost of a bond (cost of long-term debt).

**THE CALCULATION FOLLOWS:**

FV – (future value of the bond which refers to its par value, which is also called the face value, and is usually $1,000)

PV – the value of the bond today at which it is sold (after deducting the flotation cost)

PMT – payment on the bond (for example, at 8% coupon interest rate a bond issuer will have to make annual payments of $80 if the par value is $1,000). Payments can also be made more frequently, such as semi-annually or even monthly, but in such a case we need to adjust the amount of payment and number of periods.

For example, if payment is made semi-annually, we will need to divide $80 by 2 and we will need to multiply number of periods by 2.

N – Number of periods

Calculate I – the cost of the bond (for the bond’s issuer it is the cost to maturity of the cash flows, for the bond’s holders it is the return they earn on buying and holding this bond to maturity). Within the context of our discussion, it is also the before-tax cost of long-term debt.

Note that if the net proceeds from the sale of the bond is the same as the face value of the bond than the before-tax cost of long-term debt will be equal to the coupon interest rate. For example, at 8% coupon interest rate, the par value of $1,000 and net proceeds of $1,000 (no flotation costs), the before-tax cost of long-term debt will equal 8%.

### Finding the after-tax cost of long-term debt

After we found the before-tax cost of long term debt, we need to find the after-tax cost of long term debt. To do so all we need to do is to multiply the before-tax cost of long-term debt by (1-T), where T stands for the tax rate.

THEREFORE:

ri = rd * (1-T)

EXAMPLE:

If the before-tax cost of long term debt is 10% and tax rate is 28% then the calculation will be as follows:

Ri =10% * (1-.28)

Ri =10% * .72

Ri = 7.2%

### Test yourself

You need to calculate the after-tax cost of a 30-year bond. The coupon interest rate is 10%, the par value is $1,000 and the bond is currently selling at $950.

SOLUTION:

PV: -950

FV: 1,000

PMT: 100

N: 30

I: 10.56%

*Note: If you struggle with a calculation, read using a financial calculator article for some simple tips on using a financial calculator.*

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