# Level 1 CFA® Exam:

Bond Pricing

By a long-term liability, we understand a liability that will result in an outflow of an economic benefit for a period of time longer than one year.

Before we proceed to bond valuation, let’s talk about the different types of debt that the company may have. The most popular types of long-term debt are:

- bank loans,
- mortgages, and
- bonds.

If a company incurs a long-term debt, there will occur a liability on the balance sheet. The liability takes the form of notes payable when a bank loan is taken out. A mortgage results in a mortgage payable entry and if the company issues a bond, it is recognized as a bond payable on the balance sheet.

Note that interest expense does not occur in the balance sheet until the interest is due, because there is always a possibility that the company will decide to repay the debt earlier before the interest is due.

### TVM & Fixed Income Recap

Let’s start with the time value of money (TVM).

The concept of the time value of money can be applied to the valuation of different financial instruments, for example, bonds.

A bond is a financial instrument for which the issuer, called also the borrower, agrees to pay certain amounts of money at specified dates in the future. These amounts of money are:

- the par value of a bond, also called principal value, and
- interest, commonly known as coupons.

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We can imagine that a bond is equivalent to the sequence of cash flows occurring regularly in different periods. These cash flows are coupons and par value. Remember that the last coupon is paid with par value.

So, to calculate the value of a bond we should calculate the present values of all coupons and the present value of the par value and add all these present values together. To do this we will use the bond worksheet in our calculator.

To access the bond worksheet, we press [2nd] [BOND]. In the worksheet we can input:

- SDT which stands for settlement date
- CPN which stands for coupon rate
- RDT which stands for redemption date
- RV, that is the redemption value. We will not change the value here and leave 100 as it is.
- ACT or 360 which are conventions of counting days in years and months. We will not change it anyway in this lesson.
- Next there’s 1/Y or 2/Y. We use 1/Y if coupons are paid annually. 2/Y means that coupons are paid semiannually. To switch between annual coupon payment and semiannual coupon payment, we press [2nd] [SET].
- YLD stands for the market discount rate.
- Then, there is PRI which is the bond’s price per USD 100 of par value. To compute the price, we should input numbers into SDT, CPN, RDT, RV, and YLD and press Compute.
- Next, we have AI and DUR – we are not interested in them in this lesson, however.

Remember: If we input the SDT, C, RDT, RV, and YLD values, we should always accept them by pressing Enter.

It is 1 January 2023. Robots, Inc. is issuing today a 4-year bond with a par value of USD 100 and a coupon paid on an annual basis that amounts to 8% of the par value. The market discount rate is equal to 7%. What is the price of the bond?

(...)

It is 1 January 2023. Grain, Inc. is issuing today an 8-year bond with a par value of USD 100 and a coupon paid on an annual basis that amounts to 5% of the par value. The market discount rate is equal to 8%. What is the price of the bond?

(...)

It is 1 January 2023. Steel, Inc. is issuing today a 12-year bond with a par value of USD 100 and a coupon paid on an annual basis that amounts to 4% of the par value. The market discount rate is equal to 4%. What is the price of the bond?

(...)

What can we get additionally from these examples?

Notice, that the price of a bond may be:

- higher than the par value. In this case, we say that the bond sells at premium.
- lower than the par value. In this case, we say that the bond sells at a discount.
- equal to the par value. In this case, we say the bond sells at par.

Also note that:

- If the coupon rate is higher than the market discount rate, the bond will sell at a premium. Example 1 illustrated such a situation.
- If the coupon rate is lower than the market discount rate, the bond will sell at a discount. We dealt with such a bond in example 2.
- If the coupon rate is equal to the market discount rate, the bond will sell at par. Example 3 showed such a bond.

- The most popular types of long-term debt are: bank loans, mortgages, and bonds.
- The liability takes the form of notes payable when a bank loan is taken out.
- A mortgage results in a mortgage payable entry.
- If the company issues a bond, it is recognized as a bond payable on the balance sheet.
- Interest expense does not occur in the balance sheet until the interest is due because there is always a possibility that the company will decide to repay the debt earlier before the interest is due.
- The value of coupons and the price of the bond depend on the rate of return required by investors.
- The rate of return required by investors largely depends on the risks associated with investing in the bond.