# Bond Valuation

### Valuation of Bonds

The value of a bond can be calculated based on a bond's coupon rate and par value.

A bond is a long-term investment instrument that requires a corporation to return the amount of the initial investment with interest and is secured by some collateral. A bond's coupon rate and par value are used to determine the value of the bond. The coupon rate is the interest payments received by the bondholder annually until the bond matures. The originator of the bond pays the coupons. The par value is the nominal value, or the amount in dollars, returned to the bondholder at maturity.

Calculating a bond's price is a useful method to determine if the bond is appropriately valued. It is good practice to value the bond before its purchase or sale as well as when interest rates change. The bond price is calculated by adding the discounted cash flows of the expected future cash flows from the coupons to the present value of the par value. The discount rate, used to determine the present value of future cash flows and to value the bond, should be based on the risk associated with the bond. A U.S. Treasury bond is commonly accepted to be a risk-free bond because it is backed by the government. Thus, the lowest satisfactory interest rate an investor should be willing to receive is equal to the U.S. Treasury bond rate. A common practice for establishing a discount rate for commercial bonds is to use the U.S. Treasury bond rate as the base rate and then add a premium, or an additional fee that a borrower is charged to compensate for the additional risk.

The investor finds that the five-year U.S. Treasury bond rate is currently 2.65 percent. The investor knows that interest rates have recently increased and are likely to continue increasing. With this information, the investor decides to add a 3.35 percent premium to the U.S. Treasury base rate. Thus, the discount rate is 6 percent ($2.65\%+3.35\%=6\%$).
${\text{Bond Price}=\frac{\text{Coupon Payment}_1}{(1+\text{Discount Rate})^1}+\frac{\text{Coupon Payment}_2}{(1+\text{Discount Rate})^2}+\cdots\frac{\text{Coupon Payment}_n}{(1+\text{Discount Rate})^n}+\frac{\text{Par Value}}{(1+\text{Discount Rate})^n}}$
For example, Larry's Flower Company has announced its intention to issue bonds with a maturity term of 5 years, a coupon rate equal to 8 percent, and a par value of 3,000. An investor determines that a discount rate of 6 percent is appropriate. $\text{Cash Flows Discounted to Present Value:}$ \begin{aligned}\text{Year 1}&=\frac{\240}{\;(1+0.06)^1}=\226\;\\\\\text{Year 2}&=\frac{\240}{(1+0.06)^2}=\214\\\\\text{Year 3}&=\frac{\240}{(1+0.06)^3}=\202\\\\\text{Year 4}&=\frac{\240}{(1+0.06)^4}=\190\\\\\text{Year 5}&=\frac{\3{,}240}{(1+0.06)^5}=\2{,}421\end{aligned} \begin{aligned}\text{Bond Value}&=\226+\214+\202+\190+\2{,}421\\&=\3{,}253\end{aligned} The investor calculates the bond's cash flow from the coupon payments to be $8\%\;\text{or}\;0.08\times\3{,}000=\240$ annually until the bond matures. The investor calculates the present value of the coupon payments and par value to be3,253. The investor concludes that if Larry's Flower Company issues its bonds at a price less than $3,253, the investor will purchase the bond. Larry's Flower Company Bond Valuation December 31, 2019 Coupon Rate 8% Par Value$3,000
Maturity Term 5 Years
Discount Rate 6%
Year 1 Year 2 Year 3 Year 4 Year 5
Bond Cash Flow $240$240 $240$240 $3,240 Bond Value$3,253

Bond value is calculated by taking the present value of the bond's cash flows at a given coupon rate and par value.

### Interest Rate Risk and Inflation

The effects of interest rate risk and inflation can be both short and long term.

Interest rate risk can have effects in both the short and long term. Interest rate risk is the possibility that the interest rate will change in a way that is unfavorable to the bondholder before the bond actually matures or that an asset will decrease in value if an asset with a higher interest rate becomes available. The issuer of a bond determines the coupon rate based on the current interest rate at the time of issuance.

A bond's value and the nominal interest rate have an inverse correlation. This means a rise in interest rates is a risk to a bond's value. To compensate for this interest rate risk, long-term and short-term bonds' coupon rates and par value yields are structured differently. For example, a long-term bond issued by Larry's Flower Company has increased exposure to interest rate risk. To offset this risk, the yield or par value of the bond will be greater and the coupon rate will be smaller. Conversely, a short-term bond issued by Larry's Flower Company has less exposure to interest rate risk and offers a higher coupon rate with a more modest yield.

Inflation has a role in bond risk. Inflation is the continual increase in the average price levels of goods and services. In simple terms, inflation is a reduction in the buying power of a currency. This presents a risk to bonds because the cash flow from a bond is a fixed rate. Thus, inflation decreases the yield of a bond's coupon.

### Yield to Maturity Changes with Price/Value

The yield-to-maturity rate is an effective method for investors to determine a bond's potential value as well as how a bond should be appropriately priced.

Price/value and yield to maturity are interconnected. The yield to maturity (YTM) is the return on a bond from the date of purchase through the date of maturity, expressed as an annual percentage. Despite the fact that yield to maturity is a long-term measure of a bond, it is presented as a yearly rate. The yield-to-maturity calculation is an effective method of determining a bond's return. However, the calculation is highly complicated. Calculating a bond's yield to maturity requires trial and error; thus, identifying the exact yield to maturity is difficult. Instead of using this complicated method, bond investors have adopted a common practice of using approximations of the bond's yield-to-maturity value based on a bond yield table or financial software that will perform the calculations.

Yield to maturity is a valuable tool for determining how likely a specific bond is to be a profitable investment. Investors compare the yield to maturity to their required discount rate, the minimum allowable rate of return required for an investment, and determine whether the bond satisfies their return requirements. Additionally, the yield-to-maturity rate is an effective method for investors to determine a bond's potential value as well as how it should be priced. Nonetheless, the yield-to-maturity method does have its limitations. For instance, yield to maturity does not take the taxes a bondholder pays into consideration. Additionally, yield to maturity does not consider fees associated with the purchase and sale of the bond. Last, the actual return of a bond is dependent on the market price of the bond, which is reliant on the market environment; therefore, the true return may vary significantly.