So far, we have learned how to get present value or future value given payment per period, interest rate, and number of periods. Now we are ready to find value of real world assets. Let's find the value of a bond first. Bond is similar to an interest-only loan. That is, the borrower will pay the interest every period but none of the principal will be repaid until the end of the loan. For example, suppose Yonsei Corporation wants to borrow $1,000 for 30 years. The interest rate on a similar debt issued by a similar corporation is 5%. Yonsei will thus pay 5% times $1,000 is equal to $50 in interest rate every year for 30 years. At the end of 30 years, Yonsei will repay the $1,000. Let's use this example to define some of the important jargons associated with bonds. First, in this example, the $50 of regular interest payments that Yonsei promises to pay are called the bond's coupons. The amount that will be repaid at the end of the loan is called the bond's face value or par value. In this example, the face value is $1,000. The par value of the corporation bond is usually $1,000. When a bond sells for its par value, it is called a par bond. The annual coupon divided by the face value is called the coupon rate on the bond. In this example, the coupon rate is 50 divide by $1,000 is equal to 5%. The number of years until the face value is paid is called the bond's time to maturity. The maturity is the same as the bond's life when it is issued, but the number of years to maturity declines as time goes by. Suppose Yonsei Corporation were to issue a bond with 30 years to maturity. The Yonsei bond has an annual coupon of $50. Similar bonds have a yielded maturity to 5%. What would this bond sell for? This bond has a period cash flow of $50 every year for 30 years and $1,000 of face value in year 30. So, you need to discount these cash flows at 5% discount rate. You can get the bond value by finding the present value of the face value and annuity component, which is coupons. First, let's find a present value of face value. Let's just start Excel and type in =PV. For rate, type in 5%. For number of periods, type in 30. For payment amount, type in zero because we are interested in present value of face value only now. For future value, type in $1,000. The result is minus $231.38. That is the present value of $1,000 is $231.38. Next, let's find the present value of annuity. Type in =PV, for rate type in 5%, for number of periods, type in 30, for payment amount, type in 50, which is coupon amount. For future value type in 0 because we are interested in present value of coupons only now. The result is -768.62. That is the present value of $50 coupon for 30 years is $768.62. When you add the present value, or face value, and annuity, the bond value is $1,000. We can get the bond value at once, as you may have already noticed. In order to find the value of this bond, again, we can use PV function in Excel. Type in =PV. For rate, type in 5%. For number of periods, type in 30. For payment amount, type in 50. For future value, type in $1,000. That is we include annuity and face value in one function. The result is -1,000, that is the bond value is $1,000 and it is the same as what we found already. Its price is the same as its face value, because the going interest rate in the market is 5% and coupon rate is also 5%. As you may notice in this example, the price of a bond is same as the face value of the bond when its coupon rate is the same as market interest rate. Next, let's see what happens to bond value when interest rate changes. Suppose a year has gone by and the bond has 29 years to maturity. If the market interest rate has risen to 6%, what will the bond be worth? Let's start Excel and type in =PV. For rate type in 6%. For number of periods type in 29 For payment amount, type in 50. For future value, type in 1000. The result is -864.09, that is, the bond value is $864.09. The bond now sells for less than is $1000 of face value. Why? It is because the market interest rate is higher than its coupon rate. In other words, this bond pays less than the going rate. Investors are willing to lend only something less than $1,000 of promised repayment. This kind of bond is called discount bond. Next, let's see what would the bond value sell for if the market interest rate had dropped by 1%. Again, suppose a year has gone by and the bond has 29 years to maturity. Let us start Excel and type in =PV. For rate, type in 4%, which is 5% minus 1%. For number of periods, type in 29. For payment amount, type in 50. For future value, type in $1,000. The result is minus 1,169.84, that is, the bond value is $1169.84. The bond now sells for more than it's $1000 of face value. Why? It is because this bond pays coupon rate more than the going rate and investors are willing to pay premium to get this extra coupon amount. This kind of bond is called premium bond.
