There is an inverse relationship between bond prices and yields. This inverse relationship will be demonstrated by calculating bond prices to show that interest rates move inversely: if yields rise, then bond prices fall. Bonds will be sold either at a premium or a discount. With this in mind respond to the following question. You currently own a 30 year Treasury Bond at 4% interest, paid semiannually. The market interest rates for like securities rose to 5%. Would your bond sell for a premium or a discount? Why? What would the market value of your bond be? Prove your answer by showing your Inverse relationship between bond prices and yields work.
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Coupon rate = 4 %
Market interest rate = 5 %
Bond is providing lesser interest that market. So, bond will be sold at discount in order to attract investor and due to interest rate risk which is the market interest rate or yield to maturity(Warren, 2013). Otherwise the investor would shy away from purchasing.
Assume that face value of bond = $1000
Present value of semi-annual coupons = (40 / 0.05) * [1 – 1 / (1.025) ^ 60] = $618.17
Present value of $1000 principal = $1000 / (1.025) ^ 60 = $227.28
Therefore, market value of Bond = $618.17 + $227.28 = $845.45
Reference
Warren, S. C. (2013). Survey of Accounting. 6th Edition: Cengage Learning.
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