Final answer:
To find Mary's minimum yield on a 10-year par value bond with 4% semiannual coupons, we must evaluate both the yield to maturity and the yield to call. The minimum yield is the lower of the two, and it requires solving for the internal rate of return that equates cash flows to the purchase price, adjusting for whether the bond is called or held to maturity.
Step-by-step explanation:
Mary purchased a 10-year par value bond with semiannual coupons at a nominal annual rate of 4% convertible semiannually at a price of 1021.50. The bond may be called starting at the end of year 5 for a par value of 1100. To determine the minimum yield Mary could receive, expressed as a nominal annual rate of interest convertible semiannually, we would need to consider two scenarios: if the bond is held to maturity and if the bond is called at the earliest date possible.
For holding to maturity at 10 years, we calculate the yield based on the purchase price, semiannual interest payments, and face value redemption. But for an early call at 5 years, we calculate based on receiving par value at the call date plus interest payments up to that point. The minimum yield would be the lower of the two calculated yields since the company could decide to call the bond early if interest rates decline, meaning the yield to call could potentially become the realized yield.
Calculating the yield involves finding the internal rate of return (IRR) that equates the present value of expected cash flows from the bond (interest payments plus principal repaid) to the purchase price. This calculation requires a financial calculator or software capable of solving for IRR. The yield to maturity might differ from the yield to call, with the latter being relevant if the bond is repurchased by the issuer at the call date. The yield to call calculation must account for the bond being redeemed at 1100 instead of the face value, and thus yields a different return than holding until maturity.