Final answer:
To determine the difference between the bond's yield to maturity (YTM) and yield to call (YTC), one must use the present value formulas for both scenarios and subtract YTC from YTM.
Step-by-step explanation:
To calculate the yield to maturity (YTM) and yield to call (YTC) of McCue Inc.'s bonds, we need to consider the cash flows for holding the bond until maturity and until the call date. The bond sells for $1,175, pays an annual coupon of $90, has a 25-year maturity, par value of $1,000, and can be called in 5 years at $1,050.
The YTM calculation involves finding the interest rate (i) that equates the present value of all future coupon payments and the redemption value at maturity with the current market price using the formula:
PV = C * (1 - (1 + i)^-n)/i + FV/(1+i)^n
Where PV = present value ($1,175), C = annual coupon payment ($90), n = number of years until maturity (25), FV = face value ($1,000), i = YTM.
The YTC is calculated similarly, but with the cash flow ending at the call date, 5 years from now, with the call price as the future value:
PV = C * (1 - (1 + i)^-n)/i + CP/(1+i)^n
Where CP = call price ($1,050), n = number of years until call (5), i = YTC.
After we find the YTM and YTC using these formulas (which requires iterative calculation or a financial calculator), we subtract the YTC from the YTM to find the difference between them. This difference reflects the relative attractiveness of the bond based on the expected interest rate scenarios.