Magic Milling Company has 9% annual coupon bonds that are callable and have 18 years left until maturity. The bonds have a par value of $1,000, and their current market price is $1,100.35. However, Magic Milling may call the bonds in eight years at a call price of $1,060. What are the YTM and the yield to call (YTC) on Magic Milling’s bonds?

Yield to maturity 8.04%

Yield to Call 8%

Explanation:

Yield to maturity is the annual rate of return that an investor receives if a bond bond is held until the maturity. it is a long term return whereas it is expressed in annual term.

Face value = F = $1,000

Coupon payment = $1,000 x 9% = $90

Selling price = P = $1,100.35

Number of payment to maturity= n = 18 years

Call Price = CP = $1,060

Duration to call = 8 years

Use following formula to calculate the YTM.

Yield to maturity = [ C + ( F - P ) / n ] / [ (F + P ) / 2 ]

Yield to maturity = [ $90 + ( $1,000 - $1,100.35 ) / 18 ] / [ ( $1,000 + $1,100.35 ) / 2 ]

Yield to maturity = 8.04%

Yield to call is the annual rate of return that an investor receives until the date of call if a bond called before maturity.

Yield to Call = [ C + ( F - CP ) / n ] / [ (F + CP ) / 2 ]

Yield to Call = [ $90 + ( $1,000 - $1,060 ) / 8 ] / [ ( $1,000 + $1,060 ) / 2 ]

Yield to Call = 8%