On October 1, 2020, Dissux Corporation’s zero-coupon bonds, which mature 20 years later, are selling for...

On October 1, 2020, Dissux Corporation’s zero-coupon bonds, which mature 20 years later, are selling for $200. What is the effective annual yield to an investor who buys the $1,000 face value bonds on that date and holds them until maturity? What would the yield be if the same 20 year securities had an 8% coupon rate, made semi-annual payments and sold for $1050? (answer both questions in percent with two decimal places)

Solutions

Expert Solution

Yield for Zero Coupon Bond = CAGR = [(Face Value/Purchase Price)^(1/Maturity Period)]-1 = [(1000/200)^(1/20)]-1 = 5^0.05)-1 = 1.083798-1 = 0.083798 = 8.38%

Yield to Maturity = [Coupon + Pro-rated Discount]/[(Purchase Price + Redemption Price)/2]

Where,

Coupon = Par Value*Coupon Rate = 1000*8% = 80

Pro Rated Discount = [(Redemption Price-Purchase Price)/Period to Maturity] = [(1000-1050)/(20)] = -2.5

Redemption Price (assuming at par) = 1000

Therefore, YTM = [80-2.5]/[(1050+1000))/2] = 77.5/1025 = 0.0756 = 7.56%

jeff jeffy answered 2 years ago

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