Question

Please answer in excel and show formulas! Thanks!

Zero-coupon bond. What is the annual implied interest of a five-year zero-coupon bond (using the semiannual pricing convention) with a yield to maturity of 12% and a par value of $1,000? What is the first year's implied interest of the zero-coupon bond? $ (Round to the nearest cent.)

Answer 1

Zero Coupon Bond is ISSUED AT DISCOUNT & REDEEMED AT PAR. There are NO COUPONS paid. The difference between the issue price and redemption price is implied yield.

Therefore, Implied Issue Price = Redemption Price i.e. Par Value/(1+Yeild to Maturity) = 1000/(1+0.12) = $892.857

Semi Annual Implied Interest Rate = CAGR = [(Future Price/Current Price)^1/Number of Periods]-1

where, Future Price = Par Value = 100, Current Price = Issue Price = 892.857, Number of Periods = 2*5 = 10

Therefore, [(1000/892.857)^1/10]-1 = (1.12^1/10)-1 = 1.011297-1 = 0.011297 = 1.1297%

1.1297 is Semi Annual Interest Rate.

Therefore, 1st Year's Implied Interest Rate = [(1+Semi Annual Rate)^2]-1 = [(1+0.011297)^2]-1 = 1.02272-1 = 0.02272 = 2.272%