Question

Consider 2 bonds. One is a 5-year bond with an 8% coupon, paid semiannually. The other is a zero coupon, 20 year bond.

a). What must be the required rate of return for the 5 year bond for it to sell at par value?

b). If the required rate of return for the 5 year bond is 6%, does the bond sell at a premium or a discount?

c). What is the price of the zero coupon bond if the required rate of return is 7%?

d). What must be the required rate of return of the investor willing to pay $650 for the zero coupon bond?

Answer 1

Answer a)

The Required Rate of Return will have to be 8% because YTM and Coupon are same when the Value of the Bond is equal to the Par Value of the bond.

Answer b)

When YTM < Coupon. The Bond will trade at a premium because coupon payment is more than the required rate of return. i.e. Bond is paying more than expectation. Bond will be high in demand. i.e. premium

Answer C)

Value of ZCB = Maturity Value / (1+r)^n

= 1000 (1+0.07)^20

=$258.42

Answer d)

Value of ZCB = Maturity Value / (1+r)^n

650 = 1000 / (1+r)^20

(1+r)^20 = 1000 / 650

(1+r)^20 = 1.53846153846

(1+r) = 1.53846153846^1/20

(1+r) = 1.02177278767

r = 1.02177278767 - 1

r = 2.18%

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