Answer to Question #150335 in Financial Math for Arman

Question

Two bonds have 6 years to maturity and payable semi-annually, par value of 1000 and a yield to maturity 0f 7% per annum. Bond A is a zero-coupon and whereas bond B has a coupon rate of 8% per annum.
(a) Calculate the price and current yield of bond A and Bond B. Explain A and B bond selling at a discount, premium or par?
(b) One would like to invest another 8 years corporate bond, which of the term as mentioned above is desirable? How does each feature affect the required rate of return for the bond?

Answer 1

(a) B(Bond Value) = PV of coupons + PV of par

B = PV of annuity + PV of lump sum

B(A) = 1000/(1.07⁶) = 666.34

B(B) = 1000*0.08*(1-1/1.07⁶)/0.07+1000/(1.07⁶)=1047.67

current yield(A)=annual coupon / price = 0

current yield(B)=annual coupon / price = 80/1047.67 = 0.076

Bond Value(A)<par value. A bond is selling at a discount.

Bond Value(B)>par value. A bond is selling at a premium.

(b)

B(A) = 1000/(1.07⁸) = 582

B(B) = 1000*0.08*(1-1/1.07⁸)/0.07+1000/(1.07⁸)=1060

B term is more desirable.

The required rate of return on a bond is the interest rate that a bond issuer must offer in order to get investors interested. Required returns are predominantly set by market forces and determined by the price at which issuers and investors agree.

Required rate of return = Risk-Free rate + Risk Coefficient(Expected Return – Risk-Free rate)

If a bond has a coupon rate, the required rate of return is lower.