question archive Suppose you buy a bond that will pay $1000 in ten years along with an annual coupon payment of $50 and the interest rate is 4%
Suppose you buy a bond that will pay $1000 in ten years along with an annual coupon payment of $50 and the interest rate is 4%
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Suppose you buy a bond that will pay $1000 in ten years along with an annual coupon payment of $50 and the interest rate is 4%. Answer the following questions:
a) What is the value of this bond?
b) Now suppose the bond has no coupon payments (it is a “zero coupon” bond) but still pays $1000 in ten years. What is the value of this bond?
c) What would happen to the value of the bond if the inflation rate unexpectedly goes up? What the bond value increase or decrease?
d) Now suppose the bond still pays an annual coupon of $50 but the interest rate drops to 2%. What is the new value of this bond?
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Answer:
a) Value of bond = Par value * PVF(4%, 10) + Coupon payments* PVAF(4%, 10)
= $1000*0.6756 + $50*8.1109
= $675.6 + $405.55
= $1081.15
b) If payment is made in 10 years of $1000, the value of the bond will be $1000*PVF(4%, 10) = $1000*0.67556 = $675.56
c) If the inflation rate grows up, the market interest rate rises, which means that the coupon payments will be less than the market interest rate demanded by the investors which causes the price of the bond to fall sharply. So, the bond price will decrease with a rise in inflation rate
d) As calculated in the first part
Value of bond = Par value * PVF(2%, 10) + Coupon payments* PVAF(2%, 10)
= $1000*0.8203 + $50*8.9826
= $820.3 + $449.13
= $1269.43
