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Victorian Treasury has issued 20-year bonds that pay semi-annual coupons at a rate of 2
Victorian Treasury has issued 20-year bonds that pay semi-annual coupons at a rate of 2.135%. The current market rate for similar securities is 3.5%. Assume the bond has a face value of $1000.
a. What is the bond's current market value?
b. What will be the bond's price if rates in the market decrease to 1.98%.
c. Refer to your answers in part b. How do the interest rate changes affect premium bonds and discount bonds?
d. Suppose the bonds were to mature in 10 years. How do the interest rate change in part b affect the bond prices?
Expert Solution
a). We can calculate the value of the bond by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here
PV = Value of the bond
Rate = 3.5%/2 = 1.75% (semiannual)
Nper = 20*2 = 40 periods (semiannual)
Pmt = Coupon payments = $1,000*2.135%/2 = $10.675
FV = $1,000
Substituting the values in formula:
= -pv(1.75%,40,10.675,1000)
= $804.84
b). We can calculate the price of the bond by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here
PV = Price of the bond
Rate = 1.98%/2 = 0.99% (semiannual)
Nper = 20*2 = 40 periods (semiannual)
Pmt = Coupon payments = $1,000*2.135%/2 = $10.675
FV = $1,000
Substituting the values in formula:
= -pv(0.99%,40,10.675,1000)
= $1,025.50
c). The price of the bond is inversely related to interest rate . If market interest rate decreases the bond price will increase and if the market interest rate increases the bond price will decrease. The premium bond means that the bond value is higher than the face value. A bond is trading in premium when the interest rate is higher than the current prevailing interest rate. Discount bond means that the bond price is lower than the face value. A bond is trading at discount when the interest rate is lower than the current prevailing interest rate.
d). We can calculate the price of the bond by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here
PV = Price of the bond
Rate = 1.98%/2 = 0.99% (semiannual)
Nper = 10*2 = 20 periods (semiannual)
Pmt = Coupon payments = $1,000*2.135%/2 = $10.675
FV = $1,000
Substituting the values in formula:
= -pv(0.99%,20,10.675,1000)
= $1,014
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