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Suppose the Dutch government issued a bond with 20 years until maturity, a face value of €1000 and a coupon rate of 10% paid annually
Suppose the Dutch government issued a bond with 20 years until maturity, a face value of €1000 and a coupon rate of 10% paid annually. The yield to maturity when the bond was issued was 5%.
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What was the present value of the coupons when the bond was issued?
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What was the present value of the bond when it was issued?
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Assuming the yield to maturity remains constant, what is the price of the bond
immediately before it makes the first coupon payment?
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Assuming the yield to maturity remains constant, what is the price of the bond
immediately after it makes the first payment?
Expert Solution
We can calculate the desired result as follows:
Face Value (fv) = €1000
Coupon rate = 10%
Coupon Payment (pmt) = 10% * 1,000
= €100
Period (nper) = 20 years
YTM (rate) = 5%
Using the PV function, we can calculate the present value of coupon payments as:
= PV(rate, nper, -pmt)
= PV(5%,20,-100)
= €1,246.22
B) Present value of the bond is calculated as follows:
Face Value (fv) = €1000
Coupon Payment (pmt) = 10% * 1,000
= €100
Period (nper) = 20 years
YTM (rate) = 5%
Using the PV function, we can calculate the present value of bond as:
= PV(rate, nper, -pmt, -fv)
= PV(5%,20,-100,-1000)
= €1,623.11
C) Price of the bond immediately before it makes the first coupon payment is :
= Annual Coupon Payment + PV of Bond after 1 year
PV of Bond after 1 year = PV(rate, nper, -pmt, -fv)
= PV(5%,19,-100,-1000)
= €1,604.24
Annual Coupon payment = $ 100
Price of the bond = 100 + 1,604.24
= €1,704.24
D) Price of the bond immediately after it makes the first coupon payment is :
= PV of Bond after 1 year
= PV(rate, nper, -pmt, -fv)
= PV(5%,19,-100,-1000)
= €1,604.24
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