Question

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%.

1. What was the present value of the coupons when the bond was issued?

2. What was the present value of the bond when it was issued?

3. Assuming the yield to maturity remains constant, what is the price of the bond

   immediately before it makes the first coupon payment?

4. Assuming the yield to maturity remains constant, what is the price of the bond

   immediately after it makes the first payment?

Answer 1

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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