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Atlantis has been planning to develop a new warning system
Atlantis has been planning to develop a new warning system. The installation of the system costs more than what their budget allows so the mayor decides to issue a 20-year bond to finance the project. The bonds have a face value of $1,000 and it promises a coupon rate of 6.6% which will be paid quarterly to the bond holders.
Calculate the price you have to pay to purchase the bond if
- The Yield to Maturity (YTM) is 5.6% (annually)
- The Yield to Maturity (YTM) is 8.0% (annually)
Let's assume you would like to buy 50 bonds issued by Atlantis with a 20-year tenure. If the YTM is 7.2% and the coupon rate is 6.6%, calculate how much more you have to pay when you purchase a bond which makes annual coupon payments rather than quarterly.
Expert Solution
1). 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 = 5.6%/4 = 1.40% (quarterly)
Nper = 20*4 = 80 periods (quarterly)
Pmt = Coupon payment = $1,000*6.6%/4 = $16.50
FV = $1,000
Substituting the values in formula:
= -pv(1.40%,80,16.50,1000)
= $1,119.85
2). 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 = 8.0%/4 = 2% (quarterly)
Nper = 20*4 = 80 periods (quarterly)
Pmt = Coupon payment = $1,000*6.6%/4 = $16.50
FV = $1,000
Substituting the values in formula:
= -pv(2%,80,16.50,1000)
= $860.89
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 = 7.2%/4 = 1.80% (quarterly)
Nper = 20*4 = 80 periods (quarterly)
Pmt = Coupon payment = $1,000*6.6%/4 = $16.50
FV = $1,000
Substituting the values in formula:
= -pv(1.80%,80,16.50,1000)
= $936.67
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 = 7.2%
Nper = 20 periods
Pmt = Coupon payment = $1,000*6.6% = $66
FV = $1,000
Substituting the values in formula:
= -pv(7.2%,20,66,1000)
= $937.41
Total extra amount to be paid = 50 * ($937.41 - $936.67)
= 50 * $0.75
= $37.35
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