Question

The bonds have a $40,000 par value and an annual contract rate of 10%, and they mature in 10 years. Interest is paid semiannually..What is the bonds issue price with market rates of 8%, 10% and 12%

Answer 1

Issue price of bonds = Present value of lumpsum + present value of interest payments

Present value of lumpsum = Cash flow / (1+r)n

1+r whole power -n

1+r whole power n

present value of interest payments = cash flow * (( 1 - (1+r)-n / r ))

Market rate 8%

Market rate 10%

Market rate 12%

a) Face value = 40000

a) Face value = 40000

a) Face value = 40000

coupon rate = 10%

coupon rate = 10%

coupon rate = 10%

Semi anually intrest payment = 10/2 = 5%

Semi anually intrest payment = 10/2 = 5%

Semi anually intrest payment = 10/2 = 5%

Market rate of intrest = 8%

Market rate of intrest = 10%

Market rate of intrest = 12%

Semi anually = 8/2 = 4%

Semi anually = 5%

Semi anually = 6%

maturity period = 10

maturity period = 10

maturity period = 10

n = 10*2 = 20

n = 10*2 = 20

n = 10*2 = 20

interest = 40000*5% = 2000

interest = 40000*5% = 2000

interest = 40000*5% = 2000

12480

pv of lumpsum = 40000/(1+0.04)20

pv of lumpsum = 40000/(1+0.05)20

pv of lumpsum = 40000/(1+0.06)20

18240

15080

12480

pv of interest payments = ((1-0.456)/0.04)*2000

Issue price = ((1-0.377)/0.05)*2000

Issue price = 2000*((1-0.312)/0.06))

27200

24920

22940

Issue price

45440

issue price

40000

issue price

35420