Question

Complete the below table to calculate the price of a $1.2 million bond issue under each of the following independent assumptions

1. Maturity 10 years, interest paid annually, stated rate 10%, effective (market) rate 12%.
2. Maturity 10 years, interest paid semiannually, stated rate 10%, effective (market) rate 12%.
3. Maturity 5 years, interest paid semiannually, stated rate 12%, effective (market) rate 10%.
4. Maturity 10 years, interest paid semiannually, stated rate 12%, effective (market) rate 10%.
5. Maturity 10 years, interest paid semiannually, stated rate 12%, effective (market) rate 12%.

Answer 1

no of years = 10

interest paid @ 10%

= 1200000 * 10 % ( Stated Rate )

= $ 120000

For Semi Annual period

= 120000 / 2

= 60000

@ 12% ( stated rate )

= 1200000 * 12%

= $ 144000

For Semi Annual period = 144000 / 2

= $ 72000

1) paid Annually

no of years ( n) = 10

interest paid = 120000

market rate of interest ( i) = 12%

Problem 1
total values based on
N =	10
I = market Rate of interest	12%
Cash Flow	Table Value	amount	Present Value ( table Value * Amount )
par Value PVF ( i= 12% , n= 10 )	0.32197	1200000.0	386364
interest Annuity PVAF ( i= 12% , n= 10)	5.65022	120000.0	678026.40
Price of the bond			1064390.40

2)

paid Semi Annually

no of years = 10

no of periods interest paid = 10 * 2

(n) = 20

interest paid Semi Annually = 120000 /2

= $ 60000

market rate of interest ( i) = 12% /2

= 6%

Problem 1
total values based on
N =	20
I = market Rate of interest	6%
( for semi annual period )
Cash Flow	Table Value	amount	Present Value ( table Value * Amount )
par Value PVF ( i= 6% , n= 20 )	0.3118	1200000.0	374160
interest Annuity PVAF ( i= 6% , n= 20)	11.46992	60000.0	688195.20
Price of the bond			1062355.20

3)

Problem 3
total values based on
N = 5 years * 2	10
I = market Rate of interest ( 10%/2)	5%
( for semi annual period )
Cash Flow	Table Value	amount	Present Value ( table Value * Amount )
par Value PVF ( i= 5% , n= 10 )	0.61391	1200000.0	736692
interest Annuity PVAF ( i= 5% , n= 10)	7.72173	72000.0	555964.56
Price of the bond			1292656.56

4)

Problem 4
total values based on
N = 10 years * 2	20
I = market Rate of interest ( 10%/2)	5%
( for semi annual period )
Cash Flow	Table Value	amount	Present Value ( table Value * Amount )
par Value PVF ( i= 5% , n= 20 )	0.37689	1200000.0	452268
interest Annuity PVAF ( i= 5% , n= 20)	12.46221	72000.0	897279.12
Price of the bond			1349547.12

5)

When market rate and stated rate are Same bonds Are issued at Par value only

i.e. $ 1.2 million