Question

Complete the below table to calculate the price of a $2.0 million bond issue under each of the following independent assumptions (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1):

1. Maturity 15 years, interest paid annually, stated rate 10%, effective (market) rate 12%.
2. Maturity 15 years, interest paid semiannually, stated rate 10%, effective (market) rate 12%.
3. Maturity 8 years, interest paid semiannually, stated rate 12%, effective (market) rate 10%.
4. Maturity 10 years, interest paid semiannually, stated rate 10%, effective (market) rate 8%.
5. Maturity 15 years, interest paid semiannually, stated rate 12%, effective (market) rate 12%.

Find price of bonds for each one

Answer 1

Correct Answer:

Issue Price Of Bond
1	$ 1,727,565.4
2	$ 1,724,703.4
3	$ 2,216,755.4
4	$ 2,271,806.5
5	$ 2,000,000.0

Working:

1.

Annually		Formula Applied
Face Value of Bond	$         2,000,000
Interest Semi-Annually @ 10%	$             200,000	(Face Value of Bonds * Coupon rate ) / 2
Semi-Annual Effective interest Rate r = ( 12%)	0.1200	12.0%
Time Period (n) 15 years	15.00	15
Present Value of Face Value of Bond	$             365,393	Face Value/(1+r%)^2n
Present Value of Interest payment	$         1,362,173	Interest * ((1-(1+r)^-n)/r)
Issue Price Of Bond	$      1,727,565.4	PV of Face value of bond + PV of Interest Paid Annually
Premium or (Discount)	$           (272,435)	Issue Price - Face Value of Bonds

2.

semi-Annually		Formula Applied
Face Value of Bond	$         2,000,000
Interest Semi-Annually @ 10%	$             100,000	(Face Value of Bonds * Coupon rate ) / 2
Semi-Annual Effective interest Rate r = ( 12%)	0.0600	12.0%
Time Period (n) 15 years	30.00	15
Present Value of Face Value of Bond	$             348,220	Face Value/(1+r%)^2n
Present Value of Interest payment	$         1,376,483	Interest * ((1-(1+r)^-n)/r)
Issue Price Of Bond	$      1,724,703.4	PV of Face value of bond + PV of Interest Paid Annually
Premium or (Discount)	$           (275,297)	Issue Price - Face Value of Bonds
3.
semi-Annually		Formula Applied
Face Value of Bond	$         2,000,000
Interest Semi-Annually @ 12%	$             120,000	(Face Value of Bonds * Coupon rate ) / 2
Semi-Annual Effective interest Rate r = ( 10%)	0.0500	10.0%
Time Period (n) 8 years	16.00	8
Present Value of Face Value of Bond	$             916,223	Face Value/(1+r%)^2n
Present Value of Interest payment	$         1,300,532	Interest * ((1-(1+r)^-n)/r)
Issue Price Of Bond	$      2,216,755.4	PV of Face value of bond + PV of Interest Paid Annually
Premium or (Discount)	$             216,755	Issue Price - Face Value of Bonds

4.

semi-Annually		Formula Applied
Face Value of Bond	$         2,000,000
Interest Semi-Annually @ 10%	$             100,000	(Face Value of Bonds * Coupon rate ) / 2
Semi-Annual Effective interest Rate r = ( 8%)	0.0400	8.0%
Time Period (n) 10 years	20.00	10
Present Value of Face Value of Bond	$             912,774	Face Value/(1+r%)^2n
Present Value of Interest payment	$         1,359,033	Interest * ((1-(1+r)^-n)/r)
Issue Price Of Bond	$      2,271,806.5	PV of Face value of bond + PV of Interest Paid Annually
Premium or (Discount)	$             271,807	Issue Price - Face Value of Bonds

5.

semi-Annually		Formula Applied
Face Value of Bond	$         2,000,000
Interest Semi-Annually @ 12%	$             120,000	(Face Value of Bonds * Coupon rate ) / 2
Semi-Annual Effective interest Rate r = ( 2%)	0.0600	12.0%
Time Period (n) 15 years	30.00	15
Present Value of Face Value of Bond	$             348,220	Face Value/(1+r%)^2n
Present Value of Interest payment	$         1,651,780	Interest * ((1-(1+r)^-n)/r)
Issue Price Of Bond	$      2,000,000.0	PV of Face value of bond + PV of Interest Paid Annually
Premium or (Discount)	$                         -	Issue Price - Face Value of Bonds

End of Answer.

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