Question

Complete the below table to calculate the price of a $1.7 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) (Use appropriate factor(s) from the tables provided.): 1. Maturity 12 years, interest paid annually, stated rate 10%, effective (market) rate 12%. 2. Maturity 20 years, interest paid semiannually, stated rate 10%, effective (market) rate 12%. 3. Maturity 10 years, interest paid semiannually, stated rate 12%, effective (market) rate 10%. 4. Maturity 20 years, interest paid semiannually, stated rate 12%, effective (market) rate 10%. 5. Maturity 20 years, interest paid semiannually, stated rate 12%, effective (market) rate 12%.

Answer 1

Correct Answer:

Requirement 1: Issue Price of Bond = $ 1,489,391

Annually		Formula Applied
Face Value of Bond	$                      1,700,000
Interest Semi-Annually @ 10%	$                          170,000	(Face Value of Bonds * Coupon rate )
Semi-Annual Effective interest Rate ® (12%)	0.120	12%
Time Period (n) 12 years	12.00	12
Present Value of Face Value of Bond	$             436,347.65801	Face Value/(1+r%)^2n
Present Value of Interest payment	$                1,053,043.62	Interest * ((1-(1+r)^-n)/r)
Issue Price Of Bond	$                      1,489,391	PV of Face value of bond + PV of Interest Paid Annually
Premium or (Discount)	$                        (210,609)	Issue Price - Face Value of Bonds

Requirement 2:

Issue Price Of Bond

$                      1,444,213

Working:

Semi-Annually		Formula Applied
Face Value of Bond	$                      1,700,000
Interest Semi-Annually @ 10%	$                            85,000	(Face Value of Bonds * Coupon rate )
Semi-Annual Effective interest Rate ® ( 12%/2)	0.060	12%
Time Period (n) 20 years	40.00	20
Present Value of Face Value of Bond	$             165,277.71910	Face Value/(1+r%)^2n
Present Value of Interest payment	$                1,278,935.23	Interest * ((1-(1+r)^-n)/r)
Issue Price Of Bond	$                      1,444,213	PV of Face value of bond + PV of Interest Paid Annually
Premium or (Discount)	$                        (255,787)	Issue Price - Face Value of Bonds

Requirement 3:

Issue Price Of Bond

$                      1,911,858

Working:

Semi-Annually		Formula Applied
Face Value of Bond	$                      1,700,000
Interest Semi-Annually @ 12%	$                          102,000	(Face Value of Bonds * Coupon rate )
Semi-Annual Effective interest Rate ® ( 10%/2)	0.050	10%
Time Period (n) 10 years	20.00	10
Present Value of Face Value of Bond	$             640,712.12088	Face Value/(1+r%)^2n
Present Value of Interest payment	$                1,271,145.45	Interest * ((1-(1+r)^-n)/r)
Issue Price Of Bond	$                      1,911,858	PV of Face value of bond + PV of Interest Paid Annually
Premium or (Discount)	$                          211,858	Issue Price - Face Value of Bonds

Requirement 4:

Issue Price Of Bond

$                      1,991,704

Working:

Semi-Annually		Formula Applied
Face Value of Bond	$                      1,700,000
Interest Semi-Annually @ 12%	$                          102,000	(Face Value of Bonds * Coupon rate )
Semi-Annual Effective interest Rate ® ( 14%/2)	0.050	10%
Time Period (n) 4 years	40.00	20
Present Value of Face Value of Bond	$             241,477.65991	Face Value/(1+r%)^2n
Present Value of Interest payment	$                1,750,226.81	Interest * ((1-(1+r)^-n)/r)
Issue Price Of Bond	$                      1,991,704	PV of Face value of bond + PV of Interest Paid Annually
Premium or (Discount)	$                          291,704	Issue Price - Face Value of Bonds

Requirement 5:

Issue Price Of Bond

$                      1,700,000

Working:

Annually		Formula Applied
Face Value of Bond	$                      1,700,000
Interest Semi-Annually @ 12%	$                          102,000	(Face Value of Bonds * Coupon rate )
Semi-Annual Effective interest Rate ® ( 12%/2)	0.060	12%
Time Period (n) 20 years	40.00	20
Present Value of Face Value of Bond	$             165,277.71910	Face Value/(1+r%)^2n
Present Value of Interest payment	$                1,534,722.28	Interest * ((1-(1+r)^-n)/r)
Issue Price Of Bond	$                      1,700,000	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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