Question

E10-3 Computing Issue Prices of Bonds Sold at Par, at a Discount, and at a Premium LO10-2, 10-4, 10-5

LaTanya Corporation is planning to issue bonds with a face value of $105,000 and a coupon rate of 7 percent. The bonds mature in seven years. Interest is paid annually on December 31. All of the bonds will be sold on January 1 of this year. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use the appropriate factor(s) from the tables provided. Round your final answer to whole dollars.)

Required:

Compute the issue (sale) price on January 1 of this year for each of the following independent cases:

a. Case A: Market interest rate (annual): 7 percent.

b. Case B: Market interest rate (annual): 5 percent.

c. Case C: Market interest rate (annual): 8 percent.

Answer 1

Correct Answer:

Requirement 1: Issue of bonds at par, Market rate of interest 7%

Price of Bonds

105,000.00

Working:

Annually		Formula Applied
Face Value of Bond	$                          105,000
Interest Annually @ 7 % (7/100 * 105,000)	$                               7,350	(Face Value of Bonds * Coupon rate )
Semi-Annual Effective interest Rate ® (7%)	0.070	7%
Time Period (n) 7 years	7	7
Present Value of Face Value of Bond	$               65,388.72290	Face Value/(1+r%)^2n
Present Value of Interest payment	$                      39,611.28	Interest * ((1-(1+r)^-n)/r)
Issue Price Of Bond	$                          105,000	PV of Face value of bond + PV of Interest Paid Annually
Premium or (Discount)		Issue Price - Face Value of Bonds

Requirement 2: Issue of bonds at Premium, Market rate of interest = 5%

Issue Price Of Bond

$ 117,151

Working:

Annually		Formula Applied
Face Value of Bond	$                          105,000
Interest Annually @ 3 % (3/200 * 1,560,000)	$                               7,350	(Face Value of Bonds * Coupon rate )
Semi-Annual Effective interest Rate ® ( 4%/2)	0.050	5%
Time Period (n) 7 years	7.00	7
Present Value of Face Value of Bond	$               74,621.53966	Face Value/(1+r%)^2n
Present Value of Interest payment	$                      42,529.84	Interest * ((1-(1+r)^-n)/r)
Issue Price Of Bond	$                          117,151	PV of Face value of bond + PV of Interest Paid Annually
Premium or (Discount)	$                           12,151	Issue Price - Face Value of Bonds

Requirement 3: Issue of bonds at Discount, Market rate of interest = 8%

Issue Price Of Bond

$ 99,533

Working:

Annually		Formula Applied
Face Value of Bond	$                          105,000
Interest Annually @ 3 % (3/200 * 1,560,000)	$                               7,350	(Face Value of Bonds * Coupon rate )
Semi-Annual Effective interest Rate ® ( 4%/2)	0.080	8%
Time Period (n) 7 years	7.00	7
Present Value of Face Value of Bond	$               61,266.49150	Face Value/(1+r%)^2n
Present Value of Interest payment	$                      38,266.82	Interest * ((1-(1+r)^-n)/r)
Issue Price Of Bond	$                            99,533	PV of Face value of bond + PV of Interest Paid Annually
Premium or (Discount)	$                            (5,467)	Issue Price - Face Value of Bonds

End of answer.

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