Question

Computing Issue Prices of Bonds Sold at Par, at a Discount, and at a Premium Rosh Corporation is planning to issue bonds with a face value of $800,000 and a coupon rate of 8 percent. The bonds mature in four years and pay interest semiannually every June 30 and December 31. All of the bonds will be sold on January 1 of this year. Required: Compute the issue (sales) price on January 1 of this year for each of the following independent cases (show computations): a. Case A: Market interest rate (annual): 8 percent. b. Case B: Market interest rate (annual): 6 percent. c. Case C: Market interest rate (annual): 10 percent.

Answer 1

a)	Case A : Market Rate Of Return :8%
	When market rate of return is equal to the coupon interest rate of the bond,
	the bond issue price is equal to face value of the bond.
	Therefore bond price = $800000
b)	Case B= Interest rate 6%
	Bond Price = Present Value Of Interest Payments + Present Value Of Redemption Amount
		= P[1-(1+)^-n]/r + Redemption Amount * (1/(1+r)^n
		Where,
		P= Periodic payment, here interest 800000*8%*6/12=$32000
		r= interet rate i.e. 6%*6/12 = 3%
		n= number of periods i.e. 4*2= 8
		= 32000[1-(1+0.03)^-8]/0.03 + 800000*1/(1+0.03)^8
		=224630.15 +631527
		$     8,56,157.54
Case C	Market Interest Rate 10%
	Bond Price = Present Value Of Interest Payments + Present Value Of Redemption Amount
		= P[1-(1+)^-n]/r + Redemption Amount * (1/(1+r)^n
		Where,
		P= Periodic payment, here interest 800000*8%*6/12=$32000
		r= interet rate i.e. 10%*6/12 = 5%
		n= number of periods i.e. 4*2= 8
		= 32000[1-(1+0.05)^-8]/0.05 + 800000*1/(1+0.05)^8
		=206822.81 +541471.49
		$     7,48,294.30
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