Question

A tax-exempt municipal bond with a coupon rate of 8.00% has a market price of 98.03% of par. The bond matures in 10.00 years and pays semi-annually. Assume an investor has a 22.00% marginal tax rate. The investor would prefer otherwise identical taxable bond if it's yield to maturity was more than _____%

Caspian Sea Drinks needs to raise $50.00 million by issuing bonds. It plans to issue a 15.00 year semi-annual pay bond that has a coupon rate of 5.19%. The yield to maturity on the bond is expected to be 4.86%. How many bonds must Caspian Sea issue? (Note: Your answer may not be a whole number. In reality, a company would not issue part of a bond.)

Answer 1

	Let the bond face value be $1000
1)	Price of bond		=	PV of all interest payment+PV of redemption value
			=	[Coupon * PVAF (YTM,time to maturity)]+[PVF(YTM,time) *redemption value]
	Price of bond
		Price	=	$1000*98.03%=$980.3
		Coupon	=	$1000*8%*6/12=$40
		Time	=	10*2=20 half years
		YTM	=	?
		Redemption value	=	$1,000
		$980.30	=	[$40*PVAF(yeild,20)]+[PVF(yeild,20)*$1000]
		On solving the above equation we get yeild =4.417%
		Annual yeild	=	semi annualyeild*2
			=	4.147%*2
			=	8.29%
		the above equation can be sold via finacial calculator only.Thereis no direct formula to calculate it .
		If investor is in tax bracket of 22%
		equivalnet Yeild on taxable bond			=	yeild on tax exempt bond/(1-taxrate)
					=	8.29%/(1-0.22)
					=	8.29%/(0.78)
					=	10.63%
		The yeild to maturity of identicle taxable bond should be more than 10.63% to be prefered over taxfree bonds
2)		No. of bond to be issued			=	Amount tobe raised/price of bond
		Amount to be raised			=	$50,000,000
		Price of bond
			Coupon	=	$1000*5.19%*6/12=$25.95
			Time	=	15*2=30 half years
			YTM	=	4.86% *6/12=2.43% or 0.0243
			Redemption value	=	$1,000
			Price	=	[$25.95*PVAF(2.43,30)]+[PVF(2.43,30)*$1000]
				=	$25.95*21.13 + $1000*0.48661
				=	$548.25+$486.61
				=	$    1,034.86
	No. of bonds to be issued			=	$50,000,000/1034.86
				=	48316
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