Question

Cost of debt. ​Dunder-Mifflin, Inc.​ (DMI) is selling​ 600,000 bonds to raise money for the publication of new magazines in the coming year. The bond will pay a coupon rate of 12.8​% with semiannual payments and will mature in 30 years. Its par value is $100.

What is the cost of debt to DMI if the bonds raise the following amounts​ (ignoring issuing​ costs)?

a. ​$58,092,000? _______%​ (Round to two decimal​ places.)

b. ​$51,012,000?________%​ (Round to two decimal​ places.)

c. ​$63,114,000? ________ % (Round to two decimal​ places.)

d. ​$74,796,000? ________%​ (Round to two decimal​ places.)

Answer 1

Solution:
	Amount raised	cost of debt to DMI
a.	$58,092,000	13.23	%
b.	​$51,012,000	15.09	%
c.	$63,114,000	12.15	%
d.	​$74,796,000	10.16	%
Working Notes:
	cost of debt to DMI will be its annual YTM of bond,
a.	$58,092,000
	As the bond is paying coupon semi annually , its Ytm can be calculated by Excel or financial calculator
	No. of period = years to maturity x no. of coupon in a year = 30 x 2 =nper = N = 60
	Face value of bond = FV= $100 x 600,000 = $60000000
	Price of the bond = PV = -$58092000       [amount raised ]
	Semi-annual Coupon amount = PMT = coupon rate x face value/2 = 12.8% x $60,000,000 /2= $3840000
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(60,3840000,-58092000,60000000)
	6.614961204%
	=6.614961204%
	The YTM calculated is semi annual
	YTM annual = Semi annual YTM x 2
	YTM annual = 6.614961204% x 2
	YTM annual bond =13.2299224%
	cost of debt to DMI = YTM annual =13.23%
b.	​$51,012,000
	As the bond is paying coupon semi annually , its Ytm can be calculated by Excel or financial calculator
	No. of period = years to maturity x no. of coupon in a year = 30 x 2 =nper = N = 60
	Face value of bond = FV= $100 x 600,000 = $60000000
	Price of the bond = PV = -$51012000       [amount raised ]
	Semi-annual Coupon amount = PMT = coupon rate x face value/2 = 12.8% x $60,000,000 /2= $3840000
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(60,3840000,-51012000,60000000)
	7.544773813%
	=7.544773813%
	The YTM calculated is semi annual
	YTM annual = Semi annual YTM x 2
	YTM annual = 7.544773813% x 2
	YTM annual bond = 15.08954763%
	cost of debt to DMI = YTM annual =15.09%
c.	$63,114,000
	As the bond is paying coupon semi annually , its Ytm can be calculated by Excel or financial calculator
	No. of period = years to maturity x no. of coupon in a year = 30 x 2 =nper = N = 60
	Face value of bond = FV= $100 x 600,000 = $60000000
	Price of the bond = PV = -$63114000       [amount raised ]
	Semi-annual Coupon amount = PMT = coupon rate x face value/2 = 12.8% x $60,000,000 /2= $3840000
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(60,3840000,-63114000 ,60000000)
	6.075260142%
	=6.075260142%
	The YTM calculated is semi annual
	YTM annual = Semi annual YTM x 2
	YTM annual = 6.075260142% x 2
	YTM annual bond = 12.15052028%
	cost of debt to DMI = YTM annual =12.15%
d.	​$74,796,000
	As the bond is paying coupon semi annually , its Ytm can be calculated by Excel or financial calculator
	No. of period = years to maturity x no. of coupon in a year = 30 x 2 =nper = N = 60
	Face value of bond = FV= $100 x 600,000 = $60000000
	Price of the bond = PV = -$74796000       [amount raised ]
	Semi-annual Coupon amount = PMT = coupon rate x face value/2 = 12.8% x $60,000,000 /2= $3840000
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(60,3840000,-74796000 ,60000000)
	5.079794012%
	=5.079794012%
	The YTM calculated is semi annual
	YTM annual = Semi annual YTM x 2
	YTM annual = 5.079794012% x 2
	YTM annual bond = 10.159588%
	cost of debt to DMI = YTM annual =10.16%
Please feel free to ask if anything about above solution in comment section of the question.