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Cost of debt. ​Dunder-Mifflin, Inc.​ (DMI) is selling​ 600,000 bonds to raise money for the publication...

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.)

Solutions

Expert Solution

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.

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