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 9.9​%

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. What is the cost of debt to DMI if the bonds raise $57,414,000​?

​ (Round to two decimal​ places.)

b.What is the cost of debt to DMI if the bonds raise $51,546,000​?

​ (Round to two decimal​ places.)

c.What is the cost of debt to DMI if the bonds raise $67,350,000​?

​ (Round to two decimal​ places.)

d.What is the cost of debt to DMI if the bonds raise ​$80,934,000​?

​ (Round to two decimal​ places.)

Answer 1

Par Value of Bonds = Number of Bonds Issued * Par Value
Par Value of Bonds = 600,000 * $100
Par Value of Bonds = $60,000,000

Annual Coupon Rate = 9.90%
Semiannual Coupon Rate = 4.95%
Semiannual Coupon = 4.95% * $60,000,000
Semiannual Coupon = $2,970,000

Time to Maturity = 30 years
Semiannual Period = 60

Answer a.

Issue Value of Bonds = $57,414,000

Let Semiannual YTM be i%

$57,414,000 = $2,970,000 * PVIFA(i%, 60) + $60,000,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -57414000
PMT = 2970000
FV = 60000000

I = 5.185%

Semiannual YTM = 5.185%

Cost of Debt = 2 * Semiannual YTM
Cost of Debt = 2 * 5.185%
Cost of Debt = 10.37%

Answer b.

Issue Value of Bonds = $51,546,000

Let Semiannual YTM be i%

$51,546,000 = $2,970,000 * PVIFA(i%, 60) + $60,000,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -51546000
PMT = 2970000
FV = 60000000

I = 5.795%

Semiannual YTM = 5.795%

Cost of Debt = 2 * Semiannual YTM
Cost of Debt = 2 * 5.795%
Cost of Debt = 11.59%

Answer c.

Issue Value of Bonds = $67,350,000

Let Semiannual YTM be i%

$67,350,000 = $2,970,000 * PVIFA(i%, 60) + $60,000,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -67350000
PMT = 2970000
FV = 60000000

I = 4.370%

Semiannual YTM = 4.370%

Cost of Debt = 2 * Semiannual YTM
Cost of Debt = 2 * 4.370%
Cost of Debt = 8.74%

Answer d.

Issue Value of Bonds = $80,934,000

Let Semiannual YTM be i%

$80,934,000 = $2,970,000 * PVIFA(i%, 60) + $60,000,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -80934000
PMT = 2970000
FV = 60000000

I = 3.540%

Semiannual YTM = 3.540%

Cost of Debt = 2 * Semiannual YTM
Cost of Debt = 2 * 3.540%
Cost of Debt = 7.08%