Question

​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 11.3​% 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 .​$58,452,000 b.​ $52, 296,000 c. ​$64,770,000 d. ​$77,094,000

What is the cost of debt to DMI if the bonds raise ​$58,452,000​?

What is the cost of debt to DMI if the bonds raise $52, 296,000?

What is the cost of debt to DMI if the bonds raise $64,770,000 ?

What is the cost of debt to DMI if the bonds raise ​$77,094,000 ?

Answer 1

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

Annual Coupon Rate = 11.30%
Semiannual Coupon Rate = 5.65%
Semiannual Coupon = 5.65% * $60,000,000
Semiannual Coupon = $3,390,000

Time to Maturity = 30 years
Semiannual Period = 60

Answer a.

Issue Value of Bonds = $58,452,000

Let Semiannual YTM be i%

$58,452,000 = $3,390,000 * PVIFA(i%, 60) + $60,000,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -58452000
PMT = 3390000
FV = 60000000

I = 5.805%

Semiannual YTM = 5.805%

Cost of Debt = 2 * Semiannual YTM
Cost of Debt = 2 * 5.805%
Cost of Debt = 11.61%

Answer b.

Issue Value of Bonds = $52,296,000

Let Semiannual YTM be i%

$52,296,000 = $3,390,000 * PVIFA(i%, 60) + $60,000,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -52296000
PMT = 3390000
FV = 60000000

I = 6.505%

Semiannual YTM = 6.505%

Cost of Debt = 2 * Semiannual YTM
Cost of Debt = 2 * 6.505%
Cost of Debt = 13.01%

Answer c.

Issue Value of Bonds = $64,770,000

Let Semiannual YTM be i%

$64,770,000 = $3,390,000 * PVIFA(i%, 60) + $60,000,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -64770000
PMT = 3390000
FV = 60000000

I = 5.215%

Semiannual YTM = 5.215%

Cost of Debt = 2 * Semiannual YTM
Cost of Debt = 2 * 5.215%
Cost of Debt = 10.43%

Answer d.

Issue Value of Bonds = $77,094,000

Let Semiannual YTM be i%

$77,094,000 = $3,390,000 * PVIFA(i%, 60) + $60,000,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -77094000
PMT = 3390000
FV = 60000000

I = 4.315%

Semiannual YTM = 4.315%

Cost of Debt = 2 * Semiannual YTM
Cost of Debt = 2 * 4.315%
Cost of Debt = 8.63%