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 12.2?% 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.??$57,606,000

b.??$54,138,000

c.??$60,918,000

d.???$73,380,000

Answer 1

Face Value = 600,000 * $100
Face Value = $60,000,000

Annual Coupon Rate = 12.2%
Semiannual Coupon Rate = 6.1%
Semiannual Coupon = 6.1% * $60,000,000
Semiannual Coupon = $3,660,000

Time to Maturity = 30 years
Semiannual Period to Maturity = 60

Answer a.

Proceed from Issue = $57,606,000

Let semiannual YTM be i%

$57,606,000 = $3,660,000 * PVIFA(i%, 60) + $60,000,000 * PVIF(i%, 60)

Using financial calculator, i = 6.36%

Semiannual YTM = 6.36%
Annual YTM = 2 * 6.36% = 12.72%

So, Cost of Debt is 12.72%

Answer b.

Proceed from Issue = $54,138,000

Let semiannual YTM be i%

$54,138,000 = $3,660,000 * PVIFA(i%, 60) + $60,000,000 * PVIF(i%, 60)

Using financial calculator, i = 6.775%

Semiannual YTM = 6.775%
Annual YTM = 2 * 6.775% = 13.55%

So, Cost of Debt is 13.55%

Answer c.

Proceed from Issue = $60,918,000

Let semiannual YTM be i%

$60,918,000 = $3,660,000 * PVIFA(i%, 60) + $60,000,000 * PVIF(i%, 60)

Using financial calculator, i = 6.005%

Semiannual YTM = 6.005%
Annual YTM = 2 * 6.005% = 12.01%

So, Cost of Debt is 12.01%

Answer d.

Proceed from Issue = $73,380,000

Let semiannual YTM be i%

$73,380,000 = $3,660,000 * PVIFA(i%, 60) + $60,000,000 * PVIF(i%, 60)

Using financial calculator, i = 4.935%

Semiannual YTM = 4.935%
Annual YTM = 2 * 4.935% = 9.87%

So, Cost of Debt is 9.87%