Question

Dunder-Mifflin, Inc.​ (DMI) is selling​ 600,000 bonds to raise money for the publication of new magazines in the coming year. The bonds will pay a coupon rate of 11.5​% with semiannual payments and will mature in 30 years. Its par value is ​$100. DMI hires an investment banker for the sale of the​ 600,000 bonds. The investment banker charges a fee of 3​% on each bond sold. What is the cost of debt to DMI if the following are the proceeds before the​ banker's fees are​ deducted?

a.​$43,830,000 b.​$52,188,000 c.​$67,596,000 d. $77,196,000

a. What is the cost of debt to DMI if the bond proceeds are ​$43,830,000 before the​ banker's fees are​ deducted?

What is the cost of debt to DMI if the bond proceeds are ​$52,188,0000 before the​ banker's fees are​ deducted?

What is the cost of debt to DMI if the bond proceeds are $67,596,000 before the​ banker's fees are​ deducted?

What is the cost of debt to DMI if the bond proceeds are $77,196,000 before the​ banker's fees are​ deducted?

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 = 11.50%
Semiannual Coupon Rate = 5.75%
Semiannual Coupon = 5.75% * $60,000,000
Semiannual Coupon = $3,450,000

Time to Maturity = 30 years
Semiannual Period = 60

Answer a.

Issue Value of Bonds = $43,830,000 * (1 - 0.03)
Issue Value of Bonds = $42,515,100

Let Semiannual YTM be i%

$42,515,100 = $3,450,000 * PVIFA(i%, 60) + $60,000,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -42515100
PMT = 3450000
FV = 60000000

I = 8.146%

Semiannual YTM = 8.146%

Cost of Debt = 2 * Semiannual YTM
Cost of Debt = 2 * 8.146%
Cost of Debt = 16.29%

Answer b.

Issue Value of Bonds = $52,188,000 * (1 - 0.03)
Issue Value of Bonds = $50,622,360

Let Semiannual YTM be i%

$50,622,360 = $3,450,000 * PVIFA(i%, 60) + $60,000,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -50622360
PMT = 3450000
FV = 60000000

I = 6.840%

Semiannual YTM = 6.840%

Cost of Debt = 2 * Semiannual YTM
Cost of Debt = 2 * 6.840%
Cost of Debt = 13.68%

Answer c.

Issue Value of Bonds = $67,596,000 * (1 - 0.03)
Issue Value of Bonds = $65,568,120

Let Semiannual YTM be i%

$65,568,120 = $3,450,000 * PVIFA(i%, 60) + $60,000,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -65568120
PMT = 3450000
FV = 60000000

I = 5.240%

Semiannual YTM = 5.240%

Cost of Debt = 2 * Semiannual YTM
Cost of Debt = 2 * 5.240%
Cost of Debt = 10.48%

Answer d.

Issue Value of Bonds = $77,196,000 * (1 - 0.03)
Issue Value of Bonds = $74,880,120

Let Semiannual YTM be i%

$74,880,120 = $3,450,000 * PVIFA(i%, 60) + $60,000,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -74880120
PMT = 3450000
FV = 60000000

I = 4.540%

Semiannual YTM = 4.540%

Cost of Debt = 2 * Semiannual YTM
Cost of Debt = 2 * 4.540%
Cost of Debt = 9.08%