Question

Occam Industrial Machines issued 145,000 zero coupon bonds 7 years ago. The bonds originally had 30 years to maturity with a yield to maturity of 6.2 percent. Interest rates have recently decreased, and the bonds now have a yield to maturity of 5.3 percent. The bonds have a par value of $2,000 and semiannual compounding. If the company has a $81 million market value of equity, what weight should it use for debt when calculating the cost of capital? Note: Do not round intermediate calculations and round your answer to 4 decimal places, e.9., 1616.

Answer 1

To calculate the weight of debt, we first need to find the present value of the bonds.

The present value of the bonds can be calculated using the formula:

PV = (C / (1 + r)^n) + (F / (1 + r)^n)

Where:
PV = Present Value
C = Coupon payment
r = Yield to maturity / 2 (semiannual compounding)
n = Number of years remaining until maturity / 2 (semiannual compounding)
F = Face value of the bond

First, let's calculate the coupon payment:
Coupon payment = (Par value x Yield to maturity) / 2
Coupon payment = ($2,000 x 6.2%) / 2 = $62

Next, let's calculate the present value of the bonds:
PV = ($62 / (1 + 0.053/2)^(30*2)) + ($2,000 / (1 + 0.053/2)^(30*2))
PV = $981.5474 + $298.4026
PV = $1,279.95

Now, let's calculate the weight of debt:
Weight of debt = (Present value of bonds) / (Present value of bonds + Market value of equity)
Weight of debt = $1,279.95 / ($1,279.95 + $81,000,000)
Weight of debt = $1,279.95 / $81,001,279.95
Weight of debt = 0.000015801

Therefore, the weight of debt should be equal to 0.000015801 when calculating the cost of capital.