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.
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.
To calculate the weight of debt, we need to determine the current market value of the zero coupon bonds issued by Occam Industrial Machines.
First, let's calculate the current price of each bond using the yield to maturity.
Since these zero coupon bonds do not pay periodic interest, their value is derived solely from the discounted present value of their face value at maturity.
The formula to calculate the price of a zero coupon bond is:
Price = Face Value / ((1 + Yield / 2) ^ (2 * Remaining Periods))
Where:
Face Value = $2,000 (par value)
Yield = Yield to Maturity / 2 (semiannual yield)
Remaining Periods = Number of remaining periods until maturity = (Number of years to maturity - Number of years elapsed) * 2
Number of years elapsed = 7
Number of years to maturity = 30
Remaining Periods = (30 - 7) * 2 = 46
Yield = 5.3% / 2 = 0.053 / 2 = 0.0265
Now, let's calculate the price of each bond:
Price = $2,000 / ((1 + 0.0265) ^ (2 * 46))
Using a calculator, we find that the price of each bond is approximately $515.6931.
To determine the market value of the zero coupon bonds, we multiply the price of each bond by the number of bonds issued:
Market Value of Zero Coupon Bonds = Price of each bond * Number of bonds
Market Value of Zero Coupon Bonds = $515.6931 * 145,000
Using a calculator, we find that the market value of the zero coupon bonds is approximately $74,881,948.50.
Finally, to calculate the weight of debt, we divide the market value of the zero coupon bonds by the sum of the market value of debt and equity:
Weight of Debt = Market Value of Zero Coupon Bonds / (Market Value of Zero Coupon Bonds + Market Value of Equity)
Market Value of Equity = $81 million
Weight of Debt = $74,881,948.50 / ($74,881,948.50 + $81,000,000)
Weight of Debt = $74,881,948.50 / $155,881,948.50
Using a calculator, we find that the weight of debt is approximately 0.4804, or 0.4804 * 100 = 48.04% (rounded to 4 decimal places).
Therefore, the weight of debt Occam Industrial Machines should use when calculating the cost of capital is 48.04%.