Rainier Bros. has 12.0% semiannual coupon bonds outstanding that mature in 10 years. Each
bond is now eligible to be called at a call price of $1,060. If the bonds are called, the company
must replace them with new 10-year bonds.The flotation cost of issuing new bonds is estimated
to be $45 per bond. How low would the yield to maturity on the new bonds have to be in order for
it to be profitable to call the bonds today, i.e., what is the nominal annual "breakeven rate"?
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To determine the breakeven yield to maturity on the new bonds, we need to compare the cost of calling the existing bonds to the cost of issuing new bonds.
First, let's calculate the cost of calling the existing bonds:
Call price = $1,060
Number of bonds outstanding = ?
Semiannual coupon rate = 12.0%
Maturity = 10 years
Since the bonds are semiannual, we need to calculate the number of periods that have elapsed. Each year has two periods, so the total number of periods elapsed is:
Total periods elapsed = Number of years elapsed * Number of periods per year
Total periods elapsed = 10 * 2
Total periods elapsed = 20
Now, let's calculate the total cost of calling the existing bonds:
Total cost of calling = Number of bonds outstanding * Call price
Next, let's calculate the cost of issuing new bonds:
Flotation cost per bond = $45
Now, we can calculate the number of new bonds required to replace the existing bonds:
Number of new bonds = Number of bonds outstanding
Finally, let's calculate the breakeven yield to maturity on the new bonds:
Breakeven yield to maturity = Total cost of calling / Number of new bonds * 100
Note: The "breakeven yield to maturity" refers to the nominal annual rate at which the new bonds would have to yield in order to offset the costs of calling the existing bonds and issuing new ones.
Plug in the values and calculate to get the answer.
To find the nominal annual "breakeven rate," we need to determine the yield to maturity (YTM) on the new bonds.
First, let's calculate the price of the existing bonds if they were not called. To do this, we need to find the present value of the future cash flows from the bonds.
The semiannual coupon payment can be calculated as follows: Coupon Payment = Coupon Rate * Face Value / 2
Given: Coupon Rate = 12.0%, Face Value = $1000
Coupon Payment = 0.12 * $1000 / 2 = $60
Since the bonds have a tenure of 10 years, there will be 20 coupon payments (2 per year for 10 years).
Now, let's calculate the present value of the coupon payments using the yield to maturity (YTM) on the existing bonds.
To do this, we can use the present value of an ordinary annuity formula:
PV = C * (1 - (1+r)^(-n)) / r
Where:
PV = Present Value of the coupon payments
C = Coupon Payment
r = Yield to Maturity (YTM) per period
n = Number of periods
Given:
C = $60 (from the previous calculation)
r = YTM per period
n = 20
Now, let's calculate the present value of the face value payment. Since the bonds are called at a price of $1,060, the present value of the face value payment will be $1,060.
Now, let's calculate the present value of the future cash flows from the existing bonds:
PV of Coupon Payments = $60 * (1 - (1+r)^(-20)) / r
PV of Face Value Payment = $1,060
Total Present Value of Cash Flows = PV of Coupon Payments + PV of Face Value Payment
Next, let's calculate the cost of calling the bonds and issuing new ones.
Given: Flotation Cost = $45
Total Cost of Calling Bonds and Issuing New Bonds = Number of Bonds * Flotation Cost
Finally, let's set up the equation to calculate the breakeven yield to maturity (YTM) on the new bonds:
Total Present Value of Cash Flows = Total Cost of Calling Bonds and Issuing New Bonds
Now, you can solve this equation to find the nominal annual "breakeven rate" (YTM) on the new bonds.