Rearden Metal has just issued a callable,$1000 par value,twenty-year,8% coupon bond with semiannual coupon payments.The bond can be called at par in five years or anytime thereafter on a coupon payment date.If the bond is currently trading for $1040.79,then its yield to maturity is closest to:

Question

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To calculate the yield to maturity of the bond, we need to find the interest rate that will make the present value of the bond's future cash flows equal to its current price of $1040.79. We can use a financial calculator or spreadsheet program to solve the equation, or we can use trial and error.

Using trial and error, we can input different interest rates into the bond pricing formula until we find the rate that gives us a present value of $1040.79. We know that the bond has a coupon rate of 8%, semiannual coupon payments, and a par value of $1000.

Here's one way to do the calculation using trial and error:

1. Calculate the semiannual coupon payment: $1000 x 8% / 2 = $40
2. Determine the number of semiannual periods: 20 x 2 = 40
3. Calculate the present value of the semiannual coupon payments using the bond pricing formula:

P = (C / r) x (1 - (1 + r)^(-n)) + (F / (1 + r)^n)

Where:
P = current price of the bond = $1040.79
C = semiannual coupon payment = $40
r = semiannual interest rate (what we're trying to find)
n = number of semiannual periods = 40
F = par value of the bond = $1000

Plugging in the values and using trial and error, we find that an interest rate of approximately 3.8% gives us a present value of the semiannual coupon payments equal to $1040.79.

4. Calculate the present value of the bond's face value using the bond pricing formula:

P = F / (1 + r)^n

Plugging in the remaining values, we get:

1040.79 = 1000 / (1 + r)^40

Solving for r using a financial calculator or spreadsheet program, we find that the yield to maturity of the bond is approximately 7.6%. Therefore, the best choice is C.

Rearden Metal Has Just Issued a Callable,$1000 Par Value,twenty-Year,8% Coupon