Aramex, Inc is currently offering a bond with a par value of $1,000, which is priced at $1,488 in the market. The bond offers a fixed annual coupon rate of 14.05 percent, which is paid semiannually. It has a remaining time to maturity of 24 years. What is the current yield to maturity on the bond if it is acquired and retained until it reaches its maturity date?
Please express the solution to two decimal places in percentage format.
It is recommended to utilize Microsoft Excel or a financial calculator for this purpose.
To calculate the current yield to maturity (YTM) on the Aramex, Inc. bond, we can use the following formula:
\[YTM = \frac{C + \frac{(F – P)}{N}}{\frac{(F + P)}{2}} \times \frac{1}{\frac{1}{2}}\]
Where:
– \(YTM\) = Yield to Maturity
– \(C\) = Annual coupon payment
– \(F\) = Par value of the bond
– \(P\) = Current market price of the bond
– \(N\) = Number of years to maturity
Let’s plug in the values from the problem:
– \(C\) = 14.05% of $1,000, paid semiannually = \($1,000 \times 0.1405 \times \frac{1}{2}\) = $70.25
– \(F\) = $1,000 (par value)
– \(P\) = $1,488 (current market price)
– \(N\) = 24 years
Now, let’s calculate:
\[YTM = \frac{70.25 + \frac{(1,000 – 1,488)}{24}}{\frac{(1,000 + 1,488)}{2}} \times \frac{1}{\frac{1}{2}}\]
First, calculate the numerator:
\[YTM = \frac{70.25 + (-488/24)}{\frac{(1,000 + 1,488)}{2}} \times 2\]
Now, perform the calculations inside the parentheses:
\[YTM = \frac{70.25 – 20.33}{\frac{2,488}{2}} \times 2\]
Next, calculate the denominator:
\[YTM = \frac{49.92}{\frac{2,488}{2}} \times 2\]
Now, divide the numerator by the denominator:
\[YTM = \frac{49.92}{1,244} \times 2\]
\[YTM \approx 0.04015 \times 100 \times 2\]
Now, calculate the YTM as a percentage to two decimal places:
\[YTM \approx 8.03\%\]
So, the current yield to maturity on the Aramex, Inc. bond, if acquired and retained until maturity, is approximately 8.03%.
Please note that bond prices and yields can fluctuate in the market, so this YTM represents the current yield based on the provided information.
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