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A -year bond has coupons paid quarterly at a rate of . The bond can be redeemed early in years at a price of . If the bond is valued at , what is the highest and lowest return an investor can get and under what conditions?
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Q. A -year bond has coupons paid quarterly at a rate of . The bond can be redeemed early in years at a price of . If the bond is valued at , what is the highest and lowest return an investor can get and under what conditions?
- Calculate Total Coupon Payments: Calculate the total coupon payments received if held for years.Quarterly interest rate is per year, so each quarter it's .Each quarter, the payment is .There are quarters in a year, so for years, there are quarters.Total coupon payments = .
- Calculate Total Return: Calculate the total return if the bond is held to maturity (7 ext{ years}\(\newline)).Total return = Total coupon payments + Redemption value - Purchase price.Redemption value at maturity is the face value, which is \$\$1,000\).\(\newline\)Total return = \(\$630\) + \(\$1,000\) - \(\$900\) = \(\$730\).
- Calculate Annualized Return: Calculate the annualized return if held for \(7\) years.\(\newline\)Annualized return = \((\text{Total return} / \text{Purchase price}) / \text{Number of years}\).\(\newline\)Annualized return = \((\$(730) / \$(900)) / 7\).\(\newline\)Annualized return = \(0.0811\) or \(8.11\)\%.
- Calculate Total Return Early Redemption: Calculate the total return if the bond is redeemed early after \(3\) years.\(\newline\)Total coupon payments for \(3\) years = \(3\) years \(\times\) \(4\) quarters/year \(\times\) \(\$22.50\) = \(\$270\).\(\newline\)Total return = Total coupon payments for \(3\) years + Early redemption value - Purchase price.\(\newline\)Early redemption value is \(\$1,070\).\(\newline\)Total return = \(\$270\) + \(\$1,070\) - \(\$900\) = \(\times\)\(0\).
- Calculate Annualized Return Early Redemption: Calculate the annualized return if redeemed early after \(3\) years.\(\newline\)Annualized return = \((\text{Total return} / \text{Purchase price}) / \text{Number of years}\).\(\newline\)Annualized return = \((\$(440) / \$(900)) / 3\).\(\newline\)Annualized return = \(0.1622\) or \(16.22\%\).
- Determine Highest and Lowest Return: Determine the highest and lowest return. The highest return is if the bond is redeemed early at \(16.22\%\). The lowest return is if the bond is held to maturity at \(8.11\%\).
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