The yield-to-maturity on a bond is the interest rate you earn on your investment if interest rates do not change. If you actually sell the bond before it matures, your realized return is known as the holding period yield. Suppose that today, you buy a 12 percent annual coupon bond for $1,000. The bond has 13 years to maturity. Two years from now, the yield-to-maturity has declined to 11 percent and you decide to sell. What is your holding period yield?

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To calculate the holding period yield, you need to know the price at which you sell the bond and the coupon payments you receive during the holding period.

First, let's calculate the coupon payments over the holding period. The bond has a 12% annual coupon rate, so you will receive 12% of the face value ($1,000) each year. Therefore, the coupon payments over the two-year holding period would be:

Coupon payment = Coupon rate * Face value = 0.12 * $1,000 = $120 per year

Since the holding period is two years, the total coupon payments received would be:

Total coupon payments = Coupon payment * Holding period = $120 * 2 = $240

Next, let's calculate the price at which you sell the bond. The yield-to-maturity has declined to 11%, which means the market interest rate for similar bonds has decreased. Since market interest rates have declined, the bond becomes more attractive to investors, and its price typically increases.

To determine the selling price, we can calculate the present value of the future cash flow from the bond. The coupon payments received over the remaining 11 years (13 years to maturity minus the 2-year holding period) can be treated as an annuity because they occur at regular intervals. The future value of the bond at maturity is the face value of $1,000.

Using a financial calculator or spreadsheet software, you can calculate the present value of the bond as:

Present value = (Coupon payment / Yield-to-maturity) * (1 - (1 / (1 + Yield-to-maturity)^remaining time)) + (Face value / (1 + Yield-to-maturity)^remaining time)

Plugging in the numbers:

Present value = ($120 / 0.11) * (1 - (1 / (1 + 0.11)^11)) + ($1,000 / (1 + 0.11)^11)

Solving this equation will give you the present value of the bond, which represents the selling price.

Once you have the selling price, you can calculate the holding period yield using the following formula:

Holding period yield = (Selling price + Total coupon payments - Purchase price) / Purchase price

Plugging in the numbers:

Holding period yield = (Selling price + $240 - $1,000) / $1,000

By substituting the calculated selling price and solving the equation, you'll be able to determine the holding period yield.