A company XYZ Ltd. has issued a bond having a face value of ₹ 10,000 paying annual dividend at 8.5% p.a. The bond will be redeemed at par at the end of 10 years. Find the purchase value of this bond, if the investor wishes a yield rate of 8%. [Given : $(1 \cdot 08)^{-10} = 0 \cdot 46319349$ ]

Answer: ₹ 10,335.06

Step-by-step solution

Step 1: Calculate Annual Dividend Payment

First, we need to determine the annual dividend payment the bondholder will receive. This is calculated by multiplying the bond's face value by its annual dividend rate.

Step 2: Calculate Present Value of Dividends

Next, we calculate the present value of all future dividend payments. Since the dividends are paid annually for 10 years, we use the formula for the present value of an ordinary annuity, where $r$ is the yield rate and $n$ is the number of years.

Step 3: Calculate Present Value of Redemption Amount

Then, we calculate the present value of the bond's face value, which will be received at the end of 10 years. This is a single lump sum payment discounted back to the present using the investor's desired yield rate.

Step 4: Calculate Purchase Value of the Bond

Finally, the purchase value of the bond is the sum of the present value of all future dividend payments and the present value of the redemption amount.

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