1.You buy a SML Bond for $980. The bond has a face value of $1000 and an annual coupon rate of 8%. There are 5 years left until maturity.

Because of a special delivery by the stork, you decide to sell the bond at the end of year 2 for $1050. What was your return? Why does this differ from the yield to maturity? Assume you do get the first two coupon payments.

Well, well, well, looks like you're in the bond business! Let's calculate your return and explain why it differs from the yield to maturity.

To calculate your return, we'll consider the purchase price, the selling price, and any coupon payments you received.

You bought the SML Bond for $980 and sold it for $1050 after 2 years. That means you made a gain of $70 on the bond. Plus, we should also consider the two coupon payments you received during those 2 years - since it's a generous stork that always delivers. Let's assume each coupon payment was $80 (8% of the face value of $1000), so in total, you received $160 in coupon payments.

Now, let's calculate the return:

Return = (Gain + Coupon Payments) / Initial Investment
Return = ($70 + $160) / $980
Return ≈ 0.24 or 24%

So, your return on this bond investment is approximately 24%. Not too shabby, huh?

Now, let's talk about why this differs from the yield to maturity. Yield to maturity takes into account not only the selling price and coupon payments but also the time value of money and the reinvestment of those coupon payments at the yield rate. In our case, since we sold the bond before maturity, the yield to maturity calculation wouldn't reflect the same timeline or reinvestment of the coupon payments.

In simpler terms, your return is based on the actual cash flows you received (the gain and coupon payments) without considering the time value of money or reinvestment. The yield to maturity, on the other hand, considers those factors and is more of an overall measure of the bond's return if held until maturity.

Hope that helps! Now, go out there and make some bonds laugh!

To calculate your return, we need to consider the purchase price, the selling price, and any coupon payments received.

Step 1: Calculate coupon payments received
Since the annual coupon rate is 8%, each year you would receive 8% of the face value, which is $1000. Therefore, the coupon payment per year would be 0.08 * $1000 = $80.
For two years, you would receive a total of $80 * 2 = $160 in coupon payments.

Step 2: Calculate the total cash inflow
The total cash inflow would include the selling price and the coupon payments received.
So, the total cash inflow would be $1050 + $160 = $1210.

Step 3: Calculate the purchase price
The purchase price of the bond was $980.

Step 4: Calculate the return
To calculate the return, we can use the following formula:
Return = (Total cash inflow - Purchase price) / Purchase price * 100

Return = ($1210 - $980) / $980 * 100
Return = $230 / $980 * 100
Return ≈ 23.47%

Therefore, your return on the bond was approximately 23.47%.

Now, let's discuss why this differs from the yield to maturity (YTM).

The yield to maturity (YTM) represents the annualized return you would earn if you held the bond until maturity and received all the coupon payments as scheduled. It factors in both the purchase price and coupon payments.

In this case, you sold the bond before maturity and received a higher selling price than the purchase price. This means that your return was higher than the YTM. The YTM assumes that the bond will be held until maturity and that the coupon payments will be received as scheduled. Selling the bond earlier can result in a different return, depending on the selling price and coupon payments received.

To calculate your return on the bond investment, you need to consider the purchase price, the selling price, and any coupon payments received during the holding period.

1. Calculate the coupon payments received during the holding period:
- The bond has an annual coupon rate of 8%, which means you will receive 8% * $1,000 = $80 each year.
- Since you're holding the bond for 2 years, you will receive a total of 2 * $80 = $160 in coupon payments.

2. Calculate the total cash flow:
- At the end of year 2, when you sell the bond, you will receive $1,050.
- Add the coupon payments received ($160) to the selling price:
$1,050 + $160 = $1,210

3. Calculate the return on investment:
- Subtract the purchase price ($980) from the total cash flow ($1,210):
$1,210 - $980 = $230
- Divide the result by the purchase price and express it as a percentage:
($230 / $980) * 100% ≈ 23.47%

Therefore, your return on the bond investment is approximately 23.47%.

The return on investment differs from the yield to maturity because the yield to maturity considers the total return over the bond's entire holding period until maturity. In this case, you sold the bond before its maturity, so you didn't receive all the interest payments until the end of its term. The yield to maturity assumes you hold the bond until maturity and receive all the coupon payments, so it provides a comprehensive measure of the total return.