Seven years ago a semi-annual coupon bond with a 10% coupon rate, $1,000 face value and 15 years to maturity was issued by Corn Inc.. Teddy bought this bond two years ago when the market interest rate was 12%. And now the market interest rate is 5%. If teddy sells the bond now, what is Teddy’s capital gain/loss yield on the bond investment?

To calculate Teddy's capital gain/loss yield on the bond investment, we need to determine the bond's current price and then compare it to the price he paid for it. The price of a bond is influenced by changes in the market interest rate.

Step 1: Calculate the bond's current price:
To calculate the bond's current price, we need to find the present value of the bond's future cash flows, which consist of semi-annual coupon payments and the face value.

Coupon Payment: The bond has a semi-annual coupon rate of 10% and a face value of $1,000. Therefore, the annual coupon payment is (10% * $1,000) = $100.
Since the bond has a semi-annual payment frequency, the coupon payment per period is $100 / 2 = $50.

Number of Periods: As mentioned, Teddy bought the bond 2 years ago, and it has a total maturity of 15 years. Therefore, the remaining number of periods is (15 - 2) * 2 = 26 semi-annual periods.

Market Interest Rate: The market interest rate when Teddy bought the bond was 12%, and it is now 5%.

Present Value Calculation: To calculate the present value of the bond's future cash flows, we need to discount each cash flow back to the present using the market interest rate. The formula for calculating the present value of a bond is:
PV = (C/r) * (1 - (1 + r)^(-n)) + (F/(1 + r)^n)

Where:
PV = Present value of the bond
C = Coupon payment per period
r = Market interest rate per period
n = Number of periods

Using the formula above, we can calculate the current price of the bond.

PV = (50/0.05) * (1 - (1 + 0.05)^(-26)) + (1,000/(1 + 0.05)^26)
PV = 969.80

Therefore, the current price of the bond is $969.80.

Step 2: Calculate the capital gain/loss yield:
To calculate the capital gain/loss yield, we compare the current price of the bond to the price Teddy paid for it.

Teddy purchased the bond two years ago, so he paid the initial price. Let's assume he bought it at the face value of $1,000.

Capital Gain/Loss Yield = ((Current Price - Initial Price) / Initial Price) * 100

Capital Gain/Loss Yield = (($969.80 - $1,000) / $1,000) * 100
Capital Gain/Loss Yield = (-$30.20 / $1,000) * 100
Capital Gain/Loss Yield = -3.02%

Therefore, Teddy's capital gain/loss yield on the bond investment is -3.02%. This means he has incurred a loss of 3.02% on his investment.

To calculate Teddy's capital gain/loss yield on the bond investment, we need to follow these steps:

Step 1: Calculate the present value of the bond when Teddy bought it.

The bond has a 10% coupon rate with semi-annual payments. The face value is $1,000, and the remaining period to maturity is 13 years (out of the original 15-year term).

To calculate the present value of the bond, we need to discount the future cash flows using the market interest rate at that time, which was 12%.

PV = (C / (1 + r)^n) + (F / (1 + r)^n)
where:
PV = present value of the bond
C = coupon payment
r = market interest rate
n = number of periods

Since it is a semi-annual payment, the bond will pay two coupons per year (10% of $1,000/2 = $50 per coupon payment).

PV = ($50 / (1 + 0.12/2)^(13*2)) + ($1,000 / (1 + 0.12/2)^(13*2))
= ($50 / (1.06)^26) + ($1,000 / (1.06)^26)
≈ $486.38 + $295.25
≈ $781.63

Therefore, Teddy's initial investment in the bond was approximately $781.63.

Step 2: Calculate the present value of the bond if Teddy sells it now.

The bond still has a semi-annual coupon rate of 10%, a face value of $1,000, and now there are 11 years (out of the remaining 13 years) until maturity. The market interest rate is currently 5%.

Using the same calculation formula as before:

PV = ($50 / (1 + 0.05/2)^(11*2)) + ($1,000 / (1 + 0.05/2)^(11*2))
= ($50 / (1.025)^22) + ($1,000 / (1.025)^22)
≈ $458.42 + $731.89
≈ $1,190.31

Therefore, the present value of the bond if Teddy sells it now is approximately $1,190.31.

Step 3: Calculate Teddy's capital gain/loss yield.

To calculate the capital gain/loss yield, we need to find the difference between the present values when Teddy bought and when he sells the bond, and divide it by the initial investment:

Capital Gain/Loss Yield = ((Present Value when sold) - (Present Value when bought)) / (Initial Investment)

Capital Gain/Loss Yield = (($1,190.31 - $781.63) / $781.63) * 100%

Calculating the above expression:

Capital Gain/Loss Yield = ($408.68 / $781.63) * 100%
= 0.522 * 100%
≈ 52.2%

Therefore, Teddy's capital gain/loss yield on the bond investment is approximately 52.2%.