Knowee
Questions
Features
Study Tools

A 6% coupon-paying bond has a face value of $100, yield to maturity of 5% p.a. and 2 years to maturity. Coupons are paid semi-annually. If you buy the bond today at $104, you buy the bond: A. At no gain/loss B. At a loss C. At a gain D. Do not know

Question

A 6% coupon-paying bond has a face value of 100,yieldtomaturityof5100, yield to maturity of 5% p.a. and 2 years to maturity. Coupons are paid semi-annually. If you buy the bond today at 104, you buy the bond: A. At no gain/loss B. At a loss C. At a gain D. Do not know

🧐 Not the exact question you are looking for?Go ask a question

Solution

To answer this question, we need to calculate the bond's price using its yield to maturity (YTM), coupon rate, and time to maturity.

Here are the steps:

  1. First, we need to adjust the given values to a semi-annual basis because the coupons are paid semi-annually. The coupon rate becomes 6%/2 = 3% per period. The YTM becomes 5%/2 = 2.5% per period. The number of periods becomes 2*2 = 4 periods.

  2. Next, we calculate the present value of the bond's cash flows. The bond's cash flows consist of the semi-annual coupon payments and the face value payment at maturity.

  3. The present value of the coupon payments is calculated as follows: Coupon payment * [(1 - (1 + YTM)^-n) / YTM] = 3∗[(1−(1+0.025)−4)/0.025]=3 * [(1 - (1 + 0.025)^-4) / 0.025] = 3 * [1 - (1/1.1038128906)] / 0.025 = 3∗[1−0.905729578]/0.025=3 * [1 - 0.905729578] / 0.025 = 3 * 0.094270422 / 0.025 = $11.28 (approximately)

  4. The present value of the face value payment at maturity is calculated as follows: Face value / (1 + YTM)^n = 100/(1+0.025)4=100 / (1 + 0.025)^4 = 100 / 1.1038128906 = $90.57 (approximately)

  5. The bond's price is the sum of the present values of its cash flows. Bond price = 11.28+11.28 + 90.57 = $101.85 (approximately)

  6. Finally, we compare the bond's price with the price at which you buy the bond. If you buy the bond at 104,youbuythebondatalossbecauseitsprice(104, you buy the bond at a loss because its price (101.85) is less than the price you pay ($104).

So, the answer is B. At a loss.

This problem has been solved

Similar Questions

The following 6.45% p.a. semi-annual coupon U.S. treasury bond has 2 years until maturity. Calculate the fair value of the bond (rounded to 2 decimal places), assuming the current market yield for this bond is 6.45%. The bond has a face value of $100.00.

A 4% coupon-paying bond with two years’ life has a yield to maturity of 7% p.a with face valueof 100 and provides semi-annual payment.The bond’s dirty price is and clean price is under when the bond still has 20months to maturity.A. $96.6825; $95.8234B. $94.4904; $95.8234C. $94.4904; $96.6825D. $96.6825; $95.3492E. None of these are correct

A coupon bond that pays interests half yearly has a par value of $100. The bond matures in 12 years and has an annual yield to maturity of 6.5%. If the annual coupon rate is 11.65%, calculate the intrinsic value of the bond today.

A European government bond maturing in 6 years has a fixed coupon rate of 4% pa, paid annually.The bond's yield-to-maturity (YTM) is currently 4% pa, given as an annualised percentage rate (APR) compounding annually.The face value of the bond is $100. Calculate the bond price. All answer options below are rounded to 6 decimal points.Question 2Select one:a.$79.031453b.$94.665404c.$100d.$124e.$126.53190

Consider a coupon bond with a coupon rate of 10%. The face value amount is unknown. Suppose the bond is trading at a par. What can we say about yield to maturity of the bond? a. YTM = 10%. b. YTM is negative. c. There is not enough information to answer the question. d. YTM < 10%. e. YTM > 10%.

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.