On January 1st, 2005, Borrower Limited sold a 10%, five-year, $100 million bond when bonds of equivalent risk and maturity were yielding 5% annually. Interest payments are made on January 1st next year.

What is the Price of the Bond?

Question

On January 1st, 2005, Borrower Limited sold a 10%, five-year, $100 million bond when bonds of equivalent risk and maturity were yielding 5% annually. Interest payments are made on January 1st next year.

What is the Price of the Bond?

BlackTom AI · Accepted Answer

Question restatement: On January 1st, 2005, Borrower Limited sold a 10%, five-year, $100 million bond when bonds of equivalent risk and maturity were yielding 5% annually. Interest payments are made on January 1st next year. What is the Price of the Bond?

Option analysis step-by-step:
- First, identify the cash flows. The bond has a annual coupon rate of 10% on a $100 million face value, so annual coupon payment = 10% × $100,000,000 = $10,000,000. There are 5 years of coupons (years 1 through 5) and a redemption of $100,000,000 at the end of year 5.
- The market yield (discount rate) is 5% per year. To price the bond, we discount each coupon and the redemption at this yield.
- Present value of the coupons: The coupons form an ordinary annuity of 5 payments of $10,000,000. The present value factor for an ordinary annuity at i = 5% for n = 5 is a-angle-i-n = (1 − (1 + i)^(−n)) / i. Numerically, (1 − 1/(1.05)^5) / 0.05 ≈ (1 − 0.783526) / 0.05 ≈ 0.216474 / 0.05 ≈ 4.32948. Multiply by the annual coupon: 4.32948 × $10,000,000 ≈ $43,294,800.
- Present value of the redemption: The $100,000,000 redeemed at year 5 is discounted by (1 + i)^5 = (1.05)^5 ≈ 1.27628156. Therefore PV = $100,000,000 / 1.27628156 ≈ $78,352,640.
- Sum the present values: $43,294,800 + $78,352,640 ≈ $121,647,440. This aligns with the provided numeric result of about $121.6478 million.

Explanation of why this is the correct approach:
- The bond price equals the sum of the present values of all expected cash flows (coupons and redemption) discounted at the yield demanded by the market for bonds of similar risk and maturity.
- The stated coupon rate (10%) yields $10 million per year, which is consistent with a fixed-rate bond on a $100 million face value. Discounting at the market rate (5%) correctly reflects the investor’s required return.

Why the other (non-provided) options would be incorrect: (Note: there are no alternative options listed here, but generally the typical mistakes would include:)
- Using a different number of coupon payments (e.g., assuming only 4 coupons instead of 5) would understate the price because you’d be missing the final cash flow.
- Discounting all cash flows at a rate different from 5% (e.g., using 4% or 6%) would yield a price inconsistent with the market yield; if the rate is lower than 5%, the price would be too high, and if higher, too low.
- Treating the coupon as a perpetuity or miscomputing the annuity factor would lead to incorrect PV of coupons.
- Failing to include the redemption amount in year 5 would omit a substantial portion of the value, underpricing the bond.

Final numerical check (optional cross-verify): PV of coupons ≈ 10,000,000 × 4.32948 ≈ 43,294,800; PV of redemption ≈ 100,000,000 / 1.27628156 ≈ 78,352,640; total ≈ 121,647,440, matching the target price ~121.6478 million.

On January 1st, 2005, Borrower Limited sold a 10%, five-year, $100 million bond when bonds of equivalent risk and maturity were yielding 5% annually. Interest payments are made on January 1st next year. What is the Price of the Bond?数值题

类似问题

A bond will sell at a discount (below par value) if

As interest rates rise, the market price of your bond is also likely to rise.

You have purchased a bond with a 7% annual coupon rate for $1,060. What will happen to the bond's price if market interest rates rise?

All bonds considered below have a face value of $1000. The two-year zero-coupon bond is trading at $906.86 while the two-year bond with annual coupon rate 3% is trading at $962.96. In the absence of arbitrage, what is the fair price of the one-year zero-coupon bond?

A 7-year, 5% coupon bond (payable semi-annually) that was issued 4 years ago is presently trading at a YTM of 9%. Bond has a face value of $1000. Compute the bond's price.

A bond selling for an amount above face value is said to be selling at a discount.

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单