A one-year Treasury discount bond with a face value of $105 is selling for $100 today. A one-year corporate discount bond with a face value of $600 carries a risk premium of 15 percent over the Treasury bond. The price of the corporate bond must then be:

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BlackTom AI · Accepted Answer

We start by extracting the given data and clarifying what is being asked.
- Treasury bond: face value 105, price today 100, one year to maturity. This implies a 5% discount relative to face value for the Treasury.
- Corporate bond: face value 600, and it carries a risk premium of 15 percent over the Treasury bond. We are asked to determine the price of this corporate discount bond one year from now.
Now, evaluate the options by thinking about how the discount and risk premium affect price.
Option A: $400.00. If the corporate bond priced at 400, the discount from face value would be 600 − 400 = 200. That would be a 33.3% discount from par, which is far larger than the 15% risk premium described relative to the Treasury. This seems inconsistent with the stated premium level.
Option B: $450.00. The discount from 600 would be 150, i.e., the price would reflect a 25% discount to par. While this is closer to a premium above the Treasury’s discount, it still implies a larger relative discount than a 15% risk premium over the Treasury’s scenario, making it unlikely given the problem statement.
Option C: $500.00. The discount from 600 would be 100, i.e., a 16.7% discount to par. This is intriguingly close to the Treasury’s own discount (5 on 105) in a way that, when scaled with a simple interpretation of the “premium over the Treasury bond,” yields a pricing outcome that aligns with a modest premium over the Treasury’s risk. It keeps the corporate price at a round number that mirrors the base relationship between face value and discount observed for the Treasury.
Option D: $550.00. The discount from 600 would be 50, i.e., a 8.3% discount to par. This is a relatively small discount compared with the Treasury’s 5 on 105, and applying a 15% risk premium over that Treasury scenario would not typically produce such a small discount from par for a higher-face-value bond.
Option E: None of the above. This would be selected if none of the numerical outcomes could be reconciled with the given 15% risk premium over the Treasury, but the intermediate reasoning above shows at least one option is plausible within the intended framework.
In summary, considering the stated 15 percent risk premium over the Treasury and the need for a reasonable, round-number price for a higher face value, the $500 figure emerges as the most consistent choice among the provided options, reflecting a substantial but not excessive discount from par that coheres with the problem’s premium relationship.

ECN 001B C01-C06 WQ 2025 Final Examination (Winter 2025)

A one-year Treasury discount bond with a face value of $105 is selling for $100 today. A one-year corporate discount bond with a face value of $600 carries a risk premium of 15 percent over the Treasury bond. The price of the corporate bond must then be:

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ECN 001B C01-C06 WQ 2025 Final Examination (Winter 2025)

A one-year Treasury discount bond with a face value of $105 is selling for $100 today. A one-year corporate discount bond with a face value of $600 carries a risk premium of 15 percent over the Treasury bond. The price of the corporate bond must then be:

查看解析

登录即可查看完整答案

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?

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?

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 company releases a five-year bond with a face value of​ $1000 and coupons paid semi-annually. If market interest rates imply a YTM of​ 6% p.a., which of the following annual coupon rates will cause the bond to be issued at a​ premium?

更多留学生实用工具

希望你的学习变得更简单

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

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?

A company releases a five-year bond with a face value of $1000 and coupons paid semi-annually. If market interest rates imply a YTM of 6% p.a., which of the following annual coupon rates will cause the bond to be issued at a premium?