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:

Question

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.

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:单项选择题

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