Which of the following statements is FALSE?

Question

BlackTom AI · Accepted Answer

To begin, we restate the question and the available options to ensure clarity before diving into each choice.
Question: Which of the following statements is FALSE?
Options:
1) The highest interest rate for a given horizon is the rate paid on U.S. Treasury securities.
2) The equivalent after-tax interest rate is r(1 - τ).
3) It is important to use a discount rate that matches both the horizon and the risk of the cash flows.
4) The actual return kept by an investor will depend on how the interest is taxed.

Option 1: The highest interest rate for a given horizon is the rate paid on U.S. Treasury securities.
Think about what “highest interest rate” means in practice. Treasury securities are often used as the benchmark for a risk-free rate, particularly for a given horizon, since they are backed by the government and carry minimal credit risk. However, saying they are the highest rate for a given horizon ignores the fact that many other investments carry risk premia that can lead to higher expected yields, albeit with higher risk. In other words, while Treasuries are a standard reference, they are not universally the highest-yield option across all investment choices and risk profiles. This makes the statement misleading or incorrect in typical finance contexts.

Option 2: The equivalent after-tax interest rate is r(1 - τ).
This reflects the common formula for after-tax return on interest income when τ represents the tax rate on interest. If interest is taxed at rate τ, then the after-tax rate is indeed r(1 - τ). This aligns with standard tax-adjusted return calculations, so the statement is true.

Option 3: It is important to use a discount rate that matches both the horizon and the risk of the cash flows.
Choosing a discount rate that aligns with the time horizon (maturity) and the risk characteristics of the cash flows is a fundamental principle in valuation. Using an inappropriate discount rate can misprice a project or asset by either overstating or understating value, depending on misalignment with risk or time frame. This statement is true.

Option 4: The actual return kept by an investor will depend on how the interest is taxed.
Tax treatment affects the net or after-tax return an investor actually retains. Depending on tax rules, some portions of return may be taxed differently (e.g., ordinary income vs. capital gains, or tax-deferred accounts), influencing the take-home result. This statement is true.

In summary, Option 1 presents a claim that conflicts with the broader principle that higher-yield opportunities come with higher risk and that Treasuries are not necessarily the highest-yield option for every horizon and risk profile. The remaining options describe standard, correct considerations in discounting and after-tax returns.

Which of the following statements is FALSE?单项选择题

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