Question

Suppose asset \(A\) can be sold for \(\$ 11\) next period. If assets similar to \(A\) are paying a rate of return of \(10 \%,\) what must be asset A's current price?

Short answer

The current price of asset A is \( \$10 \).

Step-by-step solution

Understand the Problem

We want to find the current price of asset A given its future selling price and the rate of return. The future selling price is \( \$11 \), and the rate of return is \(10\%\).

Identify the Relevant Formula

The price of an asset today (\(P_0\)) can be found by rearranging the formula for rate of return: \[ P_0 = \frac{P_1}{1 + r} \]where \(P_1\) is the future price and \(r\) is the rate of return.

Plug Values into the Formula

Substitute \(P_1 = \$11\) and \(r = 0.10\) into the formula:\[ P_0 = \frac{11}{1 + 0.10} \]

Calculate the Current Price

Calculate \( P_0 \) by solving\[ P_0 = \frac{11}{1.10} = 10 \]Thus, the current price of asset A is \( \$10 \).

Key concepts

Rate of Return

Rate of return is a key concept in finance and investment, representing the gain or loss of an investment over a specified period. It is typically expressed as a percentage, showing how much the investment has increased or decreased as compared to its original value. A rate of return can be used to assess the efficiency of an asset in generating profit.

• For example, if you invest in a stock and it goes up by 10% in value, your rate of return is 10%.
• In our exercise, the asset has a rate of return of 10%, indicating that each dollar invested will earn an additional 10 cents by the next period.

Understanding the rate of return is essential for investors as it helps compare the profitability of different investment opportunities. It also allows an investor to make decisions based on potential risks and rewards.

Asset Pricing

Asset pricing is the process of determining the current worth of a financial asset. It is crucial for investors who need to make educated decisions when buying or selling assets. Pricing considers not only the expected future cash flows from the asset but also factors like the rate of return and risks involved.In our example, we calculate the present value of asset A using its expected future value and a known rate of return. By applying the formula:\[P_0 = \frac{P_1}{1 + r}\]we evaluate the present price by considering how much future money is worth right now.

• \( P_0 \) represents the current price of the asset.
• \( P_1 \) is the future price or the expected selling price.
• \( r \) is the rate of return expressed as a decimal.

This calculation helps investors understand whether an asset is overvalued or undervalued in the present market.

Future Value

Future value is an essential concept in finance that refers to the value of an asset or cash at a specified date in the future based on the expected growth rate. It provides an estimate of how much an investment made today will grow over a certain period.In our scenario, the future value of asset A is given as \( \$11 \), which indicates the amount expected from selling the asset in the next period. To link this back to today's context, we use the future value in conjunction with the rate of return formula to determine the asset's current worth.Understanding future value is vital for planning long-term investments and setting financial goals. It helps investors anticipate the amount they will receive from their investments in the future, allowing for more strategic financial planning.