Question

Asset \(X\) is expected to deliver 3 future payments. They have present values of, respectively, \(\$ 1,000, \$ 2,000,\) and \(\$ 7,000\) Asset \(Y\) is expected to deliver 10 future payments, each having a present value of \(\$ 1,000 .\) Which of the following statements correctly describes the relationship between the current price of Asset \(X\) and the current price of Asset Y? \( a. Asset \)X\( and Asset \)Y\( should have the same current price. b. Asset \)X\( should have a higher current price than Asset Y. c. Asset \)X$ should have a lower current price than Asset Y.

Short answer

Asset X and Asset Y should have the same current price.

Step-by-step solution

Calculate Total Present Value of Asset X

To find the current price of Asset X, sum the present values of the three future payments: \[\text{Total Present Value of Asset } X = 1,000 + 2,000 + 7,000 = 10,000.\]

Calculate Total Present Value of Asset Y

To find the current price of Asset Y, sum the present values of the ten payments:\[\text{Total Present Value of Asset } Y = 10 \times 1,000 = 10,000.\]

Compare the Current Prices of Asset X and Asset Y

Since Asset X has a total present value of \(10,000\) and Asset Y also has a total present value of \(10,000\), both assets should have the same current price.

Key concepts

Asset Valuation

Asset valuation is the process of determining the worth or value of an investment at a given point in time. In this context, understanding the present value of future payments is crucial for evaluating how much an asset is worth today. The core idea lies in the principle that money available now is more valuable than the same amount in the future due to its potential earning capacity. This is why present value calculations are essential.When valuing Asset X and Asset Y, the method used requires summing up the present value of all future payments associated with each asset. For example, if Asset X is expected to have payments worth \( \\(1,000 \), \( \\)2,000 \), and \( \\(7,000 \), the total value today is their sum, which is \( \\)10,000 \). Similarly, Asset Y has ten payments of \( \\(1,000 \) each, adding up to the same total of \( \\)10,000 \). This comparison of present values is what allows us to assess the current worth of both assets.

Future Payments

Future payments are amounts expected to be received at specified times in the future. They are contractually agreed amounts, such as installment payments or dividends, that an asset will generate over time. In investment terms, accurately assessing the present value of these payments allows investors to make informed decisions.The process of calculating future payments involves considering how the value of the money will change over time. For Asset X, expected future payments of \( \\(1,000 \), \( \\)2,000 \), and \( \$7,000 \) respectively, are planned to be realized at different points. Converting these future sums into present terms helps investors immediately understand the financial benefit they can expect from holding the asset now. It's important to factor in assumptions about the discount rate—an interest rate applied in present value calculations—which can affect the overall valuation significantly.

Current Price Comparison

Current price comparison is a critical aspect of comparing the worth of different assets based on their expected financial returns. This process requires assessing the present value of all future payments to determine the appropriate market price at the current moment.To perform a current price comparison of Asset X and Asset Y, you calculate the total present values of all expected future payments for each. Both assets have future payments resulting in a present value of \( \$10,000 \). Despite differences in the number of payments, the total present values are identical, signifying that both should have the same current market price as per the valuation process.This kind of comparison is especially useful in investment decision-making, as it gives investors a method to equate very different assets with a common valuation ground. In scenarios where factors like risk or interest rates remain constant, as in this example, knowing the present value allows investors to straightforwardly assess which asset might be a better investment choice based solely on current prices.