What is the dollar-weighted rate of return using the simple interest approximation based on the given data?
The dollar-weighted rate of return using the simple interest approximation is 0%.
Understanding Dollar-Weighted Rate of Return
In the scenario provided, the dollar-weighted rate of return serves as a crucial metric to evaluate the performance of an investment. It considers both the timing and the amount of cash inflows and outflows, such as deposits and withdrawals, throughout the investment period.
Calculation Method
To calculate the dollar-weighted rate of return using the simple interest approximation, we need to analyze the changes in the fund's value and the cash flows involved. Initially, the fund is valued at $100,000 on January 1. By June 1, the value increases to $120,000 followed by a new principal deposit of $30,000.
On October 1, the value decreases to $130,000, and $50,000 is withdrawn. This leads to the fund's value returning to $100,000 on January 1 of the following year.
Cash Flows Overview
The net effect of all deposits and withdrawals on the fund is crucial to calculate the rate of return accurately. In this case, the total deposits amount to $30,000, and the total withdrawals sum up to $50,000, resulting in a net amount of -$20,000.
Rate of Return Formula
Applying these figures to the formula for the dollar-weighted rate of return:
((Final Value - Initial Value) - Net Deposits/Withdrawals) / (Initial Value + Net Deposits/Withdrawals)
We find that the rate of return calculation results in:
($100,000 - $100,000 - (-$20,000)) / ($100,000 + (-$20,000)) = 0
The 0% rate of return indicates that the overall value of the investment did not experience any growth or decline during the investment period considered.
For additional information on calculating rate of return and its significance in investment analysis, you can refer to reliable resources and educational platforms.