Final answer:
To compute the rate of return, we must account for the loads and distributions. After purchasing and selling the fund shares at the adjusted NAV and adding distributions, we find that the rate of return is approximately 12.75%.
Step-by-step explanation:
To calculate the rate of return on an investment for the given scenario, we need to consider the initial cost of the investment, the loads charged, the distributions received, and the final value of the investment.
First, let's calculate the initial number of shares purchased. With a front-end load of 4%, for each dollar invested, only $0.96 goes towards purchasing the fund at the initial NAV (Net Asset Value) of $48 per share. The number of shares purchased will therefore be:
(Investment Amount) * (1 - Front-end load) / (Initial NAV) = $100,000 * (1 - 0.04) / $48 ≈ 2083.33 shares
The income gain and capital gain distributions are $0.4 and $0.8 per share respectively, which total to $1.2 per share. These distributions can be added directly to the investment return:
Distribution per share * Number of shares = $1.2 * 2083.33 = $2500
When the investment is sold, a back-end load of 2% is charged on the NAV. Therefore, the effective selling price per share is:
Final NAV * (1 - Back-end load) = $54 * (1 - 0.02) = $52.92
The total amount received from selling the investment is:
(Effective selling price per share) * (Number of shares) = $52.92 * 2083.33 ≈ $110,246.69
Now, we add the distributions received to the amount from selling the shares:
Total return = Amount from sale + Distributions = $110,246.69 + $2500 = $112,746.69
To find the rate of return, we subtract the original investment from the total return and then divide by the original investment:
Rate of Return = (Total return - Initial investment) / Initial investment
Rate of Return = ($112,746.69 - $100,000) / $100,000 = 0.127467 or 12.7467%
Therefore, the rate of return on this capital investment is approximately 12.75%.