24 March, 08:20

# Emily's trust fund has a value of 100,000 on January 1, 1997. On April 1, 1997, 10,000 is withdrawn from the fund, and immediately after this withdrawal the fund has a value of 95,000. On January 1, 1998, the fund's value is 1 15,000. There is also a 5000 deposit to the fund on July 1, 1997. (a) Find the dollar-weighted annual rate of investment return for the fund, assuming simple interest. (b) Find the rate of return for Emily's fund using simple interest and assuming a uniform distribution throughout the year of all deposits and withdrawals. (c) Is it possible to calculate the time-weighted rate of return? If not, why not?

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1. 24 March, 09:40
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(a) Dollar Weighted Rate of return = 0.27

(b) Simple interest-based rate of return = (115000 - 100000) / 100000 = 0.15

(c) Since, the data or investment portfolio of Emily is of one year, we can calculate the money weighted rate of return but time weighted rate of return couldn't be calculated.

Explanation:

For (a) Dollar Weighted Rate of return = 0.27

Calculations: 115000 = ((-10000) * (1 + r) ^ ((365-90) / 365)) + 100000 * (1+r)

So, using calculator we found r = 0.27

Here we've equated the value of portfolio at Jan 1, 1998 with Value of portfolio on Jan 1, 1997 and using the formula for money weighted average rate of return we've found the rate of return. Since, we are taking annual money weighted average rate of return, so we don't include the value of July cash flow, i. e. \$5000.

For (b) Simple interest-based rate of return = (115000 - 100000) / 100000 = 0.15

Since, the distribution of deposits and withdrawals is uniform, so it is simply the newer value minus original value divided by the original value and is most likely to percentage calculation.

(c) Since, the data or investment portfolio of Emily is of one year, we can calculate the money weighted rate of return but time weighted rate of return couldn't be calculated.