A portfolio manager with Churn Brothers Brokerage has recently been approached by one of its institutional accounts requesting that the dollar-weighted rate of return for the Microspeculative investment be calculated. Consider the following series of transactions:

t0: Purchase 20,000 shares for $0.90 per share
t1: Purchase 50,000 shares for $1.13 per share
t2: Purchase 50,000 shares for $1.20 per share
t3: Sell 20,000 shares of for $1.22 per share
Sell 80,000 shares of for $1.20 per share
Sell 20,000 shares of for $1.17 per share

Ignoring commissions, what is the dollar-weighted rate of return for this investment?

Explanation: Remember that the dollar-weighted rate of return uses the IRR equation in the determination of its answer. Further, the dollar-weighted rate of return is another name for the IRR equation, and this nomenclature is commonly used within the field of investment management. The logic behind this characterization is the fact that the IRR equation takes into account both the timing and scale of all project cash flows. In the determination of the dollar-weighted rate of return calculation, the first step should be to identify the cash flows for each period. This process is illustrated as follows:

t0: -20,000 shares purchased * $0.90 per share] = [$18,000]
t1: -50,000 shares purchased * $1.13 per share] ] = [$56,500]
t2: -50,000 shares purchased * $1.20 per share] = [$60,000]
t3: [(20,000 shares sold * $1.22 per share) + (80,000 shares sold * $1.20) + (20,000 shares sold * $1.17 per share)] = $143,800

Now that the cash flows have been determined, incorporating this information into your calculator's cash flow worksheet and solving for IRR will yield a dollar-weighted rate of return of 4.02% for this investment.