- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 1. Rates and Returns
- Subject 3. Money-Weighted and Time-Weighted Return

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**CFA Practice Question**

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:

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

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?

A. (3.77%)

B. 4.02%

C. 4.94%

**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.

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**User Contributed Comments**
6

User |
Comment |
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aandreassen |
CF0=-18,000, CFj=-56,500, CFj=-60,000, CFj=143,800 You will get an IRR of 4.0178%! |

christine |
how do you do this on a BAII plus calculator? |

achu |
In a true worst-case scenario, plug in the given ROR's and see which one works. In this case, there were only 2 effective ones to check because by inspection of the cash flows, ROR had to be positive. |

dwadd |
On BAII Hit CF, then -18000, then enter. Hit down arrow to CF01, then -56500, then enter. Hit down arrow to CF02, then -60000, then enter. Hit down arrow to CF03, then 143800, then enter. Hit CPT, then IRR. |

cfaeater |
I'm using the BAII and I keep getting 3.67 when I press CPT IRR, after entering the numbers into the CF... Anyone know whats going on here...? |

cwest020 |
cfaeater, i had the same problem. Make sure you put in 143,800... if you put in 143,000 you will get 3.67. |