Quantitative Methods - Quantitative Methods Section 1

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17. An investor buys two shares of Heather Corporation for $53 per share. He receives an annual dividend of $3 per share at the end of every year for four years. At the end of fourth year, just after receiving his final dividend, he sells both shares of Heather Corporation for $45 per share. The investor’s money weighted rate of return is closest to:

  • Option : A
  • Explanation : Money-weighted rate of return is the internal rate of return (IRR) of the cash flows resulting from the investment activity. To calculate the money weighted rate of return for the investor, using financial calculator enter the following cash flows: CF0 = (-53 x 2) = - 106, CF1 = 6, CF2 = 6, CF3 = 6, CF4= 6 + (45 * 2) = 96, Compute IRR: IRR = 1.998% ~ 2.0%.
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18. The table below shows information about a common stock:

 Date Amount €
Stock purchase (1 share)  1 July 201254.00
Stock purchase (1 share)  1 July 201349.00
Stock sale (2 shares @ 61.00 per share) 1 July 2014122.00

  • Option : A
  • Explanation : The money-weighted rate of return is the IRR based on the cash flows related to the investment. In this case, a cash outflow of €54 occurs at t = 0, another outflow of €49 occurs at t = 1, and an inflow of €122 occurs at t = 2. Using a financial calculator, the IRR of these cash flows is 11.64%.
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19. An investor purchases one share of a stock for $44. Exactly one year later, the company pays a dividend of $4.00 per share. This is followed by two more annual dividends of $5.00 and $4.50 in successive years. Upon receiving the third dividend, the investor sells the share for $45.0 .The money-weighted rate of return on this investment is closest to:

  • Option : B
  • Explanation : The money-weighted rate of return is the internal rate of return (IRR) of the cash flows associated with the investment. Using a financial calculator, compute IRR. CF0 = – 44, CF1 = 4, CF2 = 5, CF3 = 49.50, CPT IRR. IRR = 10.87%.
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20. An investor purchases 100 shares of a stock. The history of this investment is outlined below:

Time 

ActivityPrice per
Share ($)
Dividend per
Share ($)
Begining of Year 1

Buy 100 shares 20.00 
End of Year 1   Buy 20 shares22.002.00
End of Year 2   25.002.50
End of Year 3  Sell 120 shares24.00 

Assuming that the investor does not reinvest his dividends, which are tax-free,
the time-weighted rate of return on the investment is
closest to:

  • Option : A
  • Explanation : The time-weighted rate of return measures the compound growth rate of $1 initially invested in the portfolio over a stated measurement period. TWR = 3√{[(22 + 2)/20] * [(25 + 2.5)/22] * [(24/25)]} – 1 = 0.1292.
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