# Money weighted rate of return

Mariah Hill buys one share of a stock for \$50 on January 1, 2011. She buys an additional share on January 1, 2012 at \$60. The stock paid a dividend of \$3 per share at the end of each year. On January 1, 2013, she receives \$150 for selling the two shares. What’s the money weighted rate of return?

The way my professor solved it:

CF0 = - 50, CF1 = - 57, CF2 = 156, CPT IRR = 28.60%

Why is CF1 = -57 and not -54? By the end of Y1 we have two shares that each paid \$3 dividend … or is this context of CF1 = beginnig of year 1? In that case, the above was still solved using end mode..

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You bought the second share on January 1 2012 so you did not get the additional \$3 dividend before the end of 2012. You will have a dividend of \$6 at the end of 2012 but only \$3 at the end of 2011 because you held only one share at 31st December 2011.

Initial cash outflow at T=1 is -\$50

Cash inflow at T=1 is \$3 due to dividend and cash outflow is -\$60 which nets to -\$57.

Cash Inflow at T=2 is \$150 + the two dividends of \$3 each = \$156.

Hey, I still don’t get it with respect to calculator placements, can you help me out?

CF0 –> Dec 31/2011 (one share owned)

CF1 –> Dec 31/2012 (two shares owned) therefore  I should  get \$6 dividends

CF2 –> Drc 31/ 2013 (two shares sold)

OR

CF0 –>  Jan1 2011

CF1 –> Jan 1 2012

CF2 –> Jan 1 2013

When you are solving for a money weighted return problem, think of it as a traditional IRR problem. The IRR is the rate of return that makes cash outflows equal to cash inflows. You can consider cash inflows as positive and cash outflows as negative, however, you would obtain the same results if you decide to make cash inflows negative and cash outflow positive. You can set up the equation this way (assuming cash inflows are positive and cash outflow are negative):

- 50 (cash outflow at t=0) + -60 (cash outflow for second share at T=1)/(1+IRR) = 3 (inflow of dividend at T=1)/(1+IRR) + 6 (inflow of dividends at T=2)/(1+IRR) 2 + 150 (inflow of sale at T=2)/(1+IRR)2

If you simplifies this equation you get the following:

-50 + -57 (net outflow because you got an inflow of 3)/(1+IRR)=156 (net inflow due to two dividends)/(1+IRR)2

So,

CF0 = -50,

CF1 = -57

CF2 = 156