HPR for Time-weighted return

RogerF

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Have a problem with understanding concept in this example

Compute the investment performance of the fund during 2014:

  • On 1.01.2014, the fund had market value of $100 million

  • During the period, 1.01 to 30.04, the stocks in the fund showed a capital gain of $10 million

  • On 1.05 the stocks in the fund paid a total dividend of $2 million. All dividens were reinvested in additional shares
  • Because the fund’s performance had been exceptional, institutions invested an additional $20 million in the fund on 1.05, raising assets under management to $132 million

  • On 31.12, fund received total dividends of $2.64 million. The fund’s market value on 31.12, not including $2.64 million in dividends, was $140 million.


And this is how it’s calculated in the book :


-> 1.01 beginning portfolio value = 100 mln

-> 1.05 dividends received before additional investment = 2 mln
ending portfolio value = 110 mln

hpr1= [2+ (110-100)]/ 100 = 12 %

new investment = 20 mln

-> 31.12 beginning market value for last 2/3 of year = 132 million
dividends received = 2.64 mln

ending portfolio value = 140 mln

hpr2= [2.64 + (140-132)] / 132 = 8,06 %


And my questions:

- shouldn’t we calculate the HPR for the period 1.01 to 30.04 ?

- on 1.05 they use $100 mln as the beginning value instead of the $110 mln - why is that ? there was a capital gain of $10 mln during the period 1.01 to 30.04

- how to include the $20 mln investment made on the 1.05 ? it’s not included in calculating the HPR in this period earlier. They use it as the beginning value on the 31.12 - $132 mln
 
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