Question: Dupont University Technology Partners: Answer Sheet

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1. (6 points)
   1. What is the expected t o t a l pa y o f f ( n o t i nc l ud i ng t h e i n i t i a l i n v e s t m en t s ) of the
      DUTP portfolio?
   2. What is the p r ob a b i l i t y that the total payoff is more than the total invested?
      
      
      (ii) Assuming that the distribution is approximately normal, we compute:
      
      
      \[\Pr \left( X\ge {80.7} \right) = \Pr \left( \frac{X-{97.75}}{30.05}\ge \frac{{80.7}-{97.75}}{30.05} \right) = \Pr \left( Z\ge -0.5674 \right) = 1-\Pr \left( Z\le -0.5674 \right) = 1-{0.2852} = {0.7148}\]
2. (4 points)
   1. What is the expected number of DUTP companies that will be " su c ce s s f u l " in that
      their returns w il l ex c eed the amount originally invested in the company?
   2. What is the probability that 10 or m o r e co m pan i es will be s ucc e s s f ul by this criterion?
      (ii) For the proportion of successful companies we get:
      
      Hence, the estimate of the probability of a given company to be successful is p = 0.83. We need to approximate the following probability:
      
      
      
      
      
      
3. (4 points)
   1. What is the expected payment to Dupont University from DUTP?
   2. What is the probability that the other investors will receive any money at all?
      (ii) Now, for the amount received by other investors:
      
      They receive an average of $18.86 million, with a standard deviation of $23.26 million. We compute:
      
4. (6 points)
   1. Suppose they replace DUTP's variable original management fee (10% of gross proceeds)
      with a f i xed f ee.
      
      - What new f ee and pa y m en t s by Dupont and the other limited partners would be
      " eq u i t ab l e" in the sense of giving all parties the s a m e expe c t ed v a l ues as in the original
      deal?
      
      - Specify the fi x ed f ee t h a t t h e m ana g e r s would r e c e i v e and how m uch of t h at f ee s h ou l d
      b e p a i d by D upont and h ow m uch s hou l d b e p a i d by t he o t h er l i m it ed p a rt n e r s .

i i ) How would this "equitable" payment of fees a f f e c t t he r i s k s t a k en by D upont and the o t h er li m it ed pa r t n e r s ?

- Compare the ri sk p r o f i l e s with the new and old fee arrangements for both Dupont and
the other limited partners. S h ow an o v e r l a y cha r t and d i s c u ss t he c h a n g es ( written
explanation ).

(i.e. Consider Risk Averse, Risk Neutral and Risk Adverse Positions).

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