Question

Z. An investor has the opportunity to invest $450,000 in a project that with probability p will be successful and with probability (1-p) will fail. If the project is successful she will get back S1 Million (thus making a profit of S550,000), while if the project fails she will get back nothing (that is, she will lose her initial investment of $450,000). The alternative is to put the $450,000 into a savings account that pays 5% interest. (a) Represent her two options as lotteries where the outcomes are expressed in terms of her final wealth (assuming that her initial wealth consists of $450,000). (b) Represent her two options as lotteries where the outcomes are expressed in terms of net returns ( e) Using the wealith loteris and assumig and that she is risk-meutral, what will e (d) Using the net-return lotteries and assuming that p-\ and that she is risk-neutral, what will she final wealth -initial wealth) choose? choose?

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Answer #1

a) The final wealth of investor from investment in a successful project = $1000000

Final wealth of investor from investment in a savings account = 450000(1+.05) =472500

b) The net returns of investor from investment in a successful project = Final wealth - initial wealth

                                                                                       = $1000000-$450000= $550000

The net returns of investor from investment in a savings account = $472500-$450000= $22500                                        

c) Expected wealth of investor from investment in a project = $1000000*p +(1-p)*0

                                                                           = $1000000*1/2+1/2*0

                                                                           = $500000

Expected wealth from investment in a savings account = $472500

Therefore, the investor will choose investment in the project

d) Expected net returns from investment in a project = 1/2*550000+1/2*0 = $275000

Expected net returns from investment in a savings account = $22500

Therefore, investor will invest in project.

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