Question

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Two individuals invest in a project which takes two periods to complete. At the start of...

Two individuals invest in a project which takes two periods to complete. At the start of period one, individual A invests 4.5 and individual B invests 1.5. At the end of period one, each of the investors has a chance to withdraw her investment. The decisions whether to withdraw from the project or not are made simultaneously. If either investor withdraws, the project is scrapped and the scrapped value is 4. If both investors withdraw, they shared the scrapped value in proportion to their investment. If one investor withdraws while the other does not, the one who withdraws gets the first claim on the scrapped value up to the amount of her investment. If neither investor withdraws at the end of period one, the investors have another chance to withdraw at the end of period two. If either investor withdraws, the payoffs are the same as before. If neither investor withdraws at the end of period two, the project is completed and the investors get the total of 12 in gross return which they share in proportion to their original investment. There is no discounting. If exists find the backwards induction outcome of the game.If exists find the backwards induction outcome of the game.

Practice question

Expert Solution

At the end of the period 1:

Option A- Either of the investor withdraws and project get scrapped. In that case profit or loss will be as under:-

If A withdraws, Project get scrapped and the inflow is 4.

Profit or loss:

A= Project Inflow-Initial Investment

:4-4.5= 0.5 Loss

B:- B gets nothing because person who withdraws first gets upto the amount of his investment.

B will suffer a Loss of 1.5

If B withdraws first:-

B will get his initial investment that is 1.5, hence he will not suffer any loss.

A will get the rest of the amount from the scrapped value.

A's Loss= 4.5-2.5= 2

If no one withdraws, project continues.

At the end of period 2:-

Outcome will be the same as the year 2. ( All options same)

If no one withdraws at the end of period 2, project gets completed and the payout is 12 which will be shared by both in their investment ratio.

A:B = 4.5:1.5 = 3:1

Share of A: 3/4*12= 9

Share of B: 1/4*12= 3

A's Profit= 9-4.5 = 4.5 which is more than all the options opted

B' Profit= 3-1.5 = 1.5

Completion of the project is more fruitful if the discounting is ignored.

ekkarill92 answered 2 years ago

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