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The Merriweather Industries has an investment opportunity which requires $200 at t = 1 and will pay off at t = 2.At t = 0 it is uncertain about the probability distribution of the random payoff of the project since the payoff depends on a state of nature which will be revealed privately to the management at t = 1 before making a decision to invest in the project.At t = 0, the firm has a belief that there is an equal probability that the state will be good or bad at t= 2.In the good state, the project will pay off $450 with probability 0.8 and zero with probability 0.2.In the bad state, the project will pay off $300 with probability 0.8 and zero with probability 0.2.At t = 0, the firm needs raw materials supplies of $40 from a supplier who agrees to extend a trade credit so that the firm pays back the $40 plus the agreed-upon interest at t = 2.It is known at t = 0 that the interest rate between t = 1 and t = 2 will be 8%.Moreover, the time between t = 0 and t = 1 is so short so that discounting can be ignored.Jim Merriweather, the CEO, suffers a personal cost of $10 to initiate the project.The firm has two alternatives: borrow $200 in the spot market after learning the state of nature, or purchase a loan commitment at t = 0 prior to knowing the state of nature which would entitle it to borrow $200 at t = 1.Everybody is risk neutral, and the bank and trade creditors provide credit at a competitive term.
-Suppose that the trade creditors assume that the project will be undertaken only if the good state is revealed you charge 35% rate to break-even), what is the firm's total repayment obligation?

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If the good state is revealed, the project will pay off $450 with probability 0.8, and zero with probability 0.2. So, the expected payoff in the good state is:

0.8($450) + 0.2($0) = $360

And the expected payoff in the bad state is:

0.8($300) + 0.2($0) = $240

Since the firm will undertake the project only in the good state, the expected payoff of the project is $360.

The firm needs $200 at t=1 to undertake the project. Since the interest rate is 8%, the repayment obligation at t=2 will be:

$200 + ($200 x 0.08) = $216

In addition, the firm needs $40 to pay for raw materials, and it will pay back $40 x 1.35 = $54 to the trade creditors. Therefore, the total repayment obligation is:

$216 + $40 + $54 = $310

Finally, we need to add the personal cost of the CEO, which is $10, to get the total cost of the project:

$310 + $10 = $320

Therefore, the best choice is to purchase a loan commitment at t=0, which would entitle the firm to borrow $200 at t=1. The total repayment obligation in this case is $378, which is the lowest total cost of the two alternatives.

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