### How to compute the price of loan in two cases

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Consider a firm that can invest \$250 right now, at t=0 in a project that will yield a single cash flow one period hence, at t=1. This \$250 investment will be raised by issuing unsecured debt at t=0. This project will yield \$500 with probability 0.8 and nothing with probability 0.2 at t=1. Immediately after the initial investment but before the end of the period (say t=1/2), the firm can purchase another asset, call it asset A, for \$250 also. If purchased, A will yield a sure payoff of \$300 at t=1. Those who lend the firm money at t=0 cannot observe at t=1/2 whether the firm had this investment opportunity. Everybody is risk neutral and the riskless rate is 12%. If you are the banker the firm has approached for a \$250 loan at t=0, compute the price of your loan in two cases: (i) the firm can finance the acquisition of asset A with unsecured debt or not at all, and (ii) the firm can fiancé the acquisition of asset A with debt secured by the asset in question. Assume that in case (i), your bank (the initial lender) will have the same seniority as the new (unsecured) creditors who supply funds to purchase A. Your bank is competitive in loan pricing.

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