Suppose the government can offer to guarantee the financing of private firms. A company can borrow $100 now with a promise to repay $200 in 10 years. Think of this loan as a zero-coupon bond with a face value of $200. In 10 years, the company will be successful enough to repay this loan in full with a probability of 0.75, but with a probability of 0.25, the company will not be able to make any repayment on this loan (i.e., total default so the creditors get $0). The risk-free interest rate for government borrowing is 2% per year, and the yield curve is flat. Given that the lenders now view the promise of $200 in ten years to be risk-free, and the company can borrow at the government borrowing rate of 2% per year.

1. For each $200 promised in 10 years, how much will the company be able to borrow now?

2. What is the expected value of the government’s payment to lenders at t = 10?

3. From the company’s perspective, what is the current value of the loan guarantee

Now, suppose that whenever the company defaults, the government will pay the $200.

4. From the company’s perspective, what is the current value of the loan guarantee under this alternative assumption

5. From the perspective of the lenders, what is the current value of the loan guarantee