4. Both you and Justin Trudeau are interested in purchasing the same $10,000,000.00 property in scenic Nottawa, Ontario. You and Justin both apply to the Nearly National Trust of Nottawa for a mortgage, which will be amortized as a zero-coupon loan with a maturity of one year. The cunning loan officer with whom you both deal, however, recognizes you as a serious credit risk but regards Trudeau as a riskless borrower. Both you and Justin request an initial balance of $8,000,000.00, and while Justin is confident of receiving that, you know you may or may not, as you and Justin will likely be offered different loan terms in each of the alternatives below. For each set of terms, deduce the cost of credit risk that you bear relative to the terms offered to Trudeau. Assume the one year riskless interest rate or is two percent. Also assume that, regardless of the terms specified by the bank, it maintains the same credit rating for you as well as for Justin at their specified values.) 3 As in the original graphs of the payoffs to the call option in the slides to Lecture 2, the random value of the house at the relevant future date assumes the same low and high values, respetively denoted V11 and V,2, where Vil as usual illustrates a property value less than the value of the outstanding debt, 4 Hint: we didn't bother to include such ancillary costs in discussing credit risk because we simply aggregated them into the lower value of Vi. 5 Equivalently, why are equityholders often called "residual claimants"? 6 Yes, Nottawa is a real town. 2 a. Trudeau can borrow at the riskless rate in every case, but the loan officer tells you that to secure an initial balance of $8,000,000.00. you'd need to repay $8,500,000.00. What is the cost of your credit risk measured in terms of the difference in the annual rate you receive relative to Trudeau? b. Alternatively, the loan officer tells each of you how much they want from you in repayment to obtain a mortgage with any initial balance. He specifies that repayment as $8,160.000.00 in one year. What is Trudeau's initial balance? What is yours? What is the cost of your credit risk in current dollars? c. The loan officer announces a third alternative for the loan terms: the bank will give you each your requested initial balance, but you will have to pay your annual rate as calculated above. What is the cost of your credit risk measured in terms of dollars payable in one year? What is it in terms of current dollars? d. Assume that you still want the $8,000,000.00 mortgage loan, but you are sufficiently envious of Trudeau's loan terms that you ask your brother-in-law for a full loan guarantee, which would make you a riskless borrower just like Trudeau. Your brother-in-law is a nice enough guy, but he insists on full market compensation today for his writing you a full guarantee. How much does he want? e. What is the current market value of your option to default on your mortgage? 4. Both you and Justin Trudeau are interested in purchasing the same $10,000,000.00 property in scenic Nottawa, Ontario. You and Justin both apply to the Nearly National Trust of Nottawa for a mortgage, which will be amortized as a zero-coupon loan with a maturity of one year. The cunning loan officer with whom you both deal, however, recognizes you as a serious credit risk but regards Trudeau as a riskless borrower. Both you and Justin request an initial balance of $8,000,000.00, and while Justin is confident of receiving that, you know you may or may not, as you and Justin will likely be offered different loan terms in each of the alternatives below. For each set of terms, deduce the cost of credit risk that you bear relative to the terms offered to Trudeau. Assume the one year riskless interest rate or is two percent. Also assume that, regardless of the terms specified by the bank, it maintains the same credit rating for you as well as for Justin at their specified values.) 3 As in the original graphs of the payoffs to the call option in the slides to Lecture 2, the random value of the house at the relevant future date assumes the same low and high values, respetively denoted V11 and V,2, where Vil as usual illustrates a property value less than the value of the outstanding debt, 4 Hint: we didn't bother to include such ancillary costs in discussing credit risk because we simply aggregated them into the lower value of Vi. 5 Equivalently, why are equityholders often called "residual claimants"? 6 Yes, Nottawa is a real town. 2 a. Trudeau can borrow at the riskless rate in every case, but the loan officer tells you that to secure an initial balance of $8,000,000.00. you'd need to repay $8,500,000.00. What is the cost of your credit risk measured in terms of the difference in the annual rate you receive relative to Trudeau? b. Alternatively, the loan officer tells each of you how much they want from you in repayment to obtain a mortgage with any initial balance. He specifies that repayment as $8,160.000.00 in one year. What is Trudeau's initial balance? What is yours? What is the cost of your credit risk in current dollars? c. The loan officer announces a third alternative for the loan terms: the bank will give you each your requested initial balance, but you will have to pay your annual rate as calculated above. What is the cost of your credit risk measured in terms of dollars payable in one year? What is it in terms of current dollars? d. Assume that you still want the $8,000,000.00 mortgage loan, but you are sufficiently envious of Trudeau's loan terms that you ask your brother-in-law for a full loan guarantee, which would make you a riskless borrower just like Trudeau. Your brother-in-law is a nice enough guy, but he insists on full market compensation today for his writing you a full guarantee. How much does he want? e. What is the current market value of your option to default on your mortgage