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9. This question guides you through thinking about the role of collateral in lending. Suppose you are a mortgage lender. You have just lent to a homeowner and his house serves as the collateral. Suppose his house's current price is $100,000. Assume interest rate is zero and ignore timevalue of money throughout this problem. (a) Suppose you lent him $80,000. Thus, this mortgage has a loan-to-value ratio (LTV) of 80%. How negative does the housing price return have to be for it to be possible that you lose money on this investment? 0 Explanation: for instance, if housing price becomes $110,000, that is a - - $110 000 _ _ housmg price return of W 1 10%. Suppose you lent him $90,000 (LTV = 90%). How negative does the housing price return have to be for it to be possible that you lose money on this in vestment? Suppose you lent him $90,000 (LTV = 90%). Now, you learned that it is very slow to foreclose the house upon default. More importantly, during the foreclosure process, the homeowner will st0p maintaining the house or even vandalize it, so on average the house's value drops an additional 10% during the foreclosure process. Now, how negative does the housing price return have to be for it to be possible that you lose money on this investment? 10. This question guides you to think about the role of credit rating agencies. Sup- pose S&P credit rating is the only thing that determines companies" cost of borrow ing (interest rate on debt). Below is the interest rate associated with each credit rating. Credit rating Interest rate W AA 3.5% A 4.5% BBB 5.5% BB 7.5% Consider a company that is issuing a tenyear bond with par value $1 billion today. (3.) Suppose the company currently has a credit rating of AA. How much inter est expense can it save over the next ten years if its credit rating become AAA? (b) Suppose the company currently has a, credit rating of BBB. How much addi- tional interest expense does it incur over the next ten years if its credit rating drops to BB? 11. This question guides you to think about the nuances of scal stimulus. As explained in class, the government can stimulate the economy through giving people tax cuts. In this question, we will simply the policy to think of it as directly handing people money. This question guides you through thinking about how exactly to carry out the policy. Suppose the US. population consists of 80 million poor people, 200 million middle class people, and 20 million rich people. Suppose there are only three kinds of consumption: food, shelter, and diamonds. Let's introduce a new concept called "marginal propensity to consume" (MPC). A person's MP0 is "how much out of each additional dollar given to him will spent in consumption". For instance, if for even dollar of income given to me, I spend 70 cents, then my MPC is 70%. (a) Please compute the MP0 for the poor, the middle class, and the rich using the information below. i. For every dollar given to the poor, they spend 70 cents on food, 25 cents on shelter, and save the rest. ii. For every dollar given to the middle class, they spend 40 cents on food, 40 cents on shelter, and save the rest. iii. For every dollar given to the rich, they spend 5 cents on food, 15 cents on shelter, 30 centers on diamond, and save the rest. (b) Suppose the government has a budget of $1 trillion that it can give to only one of the three population. 1. Suppose the government's goal is to increase consumption as much as possible without regard to what is being consumed. Who should the government give the money to, and Why? ii. Suppose the government wants to stimulate consumption on shelter. Who should the government give the money to, and Why? 12. This questions guides you through the concept of the money multiplier. Suppose banks have a reserve requirement of 10%. That is, for every dollar of extra deposit a bank receives, it can (and will) lend out 90 cents. As explained in class, money lent out will create more deposits, creating a "money multiplier" effect. (a) Suppose bank 1 receives an additional $100 of deposits. How many additional dollars of loans are created by bank 1? (b) Now, suppose the loan made by bank 1 became deposits at bank 2, which will makes more loans. How many additional dollars of loans are created by bank 1 and 2 combined? (0) (Involves rnath not covered in class) Suppose this process goes on forever, to bank 3, bank 4, and bank 00 (innity). How many additional dollars of loans are created by this innite chain of banks? Hint: the formula for the sum of an innite geometric series is give below. If confusing, please search online. l 1? 1+r+r2+r3+...=
