Imagine that a bank will only lend if it can earn a rate of return of 6% on a lo
ID: 2710927 • Letter: I
Question
Imagine that a bank will only lend if it can earn a rate of return of 6% on a loan. Further, imagine it incurs administrative costs of $40 per loan it makes, regardless of the size of the loan. Throughout the problem, assume for simplicity that the loans are all repaid with certainty, i.e. there is no risk.
a. If the bank makes five loans – of $100, $200, $500, $1000, and $10,000 – what are the respective interest rates it must charge to break even on each loan?
b. Imagine the bank makes the same loans but must charge all borrowers the same interest rate. What interest rate will it charge to break even overall? Which borrowers pay less, which pay more in this case than in part a.? This practice of making losses on some loans and profits on others is called “cross-subsidization”.
c. How might competition between banks eliminate any one bank’s ability to cross-subsidize smaller borrowers? Specifically, ci) could a rival lender lure away any of the customers of a bank carrying out the policy of part b., and cii) how would this affect the ability to cross-subsidize of a bank carrying out the policy of part b.?
d. It may not be accurate to assume that every loan incurs the same administrative cost, irrespective of size. Larger loans may require more work. Redo part a. under the assumption that the administrative cost of a loan is $40 per loan plus 1% of the size of the loan. (Thus a loan of $5000 would cost the bank $40 + 1%*$5000 = $90, while a loan of $500 would cost the bank $40 + 1%*$500 = $45. The cost structure is still linear, but with a positive intercept and slope.)
Explanation / Answer
a) For breaking even calculations, look at the following table
b) Total Loan amount = 100 + 200 + 500 + 1000 + 10000 = 11800
Total costs = 11800 + 40*5 = 12000
So interest rate should be (12000 - 11800) / 11800 = 1.69%
This has to be the constant interest rate for all borrowers
c) Competitors can implement strategies, which charges interest rates on different criterion to borrowers. In the above case borrower who took loan of 10,000 is paying overall interest of 169.49 compared to Borrower 1 ($100) who is paying interest of just 1.69. By giving less interest rate loans, competitors can lure the borrowers
d) Bank total costs and borrowers loan and calculations of the interest rates are shown in the table below
Loan Amount Bank Costs Interest Rate 100 140 40.00% 200 240 20.00% 500 540 8.00% 1000 1040 4.00% 10000 10040 0.40%