contestada

A bank offers a corporate client a choice between borrowing cash at 11% per annum and borrowing gold at 2% per annum. (If gold is borrowed, interest must be repaid in gold. Thus, 100 ounces borrowed today would require 102 ounces to be repaid in 1 year.) The risk-free interest rate is 9.25% per annum, and storage costs are 0.5% per annum. Discuss whether the rate of interest on the gold loan is too high or too low in relation to the rate of interest on the cash loan. The interest rates on the two loans are expressed with annual compounding. The risk-free interest rate and storage costs are expressed with continuous compounding.

Respuesta :

Answer:

The rate of interest on the gold loan is too high in relation to the rate of interest on the cash loan.

Explanation:

Let first assume that the price of gold is $550 and the amount that the corporate client wants to borrow is $550,000.

This implies there is an option for the client to choose between borrowing $550,000 in cash and borrowing 1,000 ounces of gold.

If $550,000 borrowed in cash, the amount that must be repaid can be calculated as follows:

Amount to repaid if borrowed in cash = Amount of cash borrowed * (100% + Interest rate on cash borrowing)^Number of years = $550,000 * (100% + 11%)^1 = $610,500

If the client borrows 1,000 ounces of gold it must repay 1,020 ounces.

The forward price of gold is calculated as follows:

Forward price of gold = Price of gold * e^(Risk-free interest rate - storage costs) = $550 * e^(9.25% + 0.5%) = $606.33

Cost of repayment of gold loan = Forward price of gold * Ounces of gold to repay = $606.33 * 1,020 = $618,457

Since Amount to repaid if borrowed in cash is less than Cost of repayment of gold loan (i.e. $610,500 < $618,457), this implies that the rate of interest on the gold loan is too high in relation to the rate of interest on the cash loan.