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.
