Question

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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, 200 ounces borrowed today would require 204 ounces to be repaid in one 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. 8.

Answer 1

Sol. In the above problem we have assumed two points first Corporate Client wants to borrow $1000000 and Gold rate is $1000 per ounce. The table below shows the calculation of cost for Cash Borrowing and Gold Borrowing:-

Borrowing Cash Cost			Borrowing Gold Cost
Interest Cost	-110000		Gold Borrowed	1000	ounces
Interest Income (RFI)	96900		To be ret after one year	1020	ounces
Effective Cost	-13100		Gold Price after one year with interest and no change in Gold Price	1020000
			Thus effective interest cost	-20000
			Storage Cost	-5012
			Effective Cost	-25012

The above calculation shows that Cash borrowed @ 11% can be deposited in Risk Free Interest rate with daily compounding the effective interest rate that can be earned will be 9.69% thus effective cost will be 1.31% p.a.

Gold borrowing on the contrary will have interest and storage cost which will effectively cost 2.501% p.a. It means that borrowing gold will cost more than borrowing cash.