SMOOTHING Corporation’s Treasurer is trying to ascertain what proportion of the company’s borrowing should be floating rate debt. His immediate objective is to minimize the variance of the company’s net income before tax. He knew that the variance of net income reflects a combination of the variances of operating income, floating rate interest, and the correlation between the operating income and floating rate interest. The following are his estimates for the relevant data:

(a) Plot the relationship between the variance of net income and the proportion of floating rate borrowing. The equation is:

in which x equals the proportion of interest paid represented by floating rate payments.

(b) Demonstrate graphically or otherwise that the optimum proportion x of floating rate debt payments is given by:

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Operating Income (0) Interest payments (!) Net income (NI) Total debt (B) Standard deviation of Operating Income (oo) Standard deviation of floating rate interest payments (OF) Correlation between Operating Income and the floating rate (po,F) Floating rate (f) 10 million 5 million 5 million 100 million 0.20 0.20 0.25 5%