11.

(a) Finance managers regularly deal with the problem of determining the optimal level of cash to keep in hand. Consider a company that has regular cash needs during a period. The problem for the finance manager of this company is to determine the optimal amount of new funds to obtain from borrowing. The objective is to minimise the cost of going to the market for funds and the opportunity cost associated with "carrying" the funds.

Let Q = amount of cash obtained from each bond issue (Rs per issue).

CO= fixed cost associated with going to the market for funds by floating a bond issue (Rs per issue).

Ch= annual opportunity (carrying) cost associated with having cash in hand.

D = annual cash needs (Rs per Year).

Assume that cash needs are uniform during the year, that funds can be obtained in a deterministic period of time, and that interest rates on bonds are constant and unaffected by the size of the bond issue. Shortage of funds is not permitted.
(i) Write a general expression for the total annual cost associated with borrowing and holding cash.
(ii) If D = Rs 100 million, C0 = Rs 100,000, Ch= 8% per annum, determine the optimal size of each bond issue. How many times a year should bond issues be floated?
For the data in (ii), determine:
(iii) What is the annual cost of floating bonds? The annual opportunity cost associated with holding cash?
(iv) At what level of cash should a bond issue be initiated if it takes five days to float an issue?
Assume 255 'trading' days in a year (i.e. days when the bond market and the firm actively engage in their affairs).

(b) Because of the dynamics of the money market, analysts concede that the percentage of the opportunity cost associated with holding cash may fluctuate between 8% and 12% per annum.
Conduct sensitivity analysis to determine the effects on your answers to parts (ii), (iii) and (iv) if Ch assumes the extreme value of 12% per annum. (CA, November, 1992)