Question

Adirondack Savings Bank (ASB) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 5% for home loans, 11% for personal loans, and 8% for automobile loans. The bank’s planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans.

Suppose the total amount of new funds available is increased by $10,000. What effect would this have on the total annual return? Explain.
Assume that ASB has the original $1 million in new funds available and that the planning committee has agreed to relax the requirement that at least 40% of the new funds must be allocated to home loans by 1%. How much would the annual return change? How much would the annual percentage return change?

Answer 1

Particulars Return % Condition Amounts Home loans >= 40% of new funds ?? 5% Personal loans Automobile loans Funds available ?? 11% <= 60% of automobile loans No condition ?? 8% $1,000,000 Step 1: Find the current allocation of funds Since, home loans has the lowest return, only the minimum requirement of the funds will be allocated to home loans Therefore, 40% will be allocated to home loans (nothing greater than 40%) Assume automobile loans allocation to be x Therefore, personal loans will be 0.6x (since, personal loans has the highest return, maximum possible allocation will be done to personal loans i.e. 60% of automobile in the given case) Current allocation Particulars Calculation Amounts Home loans $400,000 $400,000 $225,000 $375,000 Personal loans Automobile loans Funds available 0.6x х $1,000,000 $1,000,000 1.6x $600,000 ($1,000,000 $400,000) Therefore, x $375,000 Step 2: Total annual return Return ($ Amounts Return % Particulars (0) $400,000 $225,000 $375,000 (I) (III) $20,000 $24,750 $30,000 Home loans Personal loans Automobile loans Funds available 5% 11% 8% $1,000,000 $74,750 Total annual return % 7.475%

Q. Suppose the total amount of new funds available is increased by $10,000. What effect would this have on the total annual return? Explain. The additonal funds of $10,000 will also be allocated in the ratio of current allocation of funds as the combination maximises the total return of the bank Return ($ Total Additional Return % Current Particulars (c*D) $22,000 $27,225 $33,000 (A) $400,000 $225,000 $375,000 (B) $40,000 C A+B D $440,000 $247,500 $412,500 Home loans 5% Personal loans Automobile loans Funds available $22,500 11% $37,500 $100,000 8% $1,000,000 $1,100,000 $82,225 7.475% Total annual return % Therefore, total annual return % will be 7.475% as the funds will be allocated in the same ratio. On absolute basis, the total return will increase from $74,750 to $82,225

Q. Assume that ASB has the original $1 million in new funds available and that the planning committee has agreed to relax the requirement that at least 40% of the new funds must be allocated to home loans by 1%. How much would the annual return change? How much would the annual percentage return change? Based on revised conditions Particulars Calculation Condition Amounts Home loans Personal loans Automobile loans Funds available $390,000 $390,000 $228,750 >= 39% of new funds <= 60% of automobile loans 0.6x $381,250 No condition X $1,000,000 $1,000,000 $610,000 ($1,000,000 $390,000) 1.6x Therefore, x $381,250 Total annual return % Return ($) (I*II) $19,500 $25,163 Return % Amounts Particulars (I) $390,000 $228,750 $381,250 (I) Home loans Personal loans Automobile loans Funds available 5% 11% $30,500 $75,163 8% $1,000,000 Total annual return % 7.516% Increase in annual return % is 0.041% (7.516%- 7.475 %) Increase in annual return is $413 (75,163 - 74,750)