Question

4(b) Question: A company is conducting a field study of delivering parcels with automated vehicles for the next 12 months. In the first month, the expenses are estimated to be $400,000. As the study progresses, the expenses are expected to increase by 6 percent each month. The company plans to pay for the experiment with income to be received from the developer of the automated vehicles, which is received in six monthly installments, starting a month after the fieldwork completion date. Determine the amount of monthly installment so that the total of the six installments will cover all expenses incurred during the field study and also will provide 10% additional money as profit. Annual nominal interest rate is 12 percent, compounded monthly.

Answer 1

Computattion of Expected Expenses to be incurred
	Expenditure Amt
Month1	$   400,000.00
Month2 (400000*6%)	$   424,000.00
Month3 (424000*6%)	$   449,440.00
Month4 (449440*6%)	$   476,406.40
Month5 (476406.4*6%)	$   504,990.78
Month6 (504990.784*6%)	$   535,290.23
Month7 (535290.23*6%)	$   567,407.64
Month8 (567407.644*6%)	$   601,452.10
Month9 (601452.1035*6%)	$   637,539.23
Month10 (637539.229*6%)	$   675,791.58
Month11 (675791.583*6%)	$   716,339.08
Month12 (716339.078*6%)	$   759,319.42
	$6,747,976.48
Add: Expected Profits @ 10%	$   674,797.65
PV of the monthly installment	$7,422,774.13
Annuity factor @ 12%p.a. for 6months	=(1/1.01)+(1/(1.01)^2)+(1/(1.01)^3)+(1/(1.01)^4)+(1/(1.01)^5)+(1/(1.01)^6)
	=5.7954
Monthly Installment Amount = PV of Monthly Installments/Annuity factor @12%p.a for 6 months =				$1,280,804.45