Question

4(b) 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 S300,000. As the study progresses, the expenses are expected to increase by 5 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

Monthly (nominal) interest rate = 12%/12 = 1%

First we calculate present value (PV) of expenses. Note that

Expense in month N = 1.05 x Expense in month (N - 1) and

PV Factor in month N = (1.01)^-N

Month	Expense ($)	PV Factor @1%	Discounted Expese ($)
	(A)	(B)	(C) = (A) x (B)
1	3,00,000	0.9901	2,97,030
2	3,15,000	0.9803	3,08,793
3	3,30,750	0.9706	3,21,023
4	3,47,288	0.9610	3,33,736
5	3,64,652	0.9515	3,46,954
6	3,82,884	0.9420	3,60,694
7	4,02,029	0.9327	3,74,979
8	4,22,130	0.9235	3,89,830
9	4,43,237	0.9143	4,05,269
10	4,65,398	0.9053	4,21,319
11	4,88,668	0.8963	4,38,005
12	5,13,102	0.8874	4,55,352
		Present Value ($) =	44,52,985

Total amount to be covered using monthly installments ($) = PV of expenses + 10% of PV of expenses

= 4,452,985 x 1.10

= 4,898,283.5

Monthly installment ($) = Total amount to be covered / P/A(1%, 6) = 4,898,283.5 / 5.7955** = 845,187.39