Question

A manufacturing company expects sales of $50,000 in quarter one, increasing by $3,000 per quarter through year 3. Calculate the present worth of the sales through a 3-year period at an interest rate of 10% per year compounded monthly

Answer 1

Given that

Sales for Quarter 1 = $50,000

Sales increases by $3,000 per quarter

Interest rate compounding monthly (r)= 10%

T = time in years

persent value factor for monthly compounding = $\small \frac{1}{(1+\frac{r}{n})^{nt}}$

By using the above formula, the following solution has been obtained. ( Formula extract attached below).

Period	Sales	Present value factor @ 10%	Present value
Quarter 1	50000	0.9754	48770.55
Quarter 2	53000	0.9514	50425.61
Quarter 3	56000	0.9280	51969.78
Quarter 4	59000	0.9052	53407.53
Quarter 5	62000	0.8830	54743.16
Quarter 6	65000	0.8612	55980.80
Quarter 7	68000	0.8401	57124.49
Quarter 8	71000	0.8194	58178.08
Quarter 9	74000	0.7993	59145.32
Quarter 10	77000	0.7796	60029.81
Quarter 11	80000	0.7604	60835.05
Quarter 12	83000	0.7417	61564.40
Present value of sales at 10% compounded monthly	672174.57

The following is the extract of formula used derive the solution.

Period	Sales	Present value factor @ 10%	Present value
Quarter 1	50000	=1/(1+(10/(12*100)))^(12*3/12)	=+SalesQ1*PVFQ1
Quarter 2	=+SalesQ1+3000	=1/(1+(10/(12*100)))^(12*6/12)	=+SalesQ2*PVFQ2
Quarter 3	=+SalesQ2+3000	=1/(1+(10/(12*100)))^(12*9/12)	=+SalesQ3*PVFQ3
Quarter 4	=+SalesQ3+3000	=1/(1+(10/(12*100)))^(12*12/12)	=+SalesQ4*PVFQ4
Quarter 5	=+SalesQ4+3000	=1/(1+(10/(12*100)))^(12*15/12)	=+SalesQ5*PVFQ5
Quarter 6	=+SalesQ5+3000	=1/(1+(10/(12*100)))^(12*18/12)	=+SalesQ6*PVFQ6
Quarter 7	=+SalesQ6+3000	=1/(1+(10/(12*100)))^(12*21/12)	=+SalesQ7*PVFQ7
Quarter 8	=+SalesQ7+3000	=1/(1+(10/(12*100)))^(12*24/12)	=+SalesQ8*PVFQ8
Quarter 9	=+SalesQ8+3000	=1/(1+(10/(12*100)))^(12*27/12)	=+SalesQ9*PVFQ9
Quarter 10	=+SalesQ9+3000	=1/(1+(10/(12*100)))^(12*30/12)	=+SalesQ10*PVFQ10
Quarter 11	=+SalesQ10+3000	=1/(1+(10/(12*100)))^(12*33/12)	=+SalesQ11*PVFQ11
Quarter 12	=+SalesQ11+3000	=1/(1+(10/(12*100)))^(12*36/12)	=+SalesQ12*PVFQ12
Present value of sales at 10% compounded monthly	=SUM(D2:D13)

Therefore, present worth of sales of the company for 3 year period is - $ 672,174.57