Question

in Some mill investment project ,construction period of 2 years, 18-year production, infrastructure investment of 600 $, floating capital of 400$, construction fund in the first year of an input, no salvage value, if the desired rate of return on investments is 10%, try begging after put into production, the project's annual profit at least how much to make the project possible?

Answer 1

Let the expected Annual Profit be x

The cashflow can be seen as below

End of year	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Initial Investment	-600
Floating Capital			-400	-400	-400	-400	-400	-400	-400	-400	-400	-400	-400	-400	-400	-400	-400	-400	-400	-400
Profit				x	x	x	x	x	x	x	x	x	x	x	x	x	x	x	x	x	x

The initial investment is

The Floating capital starts from end of year 2 when the production begins. It continues till the end of year 19 since Year 20 is the last year of Production

The profits start coming in when the 1st year of production is done. So it starts from end of year 3 and continues till end of year 20 which is the last Year of Production

PV of Initial Investment = -600

PV of Floating Capital = -400 / (1+10/100)^2 - 400 / (1+10/100)^3 - 400 / (1+10/100)^4 - ... - 400 / (1+10/100)^19

= -400/1.1^2 * (1/1.1^18 - 1) / (1/1.1 - 1)

= -400/1.21 * 0.82 / 0.091

= -2978.84

PV of Profit = x/1.1^3 + x/1.1^4 + ... x/1.1^20

= x/1.1^3 * (1/1.1^18 - 1) / (1/1.1 - 1)

= x/1.331 * 0.82 / 0.091

= 6.77x

PV of Project = -600 - 2978.84 + 6.77x = 6.77x - 3578.84

To make the project possible, the PV should be more than zero

so 6.77x - 3578.84 > 0

or x > 528.63

So if the profit is more than $528.63 annually, then the project will be possible.

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