Question

An investment has an installed cost of $412,670.The cash flows over the four-year life of the investment are projected to be$212,817, $153,408, $102,389, and $72,308. If the discount rate is zero, what is the NPV? If the discount rate is infinite, what is the NPV? At what discount rate is the NPV just equal to zero? Sketch the NPV profile for this investment based on these three points.

Answer 1

1)	If the discount rate is Zero.
	We know that
	PV = FV/(1+i)^n
	Where,
	PV= Present Value
	FV= Future Value
	i= Interest rate per annum or discount factor
	n= Number of years
	So when i= 0, in the equation PV= FV/(1+i)^n, denomenator will always be 1.
	Therefore, the PV will be same as FV.
	NPV = Present value of inflow- Present Value of outflow.
	= $212817+$153408+$102389+$72308-$412670
	= $128252
2)	If the discount rate is infinity.
	We know that,
	any number divided by infinity is 0.
	Therefore,
	PV = FV/(1+i)^n turns out to be PV= FV/0
	We know that,
	any number divided by Zero is undefined.
	So no solution exists.

3) NPV is zero when discount rate = IRR

Calculation of IRR on trail and error method.

Years	Cash Flows	Discount Factor @ 15%	Present Value	Discount Factor @ 14%	Present Value
0	-412670	1	-412670	1	-412670
1	212817	0.8696	185058	0.8772	186682
2	153408	0.7561	115998	0.7695	118042
3	102389	0.6575	67322	0.6750	69110
4	72308	0.5718	41342	0.5921	42812
NPV	-2948		3976

For 1% change	6924	change in present value
For $3976 change in present value	1*3976/6924	change in percentage
		=	0.57	change in percentage
Therefore, 14.57% is the required IRR