Question

Q. What is the net present value of a project with the following cash flows and a required return of 12%? What is the internal rate of return? What is the payback period for this project? How about PI? Year 1 Cash Flow -$28,900 $12,450 $19,630 $ 2,750

Answer 1

SOLUTION : A
	CALCULATION OF THE PRESENT VALUE OF THE PROJECT
	Years	Cash Flows	PVF @ 12%	Present Value
	0	-$28,900	1.00000	-$28,900.00
	1	$12,450	0.89286	$11,116.07
	2	$19,630	0.79719	$15,648.92
	3	$2,750	0.71178	$1,957.40
	Total			-$177.62
		Answer = NPV =		-$177.62
SOLUTION : B
	IRR : IRR Means with a particular Percentage rate , At that point the present value become the zero
	CALCULATION OF THE IRR OF THE PROJECT
	First we calculate randomly present value with @ 11% discounting rate
	Years	Cash Flows	PVF @ 11 %	Present Value
	0	-$28,900	1.00000	-$28,900.00
	1	$12,450	0.90090	$11,216.22
	2	$19,630	0.81162	$15,932.15
	3	$2,750	0.73119	$2,010.78
		Net Present Value =		$259.14
	With PVF of 11 % we are getting positive =			$259.14
	Secondly we calculate randomly present value @ 12 % discounting rate
	Years	Cash Flows	PVF @ 12%	Present Value
	0	-$28,900	1.00000	-$28,900.00
	1	$12,450	0.89286	$11,116.07
	2	$19,630	0.79719	$15,648.92
	3	$2,750	0.71178	$1,957.40
	Total			-$177.62
	With PVF of 12 % we are getting negative =			-$177.62
	In the given case the pv with 11% is coming to postive means the present value is more
	then 11 % but with 12 % Present value cash flow become negative so the prese-nt value
	is between 11% and 12 %
	So the differecne in both % net present value is =			$259.14	-	-$177.62
	Total is become =			$436.76
	So , the difference % =			$259.14	"/"By	$436.76
	So , the difference % =			0.59
	So, the IRR =			11.59%
	Answer B = IRR =		11.59%
SOLUTION : C : PAY BACK PERIOD
Period	Particulars	Inflow (Outflow)	Cumulative Value
0	Outflow	-$28,900	$          -28,900
1	Inflow	$12,450	$          -16,450
2	Inflow	$19,630	$              3,180
3	Inflow	$2,750	$              5,930
In the 2nd year we recover our all money , but full 2nd full year is not required for this
so we can caluclate the exact period of payback
Payback Period = 1 Years +		$                       16,450.00	"/ " By	$          19,630.00
Payback Period = 1 Years +		0.84	Years
Payback Period = 1.84 Years
	Answer = 1.84 Years
SOLUTION : D : PI
	Years	Cash Flows	PVF @ 12%	Present Value
	0	-$28,900	1.00000	-$28,900.00
	1	$12,450	0.89286	$11,116.07
	2	$19,630	0.79719	$15,648.92
	3	$2,750	0.71178	$1,957.40
	Total			$               -177.62
Profitability Index = 1 + Net present Value / Initial investment
Profitability Index = 1 + Net present Value / Initial investment		$                           -177.62	"/" By	$          28,900.00
Profitability Index = 1 + Net present Value / Initial investment		-0.006
Profitability Index =		0.994
Answer = PI = 0.994