Question

	Two people have come to your restaurant with different offers.
Sam	"I'll sell you a brand new soft-serve ice cream machine. It'll cost $4,000 and should provide you with an extra $1,000 of revenue every year. You'll only have to pay about $100/year to maintain it, and it should last for nine years.
Ella	"I run a party venue just down the street from your restaurant. I'll charge you $10,000 to put signage up in the venue, and you can become my preferred caterer for weddings, bar mitzvahs, etc. I bet I can get you $50,000 of additional revenue every year, and I know your contribution margin is around 10%. Let's say this arrangement will last for five years."
	Your required rate of return is 7%.
1	What's the payback period for each of these offers?
2	What's the NPV of each of these offers?
3	What's the approximate IRR of each of these offers?

Answer 1

		Present Value (PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=Discount Rate=Required return=7%=	0.07
		N=Year of Cash Flow
	ALTERNATIVE 1 (SAM)
		YEAR WISE CAH FLOWS AND PRESENT VALUE OF CASH FLOWS
		Annual cash inflow=$1000-$100=	$900
	N	Year	0	1	2	3	4	5	6	7	8	9
	ALTERNATIVE 1 (SAM)	InitialCash Flow	($4,000)
	B	Annual cash inflow		$900	$900	$900	$900	$900	$900	$900	$900	$900
	C=A+B	Net Cash Flow	($4,000)	$900	$900	$900	$900	$900	$900	$900	$900	$900
	D	Cumulative Cash Flow	($4,000)	($3,100)	($2,200)	($1,300)	($400)	$500	$1,400	$2,300	$3,200	$4,100	SUM
	PV=C/(1.07^N)	Present Value of Cash Flow	$       (4,000)	$        841	$        786	$        735	$        687	$        642	$        600	$        560	$        524	$        490	$    1,864
	NPV	Net Present Value=Sum of Present values of cash flows	$         1,864
	IRR	Internal Rate of Return	17%	(Using IRR function of excel over Net cash Flow)
		Payback period=Period when cumulative cash flow=ZERO
		Payback Period=	4.44	Years	(4+(400/900)
	ALTERNATIVE 2 (ELLA)
		YEAR WISE CAH FLOWS AND PRESENT VALUE OF CASH FLOWS
		Annual cash inflow=$50000*0.1=	$5,000
	N	Year	0	1	2	3	4	5
	ALTERNATIVE 1 (SAM)	InitialCash Flow	($10,000)
	B	Annual cash inflow		$5,000	$5,000	$5,000	$5,000	$5,000
	C=A+B	Net Cash Flow	($10,000)	$5,000	$5,000	$5,000	$5,000	$5,000
	D	Cumulative Cash Flow	($10,000)	($5,000)	$0	$5,000	$10,000	$15,000	SUM
	PV=C/(1.07^N)	Present Value of Cash Flow	$     (10,000)	$    4,673	$    4,367	$    4,081	$    3,814	$    3,565	$ 10,501
	NPV	Net Present Value=Sum of Present values of cash flows	$       10,501
	IRR	Internal Rate of Return	41%	(Using IRR function of excel over Net cash Flow)
		Payback period=Period when cumulative cash flow=ZERO
		Payback Period=	2.00	Years
			SAM	ELLA
	1	Payback Period(in Years)	4.44	2.00
	2	NPV	$         1,864	$ 10,501
	3	IRR	17%	41%