Question

Cola is considering the purchase of a​ special-purpose bottling machine for$28,000.It is expected to have a useful life of 4 years with no terminal disposal value. The plant manager estimates the following savings in cash operating​ costs:

Year		Amount
1		$12,000
2		10,000
3		9,000
4		8,000
Total		$39,000

Calculate the following for the special purpose bottling​ machine:

1.	Net present value
2.	Payback period
3.	Discounted payback period
4.	Internal rate of return​ (using the interpolation​ method)
5.	Accrual accounting rate of return based on net initial investment​ (Assume straight-line depreciation. Use the average annual savings in cash operating costs when computing the numerator of the accrual accounting rate of​ return.)

Answer 1

• (1)	NPV=
  		Years	0	1	2	3	4
  		Initial investment	-28000
  		Cash flows		12000	10000	9000	8000
  		Total cash flows	-28000	12000	10000	9000	8000
  		PV factors @ 20%	1	0.833333	0.694444	0.578704	0.482253
  		PV of cash flows	-28000	10000	6944.444	5208.333	3858.025
  		NPV =	-1989.2
  	(2)	Payback period =
  		Year	cash flows	Cumulative cash flows
  		0	-28000	0
  		1	12000	12000
  		2	10000	22000
  		3	9000	31000
  		4	8000	39000
  		Payback period = 2 + [(28000-22000)/31000]
  			= 2 + (6000/9000)
  			= 2.6667 years
  	(3)	Discounted payback period -
  		It is similar to payback period except it uses PV of cash flows instead of actual cash flows
  		Year	cash flows	Pv factors @ 20%	Pv of cash flows	Cumulative PV cash flows
  		0	-28000	1	-28000	-28000
  		1	12000	0.833333	10000	-18000
  		2	10000	0.694444	6944.444	-11055.6
  		3	9000	0.578704	5208.333	-5847.22
  		4	8000	0.482253	3858.025	-1989.2
  		Here the cumulative cash flows are negative therefore the payback period is beyond the life of machine i.e. More then 4 years
  	(4)	IRR =
  		if we discount cash flows @ IRR NPV = 0
  		r=		NPV =
  		20%		-1989.198
  		r		0
  		18%		487.8913
  		r-20/18-20 =		(0-(-1989.198))/(487.8913-(-1989.198))
  		r-20 =		1.2453 x (-2)
  		r =		18 - 2.4905
  		r =		15.5095	(%)
  				Approx
  	(5)	Accounting rate of return -
  		Annual depreciation =			(28000/4)			7000
  		Years	0	1	2	3	4	Total
  		Initial investment	-28000					-28000
  		Cash flows		12000	10000	9000	8000	39000
  		Less: Depreciation -		7000	7000	7000	7000	28000
  				5000	3000	2000	1000	11000
  		total profit for 4 years =						11000
  		Average profit =			11000/4			2750
  		Average investment =			28000/4			7000
  		Accounting ROR =		Average Profit/ average investment x 100 =
  				= 2750/7000 X 100				39.2857%
  		Summarized results -
  		Criteria
  		NPV	(Higher)	-1989.2
  		Payback Period	(Lower)	2.666667
  		Discounted payback period	(Lower)	More then 4
  		IRR	(Hiigher)	15.5095
  		AROR	(Higher)	39.2857%