Question

Grove Corp. is considering the purchase of a new piece of equipment. The cost savings from the equipment would result in an annual increase in net income of $200,300. The equipment will have an initial cost of $1,200,300 and have an 8 year life. The salvage value of the equipment is estimated to be $200,300. The hurdle rate is 12%. Ignore income taxes. (Future Value of $1, Present Value of $1, Future Value Annuity of $1, Present Value Annuity of $1.) (Use appropriate factor from the PV tables.)


a. What is the accounting rate of return? (Round your answer to 2 decimal places.)



b. What is the payback period? (Round your answer to one decimal place.)



c. What is the net present value? (Do not round intermediate calculations and round your final answer to the nearest dollar amount.)



d. What would the net present value be with a 15% hurdle rate? (Do not round intermediate calculations and round your final answer to the nearest dollar amount.)



e. Based on the NPV calculations, in what range would the equipment’s internal rate of return fall? (Round your answer to 2 decimal places.)

Answer 1

a.
	Accounting rate of return			=	Average income / Avreage Investment
				=	$       2,00,300	/	$ 7,00,300
				=	28.60%
	Working:
	Average Investment			=	(Cost + Salvage Value )/2
				=	(1200300+200300)/2
				=	$       7,00,300
b.	Payback period			3.7 Years
	Payback period is the time within which cost of project is recovered back.
	# 1	Straight Line depreciation			=	(Cost - Salvage Value)/Useful Life
					=	(1200300-200300)/8
					=	$           1,25,000
	# 2	Annual Cash inflows			=	Annual Net Income + Annual Depreciation
					=	$           2,00,300	+	$ 1,25,000
					=	$           3,25,300
	# 3	Payback Period			=	Cost of Project/Annual Cash inflows
					=	$         12,00,300	/	$ 3,25,300
					=	3.7
c.	Net Present Value				$       4,96,571
	Working:
	# 1	Year	Cash flows	Present Value of 1		Present Value of Cash flows
		a	b	c=1.12^-a		d=b*c
		0	$ -12,00,300	1.0000		$       -12,00,300
		1	$     3,25,300	0.8929		$           2,90,446
		2	$     3,25,300	0.7972		$           2,59,327
		3	$     3,25,300	0.7118		$           2,31,542
		4	$     3,25,300	0.6355		$           2,06,734
		5	$     3,25,300	0.5674		$           1,84,584
		6	$     3,25,300	0.5066		$           1,64,807
		7	$     3,25,300	0.4523		$           1,47,149
		8	$     5,25,600	0.4039		$           2,12,281
			Net Present Value			$           4,96,571
	# 2	Year 8 Cash inflows		=	Operating Cash inflows + Salvage Value
				=	$       3,25,300	+	200300
				=	$       5,25,600
d.	Net Present Value				$       3,24,904
	Working:
	# 1	Year	Cash flows	Present Value of 1		Present Value of Cash flows
		a	b	c=1.15^-a		d=b*c
		0	$ -12,00,300	1.0000		$       -12,00,300
		1	$     3,25,300	0.8696		$           2,82,870
		2	$     3,25,300	0.7561		$           2,45,974
		3	$     3,25,300	0.6575		$           2,13,890
		4	$     3,25,300	0.5718		$           1,85,991
		5	$     3,25,300	0.4972		$           1,61,732
		6	$     3,25,300	0.4323		$           1,40,636
		7	$     3,25,300	0.3759		$           1,22,292
		8	$     5,25,600	0.3269		$           1,71,820
			Net Present Value			$           3,24,904
e.	Internal rate of return falls between 15% to 25%
	and it is 22.95%
	Working:
	Internal rate of return is the rate at which Net Present Value is zero.
		Net Present Value at 25% hurdle rate:
		Year	Cash flows	Present Value of 1		Present Value of Cash flows
		a	b	c=1.25^-a		d=b*c
		0	$ -12,00,300	1.0000		$       -12,00,300
		1	$     3,25,300	0.8000		$           2,60,240
		2	$     3,25,300	0.6400		$           2,08,192
		3	$     3,25,300	0.5120		$           1,66,554
		4	$     3,25,300	0.4096		$           1,33,243
		5	$     3,25,300	0.3277		$           1,06,594
		6	$     3,25,300	0.2621		$               85,275
		7	$     3,25,300	0.2097		$               68,220
		8	$     5,25,600	0.1678		$               88,181
			Net Present Value			$             -83,800
	Discount rate and Net Present Value has adverse relation. It means increase in hurdle rate will decrease Net Present Value.
	So, Bring Net Present Value to 0 hurdle rate must be lower than 25%
	Internal rate of return			=	15%+(25%-15%)*((324904/(324904+83800))
				=	22.95%