Question

1. Given the following information and ignoring taxes, what is the annual cash revenue that will make the net present value equal to zero (i.e., the annual cash revenue that will cause us to break-even in the financial sense)?                             

• Annual cash costs = $14,000
• Life of project = 8 years
• Initial cost of project = $30,000
• Salvage value at end of project = $2,000
• Required rate of return = 15%

Answer 1

Present value of annual cash costs	=	$       14,000	*	4.487322	=	$ 62,822.50
Present value of initial cost	=	$       30,000	*	1	=	$ 30,000.00
Present value of salvage value	=	$        -2,000	*	0.326902	=	$     -653.80
Present value of annual cash outflow	=					$ 92,168.70
/ Present value of annuity of 1	=					4.48732151
Equivalent annual cost	=					$ 20,539.80
and So, annual cash revenue to make net present value to zero is						$ 20,539.80
Working:
Net Present value of a project is zero when present value of annual cash outflows and present value of annual cash inflows are equal.
So, at zero net present value, equivalent annual cash cost and equivalent cash revenue will be same.
Present value of annuity of 1 for 8 years		=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.15)^-8)/0.15		i	15%
		=	4.487322		n	8
Present value of 1 received at the end of year 5		=	(1+i)^-n
		=	(1+0.15)^-8
		=	0.326902