Question

NPV and IRR   Benson Designs has prepared the following estimates for a​ long-term project it is considering. The initial investment is

​$46,830​,and the project is expected to yield​ after-tax cash inflows of

​$5,000per year for 14years. The firm has a cost of capital of14​%.

a.  Determine the net present value​ (NPV) for the project.

b.  Determine the internal rate of return​ (IRR) for the project.

c.  Would you recommend that the firm accept or reject the​ project?

Answer 1

a.	NPV	$                     -16,819.64
Working:
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.14)^-14)/0.14		i	=	14%
	=	6.002071503		n	=	14
Present value of annual cash inflows	=	$                               5,000	*	6.002072
	=	$                      30,010.36
Present value of annual cash inflows		$                      30,010.36
Initial cash outlay		$                      46,830.00
NPV		$                     -16,819.64
b.	IRR	6%
Working:
Present value at 5%	=-pv(rate,nper,pmt,fv)				Where,
	=	$                      49,493.20			rate	=	5%
					nper	=	14
Initial cost		$                      46,830.00			pmt	=	$    5,000
					fv	=	0
NPV		$                         2,663.20
IRR	=	5%+(14%-5%)*(2663.20/(2663.20+16819.64))
	=	6%
c.		No
Both NPV is negative at 14% required return and IRR is less than cost cost of capital.