Question

A project has annual cash flows of $7,000 for the next 10 years and then $10,500 each year for the following 10 years. The IRR of this 20-year project is 13.96%. If the firm's WACC is 9%, what is the project's NPV? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Project's NPV is $ 21,969.28

Step-1:Calculation of cost of project
IRR is the rate at which present value of cash inflows is equal to its cost.
Present value of annuity of 1 for 10 years	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.1396)^-10)/0.1396		i	=	13.96%
	=	5.22426857		n	=	10
Present value of 1	=	(1+i)^-n
	=	(1+0.1396)^-10
	=	0.27069211
Present value of cash flows of first 10 years	=	$   7,000.00	*	5.224269			=	$ 36,569.88
Present value of cash flows of next 10 years	=	$ 10,500.00	*	5.224269	*	0.270692	=	$ 14,848.77
Present value of cash flows of next 20 years								$ 51,418.65
So, cost of project is		$ 51,418.65
Step-2:Calculation of present value of project's cash inflows at WACC that is discounted rate
Present value of annuity of 1 for 10 years	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.09)^-10)/0.09		i	=	9.00%
	=	6.4176577		n	=	10
Present value of 1	=	(1+i)^-n
	=	(1+0.09)^-10
	=	0.42241081
Present value of cash flows of first 10 years	=	$   7,000.00	*	6.417658			=	$ 44,923.60
Present value of cash flows of next 10 years	=	$ 10,500.00	*	6.417658	*	0.422411	=	$ 28,464.32
Present value of cash flows of next 20 years								$ 73,387.93
Step-3:Calculation of project's NPV
Present value of cash inflow		$ 73,387.93
Less cost of project		$ 51,418.65
Project's NPV		$ 21,969.28