Question

A project has annual cash flows of $7,000 for the next 10 years and then $8,500 each year for the following 10 years. The IRR of this 20-year project is 12.17%. If the firm's WACC is 12%, what is the project's NPV? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Project's NPV is $ 611.89

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+0.1217)^-10)/0.1217		i	=	12.17%
	=	5.61112001		n	=	10
Present value of 1	=	(1+i)^-n
	=	(1+0.1217)^-10
	=	0.31712669
Present value of cash flows of first 10 years	=	$   7,000.00	*	5.61112			=	$ 39,277.84
Present value of cash flows of next 10 years	=	$   8,500.00	*	5.61112	*	0.317127	=	$ 15,125.21
Present value of cash flows of next 20 years								$ 54,403.05
So, cost of project is		$ 54,403.05
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+0.12)^-10)/0.12		i	=	12.00%
	=	5.65022303		n	=	10
Present value of 1	=	(1+i)^-n
	=	(1+0.12)^-10
	=	0.32197324
Present value of cash flows of first 10 years	=	$   7,000.00	*	5.650223			=	$ 39,551.56
Present value of cash flows of next 10 years	=	$   8,500.00	*	5.650223	*	0.321973	=	$ 15,463.38
Present value of cash flows of next 20 years								$ 55,014.94
Step-3:Calculation of project's NPV
Present value of cash inflow		$ 55,014.94
Less cost of project		$ 54,403.05
Project's NPV		$       611.89