Question

What is the present value of a cash flow stream of $1,000 per year annually for 15 years that then grows at 2.0 percent per year forever when the discount rate is 8 percent? (Round intermediate calculations and final answer to 2 decimal places.)

Answer 1

Step-1:Calculation of present value of annual cash flow for next 15 years
Present value	=	Annual Cash flow	*	Present value of annuity of 1
	=	$         1,000	*	8.56
	=	$   8,560.00
Working;
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.08)^-15)/0.08		i	=	8%
	=	8.56		n	=	15
Step-2:Present value of annual cash flow after year 15
Present value	=	C15*(1+g)/(Ke-g)*DF15		Where,
	=	$   5,440.00		C15			=	$    1,000
				g			=	2%
				Ke			=	8%
				DF15	=	1.08^-15	=	0.32
Step-3:Present value of cash flows
Present value of cash flows	=	$   8,560.00	+	$ 5,440.00
	=	$ 14,000.00