Question

You are considering a project that will pay you $710 in the first year, $2,000 in the second year, and $1,090 in the third year. In the fourth year, the project will pay you a cash flow of 3,000, which starting from the fifth year will grow forever at a rate of 2%. If the interest rate for this project is 12%, and the time-zero cost of starting this project is $10,000, what is the Net Present Value (PV of benefits minus PV of costs) of the project? Round your answer to the first two decimal places.

Answer 1

Step-1:Calculation of present value of cash inflows of first 4 years
Year	Cash flow	Discount factor	Present value
a	b	c=1.12^-a	d=b*c
1	$           710	0.893	$       633.93
2	$       2,000	0.797	$   1,594.39
3	$       1,090	0.712	$       775.84
4	$       3,000	0.636	$   1,906.55
Total			$   4,910.71
Step-2:Calculation of present value of cash flows after year 4
Present value		=	CF4*(1+g)/(K-g)*DF4			Where,
		=	$ 19,446.85			CF4	Cash flow of year 4	$    3,000
						g	Growth rate	2%
						K	Interest rate	12%
						DF4	Discount factor of Year 4	0.636
Step-3:Calculation of net present value of the project
Present value of cash inflows of first 4 years				$   4,910.71
Present value of cash inflows after year 4				$ 19,446.85
Total present value of cash inflows				$ 24,357.56
Less Cost of project at time zero				$ 10,000.00
Net Present value of the project				$ 14,357.56