The value of a project, investment, or any set of cash flows is estimated using NPV analysis.
Net present value = Present value of cash inflows - Initial cash outflow
Year 0:
[tex]&\text { Present value }=\text { Cash flows } \times \frac{1}{(1+\text { Discount rate })^0} \\[/tex]
Present value =[tex]-13,000 \times \frac{1}{(1+14 \%)^0} \\[/tex]
Present value =-[tex]13,000 \times 1 \\[/tex]
Present value =-[tex]\$ 13,000[/tex]
Year 1:
[tex]&\text { Present value }=\text { Cash flows } \times \frac{1}{(1+\text { Discount rate })^1} \\[/tex]
Present value =[tex]420 \times \frac{1}{(1+14 \%)^1} \\[/tex]
Present value =[tex]420 \times 0.877 \\[/tex]
Present value =[tex]\$ 368[/tex]
Year 2 :
[tex]&\text { Present value }=\text { Cash flows } \times \frac{1}{(1+\text { Discount rate })^2} \\[/tex]
[tex]Present value =420 \times \frac{1}{(1+14 \%)^2} \\[/tex]
[tex]&\text { Present value }=420 \times 0.769 \\[/tex]
[tex]&\text { Present value }=\$ 323[/tex]
Year 3:
[tex]&\text { Present value }=\text { Cash flows } \times \frac{1}{(1+\text { Discount rate })^3} \\[/tex]
[tex]&\text { Present value }=(16,000+420) \times \frac{1}{(1+14 \%)^3} \\[/tex]
[tex]&\text { Present value }=16,420 \times 0.675 \\[/tex]
[tex]&\text { Present value }=\$ 11,083 \\[/tex]
[tex]&N P=368+323+11,083-13,000 \\[/tex]
[tex]&N P V=(\$ 1,226)[/tex]
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