Question

Present values. Lofting Snodbury is considering investing in a new boring machine. It costs $380,000 and is expected to produce the following cash flows:

Year:	1	2	3	4	5	6	7	8	9	10
Cash flow ($000s)	50	57	75	80	85	92	92	80	68	50

If the cost of capital is 12%, what is the machine’s NPV?

Answer 1

Solution:
	Machine’s NPV     $23,696.15
Working Notes:
	Net present value (NPV) = Present value of cash inflows - Present value of Costs
	Present value of Costs = Cost /(1+ cost of capital)^n
	Present value of Costs = 380,000 /(1+ 0.12)^0
	n= period = 0 as its today investment at start of the year
	Present value of Costs = 380,000 /(1+ 0.12)^0
	Present value of Costs = 380,000
	Present value of cash inflows
	=(50000/(1+0.12)^1) + (57000/(1+0.12)^2) + (75000/(1+0.12)^3) +(80000/(1+0.12)^4) + (85000/(1+0.12)^5) + (92000/(1+0.12)^6) + (92000/(1+0.12)^7) + (80000/(1+0.12)^8) + (68000/(1+0.12)^9) + (50000/(1+0.12)^10)
	=403,696.1485
	Net present value (NPV) = Present value of cash inflows - Present value of Costs
	Net present value (NPV) =403,696.1485 - 380,000
	Net present value (NPV) =$23,696.1485
	Net present value (NPV) =$23,696.15
Alternatively
	A	B	C= A x B
Year	Cash flows	PVF @ 12%	Present Value
0	-380,000	1	-380000
1	50,000	0.892857143	44642.85714
2	57,000	0.797193878	45440.05102
3	75,000	0.711780248	53383.51859
4	80,000	0.635518078	50841.44627
5	85,000	0.567426856	48231.28274
6	92,000	0.506631121	46610.06315
7	92,000	0.452349215	41616.12781
8	80,000	0.403883228	32310.65824
9	68,000	0.360610025	24521.4817
10	50,000	0.321973237	16098.66183
		NPV	23,696.15
Notes: PVF is calculated @ r% = 1/(1+r%)^n     where n is the period for which PVF is calculated.
Please feel free to ask if anything about above solution in comment section of the question.