Question

A project will cost $204,661.00 today. The project is then expected to generate after-tax cash flows of $30,000.00 per year. An economist also projects that the project will create synergies with other products for the firm and the synergies will create an after-tax cash flow of $12,261.00 per year. The cost of capital for the firm is 10.00%. The firm will run the project for 11.00 years. What is the NPV of this project?

Answer 1

Cost of Capital = r = 10% or 0.10

PV of a cash Flow = CF_n*PV Factor_n, where CF_n is the cash flow in Year n and PV Factor_n is the PV Factor for Year n

PV Factor_n = 1/(1+r)ⁿ

Cash Flow each Year from 1 to 11 = 30000 + 12261 = $42261

Year	Cash Flow	PV Factor	PV
0	-204661	1.00	-204661.00
1	42261	0.91	38419.09
2	42261	0.83	34926.45
3	42261	0.75	31751.31
4	42261	0.68	28864.83
5	42261	0.62	26240.76
6	42261	0.56	23855.23
7	42261	0.51	21686.58
8	42261	0.47	19715.07
9	42261	0.42	17922.79
10	42261	0.39	16293.44
11	42261	0.35	14812.22
		NPV	69826.77

Hence, NPV = $69826.77