The management of idaho corporation is considering the purchase of a new machine costing $430,000. the company's desired rate of return is 10%. the present value factors for $1 at compound interest of 10% for 1 through 5 years are 0.909, 0.826, 0.751, 0.683, and 0.621, respectively. in addition to the foregoing information, use the following data in determining the acceptability in this situation:
year income from operations net cash flow
1 $100,000 $180,000
2 40,000 120,000
3 20,000 100,000
4 10,000 90,000
5 10,000 90,000
the net present value for this investment is:
a. negative $126,800
b. negative $99,600
c. positive $16,400
d. positive $25,200

d. positive $25,200

Explanation:

The computation of the Net present value is shown below

= Present value of all yearly cash inflows after applying discount factor - initial investment

The discount factor should be computed by

= 1 ÷ (1 + rate) ^ years

where,  

rate is 10%  

Year = 0,1,2,3,4 and so on

Discount Factor:

Year 1 = 0.909

Year 2 = 0.826

Year 3 = 0.751

Year 4 = 0.683

Year 5 = 0.621

So, the calculation of a Present value of all yearly cash inflows are shown below

= Year 1 cash inflow × Present Factor of Year 1 + Year 2 cash inflow × Present Factor of Year 2 + Year 3 cash inflow × Present Factor of Year 3 + Year 4 cash inflow × Present Factor of Year 4 + Year 5 cash inflow × Present Factor of Year 5

= $180,000 × 0.909 + $120,000 × 0.826 + $100,000 × 0.751 + $90,000 × 0.683 + $90,000 × 0.621

= $163,620 + $99,120 + $75,100 + $61,470 + $55,890

= $455,200

So, the Net present value equals to

= $455,200 - $430,000

= $25,200