The management of retz corporation is considering the purchase of a new machine costing $500,000. 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 of this investment:
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 present value index for this investment is:

The present value index is 0.91 which is less than 1. So, the investment should not be accepted.

Explanation:

Present Value Index : It shows the ratio between the sum of present value of all years cash inflows after applying the discount rate and initial investment.

In mathematically,

Present value index = Sum of present value of all years cash flows with discount rate ÷ Initial Investment

where,

Present value = Net cash flow × Discount rate

So,

Year 1 = $180,000 × 0.909 = $163,620

Year 2 = $120,000 × 0.826 = $99,120

Year 3 = $100,000 × 0.751 = $75,100

Year 4 = $90,000 × 0.683 = $61,470

Year 5 = $90,000 × 0.621 = $55,890

Now, Sum all the yearly cash inflows which equals to

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

= $455,200

So, the present value index = $455,200 ÷ $500,000 = 0.91

Hence, the present value index is 0.91 which is less than 1. So, the investment should not be accepted.