A firm decides to invest in a new piece of machinery which is expected to produce an
additional revenue of $8000 at the end of every year for 10 years. At the end of this
period the firm plans to sell the machinery for scrap, for which it expects to receive
＄5000. What is the maximum amount that the firm should pay for the machine if it is
not to suffer a net loss as a result of this investment? You may assume that the discount
rate is 6% compounded annually.

The maximum amount that the firm should pay for the machinery can be determined by calculating the present value of the cash flows expected from the new piece of machinery

Present value is the sum of the discounted cash flows from the investment

Discounted year 1 cash flow: $8000 ÷ 1.06 = 7547.17

Discounted year 2 cash flow: $8000 ÷ 1.06² = 7119.97

Discounted year 3 cash flow: $8000 ÷ 1.06³ = 6716.95

Discounted year 4 cash flow: $8000 ÷ 1.06^4 = 6,336.75

Discounted year 5 cash flow: $8000 ÷ 1.06^5 = 5,978.07

Discounted year 6 cash flow: $8000 ÷ 1.06^6 = 5,639.68

Discounted year 7 cash flow: $8000 ÷ 1.06 ^7= 5,3204.57

Discounted year 8 cash flow: $8000 ÷ 1.06^8 = 4,322.15

Discounted year 9 cash flow: $8000 ÷ 1.06^9 = 4,735.19

Discounted year 10 cash flow: $8000 ÷ 1.06^10 = 4,467.16

Discounted year 10 cash flow: $5000 ÷ 1.06^10 = 2,791.97

The sum of the discounted cash flows is $61,672.67

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