High School

Your firm intends to buy a CNC lathe for £100,000. In each of the first three years of operation, the lathe will contribute £33,000 per year. In the fourth year, the lathe will be sold for scrap for £20,000 and not used further. Calculate the present value of the purchase of the lathe if the interest rate is 7%.

Give the present value of the lathe to the nearest £10.

Answer :

The present value of the purchase of the lathe is £102,335.32 to the nearest £10.

How do we calculate?

We have the cash flows for the lathe as:

Year 1: £33,000

Year 2: £33,000

Year 3: £33,000

Year 4: £20,000

Present value

= CF1 / (1 + r)[tex]^1[/tex] + CF2 / (1 + r)² + CF3 / (1 + r)[tex]^3[/tex] + CF4 / (1 + r)[tex]^4[/tex]

Present value

= £33,000 / (1 + 0.07)[tex]^1[/tex] + £33,000 / (1 + 0.07)² + £33,000 / (1 + 0.07)[tex]^3[/tex] + £20,000 / (1 + 0.07)[tex]^4[/tex]

Present value

= £30,841.12 + £28,824.08 + £27,007.16 + £15,662.96

Present value = £102,335.32

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