Question

a small business is considering purchasing a new machine that is projected to yield savings in monetary terms of £1000 per year over a period of 10 years. Using 12 percent discount rate, calculate the present value of the savings (Hint: assume that the savings occur at the end of each year)

Answer 1

Answer on Question #43951 – Economics - Finance

A small business is considering purchasing a new machine that is projected to yield savings in monetary terms of £1000 per year over a period of 10 years. Using 12 percent discount rate, calculate the present value of the savings (Hint: assume that the savings occur at the end of each year)

Solution:

Future value can be calculated as follows:

$$FV = PV \cdot (1 + i)^n$$

Present Value is

$$PV = FV / (1 + i)^n$$

In our case we have annuity because savings occur each year

Present value =

$$P \times \frac{1 - \frac{1}{(1 + r)^n}}{r}$$

where P is annuity amount, r is rate of Interest, n is number of years

Present Value =

$$1000 \times \frac{1 - \frac{1}{(1 + 0.12)^{10}}}{0.12} = 5650.22$$

Answer: £5650.22.

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