Question

Year Cash Flow

0 $0

1 $250

2 $400

3 $500

4 $600

5 $600

What is the present (Year 0) value if the opportunity cost (discount) rate is 10 percent?

Add an outflow (or cost) of $1,000 at Year 0.

What is the present value (or net present value) of the stream?

Answer 1

Here the cash outflows per year are not uniform or equal, so it is not an annuity. For calculating the present value,we will use the following formula.

PV = C₁ / (1 + r)ⁿ

where, PV = Present value, C = Cash flow at year 1, r is the rate of interest = 10% and n is the time period.

PV = ($250 / (1 + 10%)) +   ($400 / (1 + 10%)²) +   ($500 / (1 + 10%)³) +   ($600 / (1 + 10%)⁴) + ($600 / (1 + 10%)⁵)

PV = ($250 / (1.10) +   ($400 / (1.10)²) +   ($500 / (1.10)³) +   ($600 / (1.10)⁴) + ($600 / (1.10)⁵)

PV = ($250 / (1.10) +   ($400 / 1.21) +   ($500 / 1.331) +   ($600 / 1.4641) + ($600 / 1.61051)

PV = ($227.2727) +   ($330.5785) +   ($375.6574) +   ($409.808) + ($372.55279)

PV = $1715.87

If we add $1000 at year 0, then net present value will be:

Net Present value = Present value of cash inflows - Cash outflow at year 0

Net Present value = $1715.87 - $1000

Net Present value = $715.87