NET present value

Question

Find NPV, if the Future income for next 15 years is 30 billion with interest rate of 3%, fixed cost at 5 billion and Variable cost 18 million /year?

Answer 1

It almost seems as if this question is incomplete. Usually, you would have to factor in taxes, depreciation, initial outlay, and terminal value. Since it doesn't mention any of these, we will ignore them.

The Net Present Value is the total present value of the annual net cash flows discounted at their required rate of return minus the initial outlay. We will ignore that last part for this problem. The time value of money dictates that the passage of time impacts the value of cash flows, so you cannot add up cash flows that occur at different periods in time without discounting them at the required rate of return.

The present value formula is as follows:

PV = FV / (1+ i)ⁿ Let PV represent present value, let FV represent future value, let i represent interest rate, and let n represent the number of years.

You can do this 15 times and add them all up to get your NPV. However, since the cash flows will be the same each year, it can be considered an annuity that we can use a financial calculator to solve for. An annuity is equal cash flows occurring consecutively over a period of time. For 15 years, the expected future income each year is 30 billion, fixed costs are 5 billion, and variable costs are 18 million (or .018 billion).

ΔRevenue - ΔExpenses = Annual Cash Flows

30 billion - 5 billion - .018 billion = 24.982 billion

Now we can use the financial functions on our calculator to solve for the present value of this annuity.

N = 15, I/y = 3, pmt = 24.982, compute PV

PV = 298.2334943 or

NPV = $298,233,494,300