The Net Present Value of an investment is the present value of the investment minus the amount of money it costs to buy into the investment. All of the investment’s cash flows must occur at the same interval for the calculation to be accurate. If all of the investments have the same level of risk, then you should go with the investments with the highest net present value.
- [Instructor] The net present value of an investment is the present value of the investment minus the amount of money it costs to buy in. For example, in this case I have two different cash flows. One shows an initial investment of 160 thousand dollars. You earn 200 thousand dollars over the course of five years. On the other hand, we have the same investment almost, except that, in this case, we earn our original investment of 160 thousand dollars back over five years and earn 40 thousand dollars in year six.
So what this means is that we get the same 200 thousand dollars of return from each investment, but in one case we get that extra 40 thousand dollars one year later, and earn a little bit less each year as we go along. So the question is, how much difference does that make in terms of net present value? We need to know three things to calculate the net present value of an investment. The first is the discount rate. The discount rate is the rate of return that we can count on, in other words, it is risk-free.
This could be a product that has absolutely rock-solid sales within our company, or it could be a government bond, such as a US Treasury bond. We use the discount rate because if we weren't putting our money into this investment, we could safely, again with zero risk, put our money into that other investment and make four percent a year. What we want to do then, is to compare the investment to our risk-free investment. The second thing we need to know is the amount of money we have to put in, that's in cell A6 and D6 for these two cash flows, and then finally, we have the returns and the cash flows of the investment, and here we have in cells A7 through A11, our 40 thousand dollar yearly return and in cells D7 through D12, 32 thousand until the last year when we make 40 thousand, and again, the total return from these investments is 200 thousand dollars.
The question is whether they are equivalent in terms of net present value. Let's take a look. I'll click in cell B14 to calculate the net present value for the first investment, so I'll type equals to start the formula, then npv, left parenthesis, first is the rate, that's in cell B3, and this is a yearly return, so I don't have to worry about dividing by 12 for months or anything like that, comma, and then I have the values, these are the cash flows after the original investment, so I'm going to select cells A7 through A11, and yes, I am intentionally bypassing the original investment, we'll include that in a second.
Then I'll type a right parenthesis. Now the reason that we don't put the investment in to the NPV formula is because the first investment, or the first cash flow, is assumed to happen at year one. In other words, after one year of investment. The original investment, the amount of money that we put into the project starts at times zero. So rather than including it in NPV, we need to subtract it, although in this case it's a negative number already, so I will add cell A6.
To reiterate, what our formula does is find the net present value of investments, assuming a discount rate, risk-free rate, of four percent, and cash flow returns of 40 thousand dollars for five years. We then need to account for the initial investment, which is 160 thousand, and when I press enter, I see that the net present value in today's terms, given a four percent discount rate is 18,072 dollars and 89 cents. Now let's take a look at the second investment to see how it looks, and again, it's the same 200 thousand dollar return on a 160 thousand dollar investment, but we're making a little bit less each year until the final year and we're going one year longer.
So I'll click in cell E14, type an equals sign, and I'll go a little more quickly this time. We have npv, with a rate in B3, comma, our returns are D7 to D12, right parenthesis, then plus the amount of the original investment in D6, and enter, and we see that net present value is only 14,070 dollars and 90 cents. As you can see, this seemingly simple change extending the investment payback by one year and having lower amounts, slightly lower amounts, only lower by 20 percent, over the first five years, make a big difference in net present value.
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- Calculating security prices and yields
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- Analyzing simulation results