Video Transcript: Net Present Value

Hello, welcome. We're going to be discussing net present value. Net Present  Value is the first step involved in the calculation of Net Present Value is the  estimation of net cash flows from the project over its life. The second step is to  discount those cash flows at the hurdle rate. The next cash flow may be even  equal, cash flows in different periods or uneven. Different cash flows in different  periods when they are even. Present value can be easily calculated by using the formula for present value of annuity. However, if they are uneven, we need to  calculate the present value of each individual net cash inflow separately. Once  we have the total present value of all project cash flows, we subtract the initial  investment on the project from the total present value of inflows to arrive at Net  Present Value the decision rule in case of standalone projects, accept a project  only if its net present value is positive, reject it if it is if its NPV is negative, and  stay indifferent between accepting or rejecting if the net present value is zero. In  case of mutually exclusive projects, ie competing projects, except the project  with the higher net present value. So if I am looking to undertake a construction  project, and I want to build a shopping center and this neighborhood, and I want  to build a shopping center and this neighborhood over here, I want to gather the  cash flow information, or project out those cash flows. Know What My discount  rate is, apply that, and then, based on those cash flows between those two  projects, the one with the higher net present value is the one that you should  invest in. So let's look at this example, when cash flows are even Net Present  Value is the rate of return times one minus one plus the interest rate raised to  the number of periods divided by the interest rate minus the initial investment.  So R is the net cash flow, net cash inflow expected to be received in each  period. I is required rate of return for the period, and n are the number of periods the project is expected to operate and generate cash inflows. When cash inflows are uneven, we calculate net present value like this. So inflows, cash inflows at  period one, two and three over one plus the interest rate raised to the number of periods minus the initial investment. So if we have uneven cash flows, we can't  just project out one cash flow and raise that by the number of periods we've got  to solve for each individual cash flow. And then add them together. Example one even cash flows. Calculate the net present value of a project which requires an  initial investment of 243,000 and is expected to generate a cash inflow of  $50,000 each month for 12 months. Assume that the salvage value of the  project is zero, the target rate of return is 12% per year. So we have an initial  investment at 243,000 our net cash inflows are 50,000 per period with 12  periods, and our discount rate per period is at 1% so we'll see that the 50,000 as our net cash inflow per period is multiplied by one minus one plus the 1% raised  to 12 divided by 1% that gives us as we as we work through this, you can see  the order of operations. So now we go to the third line down. Okay, so we've  multiplied through one minus the 1.01 raised to 12, calculated to one minus  0.887449 so we're now going to divide that by 0.01 so now we have two. 50,000

times 11.2551, minus our initial investment of 243,000 so we'll have 50,000  times 11.2551. Gives us 562,754 and after we subtract out our initial investment, that leaves us with a net present value of $319 $319,754 so obviously this is a  project worth taking, because our net present value is considerably high, and  this would be a great opportunity for profit. Now let's look at an uneven cash  flow. Example, an initial investment of 8.32 million on plant and machinery is  expected to generate cash inflows of 3.41 1,000,004.07 0 million, 5.82  4,000,002.06 5 million at the end of the first, second, third and fourth years,  respectively, at the end of the fourth year, the machinery will be sold for 900,000  calculate the net present value of the investment if the discount rate is 18% So  now we have to set our present value factor. So we'll take one divided by one  plus the 18% raised to one, so we'll have .8475, is our year one present value  factor repeating through year two, three and four. So we'll see our net cash  inflows. Year one, the 3.411 million. Year two, the 4.070 million, three,  5.824,000,004 2.06 5 million. So we have a $900,000 salvage value that will and that will add to the end of year four, because we'll end up selling off our assets  of the company. So we'll salvage those. So you can see that our total cash  inflows will then be multiplied by the present value factor with the correlating  time period. So year one will be multiplied by .8475, year two will be multiplied  by .7182, year three, we multiplied by .6086, year four, we multiplied by .5158,  now you can see the present value of the cash flows is calculated below. So  3.411 million times 0.8475 gives us 2.890, million, etc. You can see the  calculations the 4.070 million is multiplied by the .7182, etc. So that gives us a  total present value of cash inflows of 10.888 million. We'll subtract out our initial  investment of 8.32 million, and we will be left with a net present value of 2.568  million. So we are looking pretty strong here, and should accept this project. So  what are some strengths and weaknesses of net present value? Net Present  Value accounts for the time value of money, which makes it a sounder approach  than any other investment appraisal technique which do not discount future cash flow such as payback period and accounting rate of return, net present value is  even better than some other discounted cash flow techniques, such as IRR, in  situations where IRR and Net Present Value give conflicting decisions, Net  Present Value decision should be preferred some weaknesses of NPV. Net  Present Value is, after all, an estimation. It is sensitive to changes in estimates  for future cash flows, salvage value and the cost of capital. Net Present Value  does not take into account the size of the project. For example, say, Project A  requires initial investment of 4 million to generate a net present value of 1  million, while competing project B requires 2 million investment to generate a net present value of 800,000 if we base our decision on NPV alone, we will we will  prefer project A because it has a higher NPV, but project B has generated more  shareholders wealth per dollar of initial investment, 800,000 divided by 2 million  versus 1 million, over 4 million.