# NPV - Net Present Value

What is the decision rule for NPV?

a. accept if NPV>0
b. accept if NPV>AAR
c. accept if NPV>cost
d. accept if NPV>target NPV
e. accept if NPV is negative, as long as IRR is positive

### Comments for NPV - Net Present Value

 Apr 26, 2013 NPV by: Staff Answer Part I The decision rule for NPV is choice "a": When the NPV is > 0, strongly consider accepting the project When the NPV is greater than zero, the investment/project being considered is projected add value to the company. NPV (Net Present Value) measures the time value of money. It is the net present value of all future cash flows for a particular investment. The NPV is the PV (present value) of all cash inflows minus the PV of all cash outflows. Because of this, the NPV is called a "difference amount". The NPV can be calculated using the following formula: i = marginal cost of money for the company          or i = discount rate (the rate of return the company expects with a project with similar risk) C1 is the net cash flow during the first period; C2 is the net cash flow during the second period;                      ∙                      ∙                      ∙ Cn is the net cash flow during the nth period The NPV can be easily calculated: 1. using a financial calculator. 2. using the NPV formula (shown above in blue) with an Excel spread sheet. 3. using the built in NPV function in an Excel spread sheet. -----------------------------------------

 Apr 26, 2013 NPV by: Staff ----------------------------------------- Part II For example, suppose an investment is expected to produce the following cash flow with a discount interest rate of 11%: Initial Investment: \$1000 time period 1: \$100 time period 2: \$500 time period 3: \$600 time period 4: \$300 time period 5: \$700 These values can be entered into an Excel spread sheet as shown below. Cash Flow is entered: cell B9 : -1000 cell B10 : 100 cell B11 : 500 cell B12 : 600 cell B13 : 300 cell B14 : 700 Discount Interest Rate is entered: cell C7 : 0.11 Formulas for computing the Present Value (PV) of the cash flow in each time period are entered: cell C9 : =B9 cell C10 : =B10*1/(1+\$C\$7) cell C11 : =B11*1/(1+\$C\$7)^2 cell C12 : =B12*1/(1+\$C\$7)^3 cell C13 : =B13*1/(1+\$C\$7)^4 cell C14 : =B14*1/(1+\$C\$7)^5 -----------------------------------------

 Apr 26, 2013 NPV by: Staff ----------------------------------------- Part III Formulas for combining the Present Value (PV) of the discounted cash flow for each time period are entered: cell C16 : =C9 cell C18 : =SUM(C10:C14) cell C20 : =C16+C18 Formula for computing the Net Present Value using the Excel built-in function "NPV" is entered: cell C23 : =NPV(C7,B10:B14)+B9 Regardless of whether the NPV is calculated using the general formula for NPV, or using the built-in Excel function, the result is the same. The results of both methods are shown and highlighted in purple as follows: -----------------------------------------

 Apr 26, 2013 NPV by: Staff ----------------------------------------- Part IV The ARR (Average Accounting Return) can also be used to evaluate projects being considered. However, it is should be noted that the ARR is not a true rate of return because is does not take the time value of money into account. The ARR (Average Accounting Return) can be calculated in a couple of different ways: 1) using the initial investment ARR_1 = the average annual accounting profit during the years of the investment, divided by the initial investment. 2) using the average book value of the investment. ARR_2 = the average annual accounting profit during the years of the investment, divided by the average book value of the investment. The average book value of the investment is the sum of the initial book value of the investment and the final book value of the investment, divided by 2. When a company uses the ARR to evaluate a project, the general rule of thumb is to accept the project if the ARR is greater than a target rate (or goal). The IRR (internal rate of return) is widely used to evaluate investments being considered. The IRR (internal rate of return) can be thought of as a break even interest rate. The IRR is the interest rate where the NPR equals zero. Internal rate of return (IRR) is the interest rate at which the net present value of all the cash flows (both positive and negative) from a project or investment equal zero. The IRR is calculated using exactly the same equation as the NPV. However, there is one major difference. Instead of using a known interest rate and solving for the NPV, the NPV (left side of the equation) is set to equal zero. The interest rate (IRR) is the unknown value. -----------------------------------------

 Apr 26, 2013 NPV by: Staff ----------------------------------------- Part V The IRR is difficult to calculate by hand because the equation is solved by iteration (trial and error). However, the IRR can be calculated using a financial calculator or the built-in function "IRR" provided by Microsoft Excel. Applying the "IRR" function to the example used to calculate the NPV: Applying the "IRR" function to the example cash flow used to calculate the NPV (above): cell B26 : =IRR(B9:B14) When this function is included on the Excel spread sheet used for the NPV example calculation, the results are as follows: The IRR calculation is convenient, but does have some major shortcomings. Beware of the fact that the IRR is the solution to a polynomial equation. When the future anticipated cash flows change signs more than once over the time periods being considered, the calculation of the IRR will yield two or more solutions. The IRR does not measure the size of the return, or the size of the initial investment. The IRR for an investment of \$7 which returns \$21 will be high. The IRR for an investment of \$250,000 which returns \$500,000 will not be as high. However, the \$250,000 investment is the better of the two. The IRR can't compare projects with differing life spans. The IRR does not take the cost of capital into account. Thanks for writing. Staff www.solving-math-problems.com