1. 1 Teaching Net Present Value (NPV) and Future Value (FV) BUS 401 Name Date Instructor

2. Net Present Value (NPV)  NPV is used to compare the value of money that is to be received in the future with the present value of the same amount of money (Hickman, K. and Byrd, J. 2013)  The value of money changes with time. NPV is calculated while making investment decision in order to factor in changes in the value of money in the decision making process.  A given amount of money will have less worth in the future than in the present in any situation. 2

3. Reasons for Time Value of Money  A dollar will always have low value in the future than in the present because: 1. People would rather consume money in the present than in the future (Hickman, K. and Byrd,2013) 2. Monetary inflation means that the same amount of money would purchase few items in the future (Fabozzi & Markowitz, 2002). 3. Uncertainty of future events exposes the investment to significant risks. 3

4. Calculating the NPV  Obtain the cash outflows from the investments.  Get the net cash flow for each period by subtracting the cash outflows from the cash inflows.  Determine the discounting rate. The discounting rate represent the cost at which present benefits are traded for future benefits (Dayananda, 2002).  The discounting also represent the opportunity cost as factors the gains that the investor would have made if he would have undertaken a different project (Chass, 2005). 4

5. Determine the Discounting Rate  The following factors will affect the value of the discounting rate: 1. Preferences for present consumption. 2. The opportunity cost of the investment (Fabozzi & Markowitz, 2002). If there are other numerous projects that the money can be directed to in the present then a higher discount rate is required to cater for the opportunity cost. 5

6. Determine the Discounting Rate  The following factors will affect the value of the discounting rate: Cont’d 3. The expected inflation rate. If a high inflation rate is expected in the future, a high discounting rate is required to compensate for the loss in monitory value. 4. The uncertainty concerning future events (Fabozzi F. & Markowitz, 2002). Investments that have a high level of uncertainty require a high discounting rate to cater for the risks involved in making the investment. 6

7. Discounting  Discounting is the process of converting future cash flow into the present value (Dayananda, 2002). The following formulae is used:  Lump Sum  NPV={ FC /(1+i) n } – Initial Investment  Annuity  NPV = { FC 1 / (1+ i) 1 + FC 2 / (1+i) 2 + FC 3 / (1+i) 3 +…. FC n / 1 + i) n } – Initial Investment Where: FC= Net value of Future Cash flow i= Discounting rate n= Number of years 7

8. Using NPV in Stock Investment Decisions  Investor can use the NPV concept to make stock investment decision. However, stocks are unique investments since they have no definite period. Investments that post returns over an infinite period are known as perpetuity (Dayananda, 2002). Perpetuity have cash flow stream that continue forever. The formulae for calculating the NPV of a perpetuity is as follows: NPV = FV/ r Where FV= Future value r= Required rate of return/ discounting rate 8

9. Using NPV in Stock Investment Decisions  In the case of stock investment, the dividends paid on stock represent the future value of the investment.  Investment in stock can also record gains through the growth of stock. The value of stock may grow over time thus resulting in returns for the investor.  The NPV formulae factors this grow by deducting the growth rate from the required rate of return  Thus, NPV= Div/ (r-g)  Where g = growth rate 9

10. Illustration  A stock pays an average dividends of $1. The stock has a potential growth rate of 5% per annum. What is maximum price that the investor should pay if the required rate of return is 10% NPV= Div/ (r-g) NPV= 1/ (0.1- 0.05) NPV= 1/ 0.05 = $ 20  The NPV calculation suggest that $ 20 is the maximum price that can give the investor a return rate of 10% 10

11. Future Value (FV)  The concept of future value uses the same principles as the Net Present Value. It involves calculating the value of present cash flow in the future. (Dowd, K. 1990).  Calculating the Future Value helps an investor to factor the time value of money when making investment decisions.  The process of converting present cash flow into future value is known as compounding (Peavler, 2010) 11

12. Compounding Lump Sum FV = PV(1 + i) n  This formulae is used when the present value is paid once. In this case, only one present value is compounded (Peavler, 2010). Where PV= Present Value i= Interest rate n= Time period Illustration  Let say we deposit $ 10,000 in a bank that pay an interest at the rate of 5% per annum for period of 5 years. FV= 10,000 (1 + 0.05) 5 FV =12,762. 82 12

13. Compounding Annuity  FV = PV 1 (1+i) 1 + PV 2 (1+i) 2 …..+ PV n (1 +i) n  This formulae is used when regular payments are made into the investment. Where PV= Present Value i= Rate of Interest n= time period Illustration We deposit $8,000 every year for 3 years in a bank that pays an interest of 10% per annum. FV= 8000 (1+ 0.1)+ 8000 (1+ 0.1) 2 + 8000 (1+0.1) 3 FV= 8,800 + 9,680 + 10,648= $29, 128 13

14. Using FV in Stock Investment Decision  The concept of future value can also be used to make stock investment decision when an investor plans to hold a stock for a given period and then sell the stock (Dayananda, 2002).  In this case, the investor will use the annuity formulae to calculate the future value  For instance, An investors plans to purchase a stock that goes for $ 15 and hold it for a period of five years. The stock yields an average dividend of $1. What will be the future value of this investment if the stock grows at the rate of 5% per annum.  The first step is to determine the compounding rate. The compounding rate may be determined by factors such as; interest rate, if the investor plan to deposit the dividend in a bank. 14

15. Using FV in Stock Investment Decision  The compounding rate may also be determined by the rate of return, if the investor plans to channel the dividends into another investment. The rate in this case has been set at 10  FV= 1(1+ 0.1) 1 + 1(1 +0.1) 2 + 1(1+0.1) 3 + 1(1+0.1) 4 + 1(1 + 0.1) 5 + 15 (1+0.05) 5  FV= 1.1 + 1.21 + 1.33 + 1.46 + 1.61 + 15.38  FV= $ 22.09  The FV calculation indicate that the investor will receive a total value of $ 22.09 from the stock at the end of five years. 15

16. References Chass U. (2005). Present Value and the Opportunity Cost. June 27, 2013. Retrieved from the ProQuest database Dayananda D. (2002).Financial Appraisal and Capital Budgeting of Investment Project. USA. Cambridge University Press Dowd, K. (1990). The value of time and the transactions demand for money. Journal of Money, Credit, and Banking, 22(1), 51-51. Retrieved from the ProQuest database Hickman, K.A., Byrd, J. W. & McPherson, M. (2013). Essentials of finance. San Diego, CA:Bridgepoint Education Inc. Peavler R. (2010). How to Calculate the Future Value of an Investment. June 27, 2013. http://bizfinance.about.com http://bizfinance.about.com Fabozzi F. & Markowitz H. (2002). The Theory and Practice of Investment Management. USA. John Wiley and Son 16