1. Time Value of Money Dr. Himanshu Joshi

2. Finance Concepts Discussed Future Value Present Value Net Present Value Internal Rate of Return Pension and Savings plans and other accumulation problems.

3. Excel Functions Used FV,PV, NPV, IRR, PMT, NPER Goal Seek

4. Future Value Future value is the value at some date of a payment (or payments) made before this future date. The future value includes the interest earned on the payment. Example: you put $100 in a saving account in your bank today and that the bank pays you 6% interest at the end of every year. if you leave the amount in bank for two years, what is Future Value?

5. Future Value

7. Important Absolute Cell Referencing.

8. Future Value

9. Future Value at different rates

10. Accumulation-Savings Plans and Future Value In the previous example you deposited $100 and left it in your bank. Suppose that you intend to make ten annual deposit of $100, with the first deposit made in year 0 (today) and each succeeding deposit made at the end of years 1,2,….9. The future value of all these deposits at the end of year 10 tells you how much you will have accumulated in the account.

11. Accumulation-Savings Plans and Future Value If you are saving for the future (whether to buy a car at the end of your college years or to finance a pension at the end of your working life), this is obviously an important and interesting calculations.

12. Accumulation-Savings Plans and Future Value

13. Excel FV Function.. Excel has an FV function, which computes the future value of any series of constant payments. =FV(rate,nper,-pmt,,1) Or =FV(Int.Rate, Period, -Amount,,1)

14. Excel FV Function.. Formulas  fx Insert Function  Financial  FV PV is the present value, or the lump sum amount that a series of future series worth now, if omitted PV is 0. Type of a value representing the timing of payment: payment at the beginning of the period = 1; payment at the end of the period = 0, or omitted.

15. Beginning vs. End of Period (1 vs. 0) Beginning 0 1 2 3 4 5 6 7 8 9 10 $100 $100 $100 $100 $100

16. Beginning vs. End of Period (1 vs. 0) End 0 1 2 3 4 5 6 7 8 9 10 $100 $100 $100 $100 $100 $100 $100 $100 $100 $100

17. Present Value (PV) The Present Value is the value today of a payment that will be made in the future. Example: Suppose that you anticipate getting $100 in three years from now. suppose that the bank pays 6% interest on savings accounts. How much is the anticipated future payment worth today? $83.96 = 100/(1.06) 3

18. P.V

20. Present Value of an Annuity Recall that an annuity is a series of periodic payments. The present value of an annuity tells you the value today of all the future payments on the annuity. Suppose you have been promised $100 at the end of the next five years. Assuming that you can get 6% at the bank, this promise is worth $421.24 today.

21. PV of Annuity

22. The Excel P.V. Function The PV function calculates the present value of an annuity (a series of equal payments). = PV(rate, nper, pmt, (fv),(type))

23. The Excel NPV Function The NPV function computes the present value of a series of payments. The payments need not be equal. (this is the main differentiating factor with PV function). One of the most frequently used function in Excel. The present value concept can also be applied to non-annuity cash flow streams, meaning cash flows that are not the same every period?

24. The Excel NPV Function: Example Suppose, your father has promised to pay you $100 at the end of year 1, $200 at the end of year 2, and $300 at the end of year 3, $400 at the end of year 4, and $500 at the end of year 5. =NPV(rate, C 1 : C N )

25. Present Value Using NPV Function CALCULATING PRESENT VALUES WITH EXCEL r, Int. rate6% YearPayment at the end of yearPresent Value 110094.33962264 2200177.999288 3300251.8857849 4400316.8374653 5500373.6290864 PV1214.691247 Using Excel NPV Function$1,214.69

26. Important Note There is an important difference between the finance concept of net present value (NPV) and the excel NPV function. The Excel NPV function calculates the present value of the future cash flows, whereas the finance concept of NPV computes the present value of future cash flows minus the initial cash outflow.

27. NPV Example.. Would you pay $1500 today to get the series of future cash flows as $100,200,300,400, and 500 respectively at the end of 1,2,3,4,and 5 years? Would you pay $1000?

28. NPV Calculation Example: r, Int rate6% yearCash flowsPV of Cash flows 0-1000 110094.33962264 2200177.999288 3300251.8857849 4400316.8374653 5500373.6290864Decision NPV214.6912473Accepted Using Excel NPV Function214.691247282285

29. NPV depends on the Discount Rate Example: you have found an interesting investment-if you pay $800 today to your local pawnshop, the owner promises you to pay $100 at the end of year 1, $150 at year 2, $200,$250, and $300 at year 3,4,and 5 respectively. The pawnshop owner is as reliable as your local bank, which is currently paying 5% interest.

30. NPV Example Example:PawnShop Investment r, Int rate5% yearCash flowsPV of Cash flows 0-800 1100100.00 2150150.00 3200200.00 4250250.00 5300300.00Decision NPV200.00Accept Using Excel NPV Function44.79

31. NPV Profile

32. Internal Rate of Return The IRR of a series of cash flows is the discount rate that sets the net present value of cash flows equal to zero.

33. What does IRR Mean? The Internal rate of Return is the compound interest rate you earn on an investment. 6.70% yearCash flows PVFV at IRR 0-800 1100 93.72375100 2150 131.7621150 3200 164.6565200 4250 192.9028250 5300 216.9549300 NPV0.00013