1. THE TIME VALUE OF MONEY TVOM is considered the most Important concept in finance because we use it in nearly every financial decision

2. THE FOUR BASIC TVOM EQUATIONS 1.Future Value of Single SumFuture Value of Single Sum 2.Present Value of Single SumPresent Value of Single Sum 3.Future Value of an AnnuityFuture Value of an Annuity 4.Present Value of an AnnuityPresent Value of an Annuity

3. Time-value-of-money operations employ the same five pieces of information 1.Periodic interest rate (I) 2.Number of periods (N) 3.Periodic payment (PMT) 4.Present value (PV) Or Future value (FV) 5.Payment is at the beginning or end of period Given any four of these operations, you should be able to solve for the fifth unknown quantity.

4. Future value (FV) of a single sum Example (multiple periods ): How much will I receive (will accumulate ) at the end of 3 years if I invest a single sum of $ 50 today at 8% interest compounded annually?

5. as:

10. Example (interest is compounded monthly): Referring back to our previous example ($50 compounded annually at 8% for multiple period), determine how much will I accumulate by the end of 3 years if interest is compounded monthly.

12. Present Value Present Value of a Lump Sum Example : How much should I be paid today for the future value of $62.99 received at the end of three years, assuming that an 8% return compounded yearly is required?

15. Future Value Annuity Compound or Future Value of an Ordinary Annuity The future value of an ordinary annuity is used in determining the amount to which a constant periodic investment (payment) of a specified amount will grow, assuming compound growth at a specified return for a specified number of compounding periods. The periodic payments are assumed to be made at the end of each period.

16. Example (annual compounding): An investor plans to deposit $1,000 at the end of each year in an account for a period of 5 years and interest is compounded at an annual rate of 5%. What is the future value of this series of deposits at the end of 5 years? To solve this problem, first clear all information from your spreadsheet template except the input section labels. Then enter the new assumption information into the input section of the template as shown.

19. PMT Accumulation of a Future Sum (Sinking Fund) PMT The accumulation of a future sum, or sinking fund calculation is used to determine the level payment required to be periodically invested at the end of each period and compounded at a specific rate to grow to some specified amount over a specific time period.

23. Due PMT Future Value of an Annuity Due PMT start at the beginning of the period Annuities can also be assumed to start at the beginning of the period. Such an annuity is referred to as an annuity due.

26. Present Value of an Annuity Due

29. Determining (Yields) Interest Rates (internal rates of return) on investments

33. NPV Present Value of an Uneven Series (NPV): If you want to estimate the present value of a variable cash flow forecast then, you must find the sum of the present values of the income for each year.

36. Net Present Value (NPV) The net present value (NPV) is defined as the difference between the present value of the cash inflows from an investment and the present value of the cash outflows.

38. Internal Rate of Return (IRR) The internal rate of return (IRR) is the rate of return that equates the present value of the cash inflows and the present value of the cash outflows.

42. Amortized Loans — Most consumer loans, such as mortgages and automobile loans, and some business loans are amortized, which means that the loan agreement requires equal periodic payments, a portion of which constitutes interest on the debt and the remainder is applied to the repayment of the debt.

43. It is important to understand what portion of the payment is interest and what portion is repayment of debt, because, when applicable, only the interest portion is considered an expense for tax purposes. A business owner reports interest as a deductible cost while the lender reports the same amount as taxable income

44. Example: Computing Monthly Amortization on Loans You want to purchase a car worth $1, 00,000. You are asked to put up 30% of the purchase price, and use bank financing for the balance of &70,000 for a five-year loan with monthly amortization. How much do you have to pay every month? If interest is 0.12 per year. Using the PMT function in Excel we can compute the monthly amortization as follows:

45. Things to note in PMT inputs: a. For the Rate, the per annum interest rate (0.12) must be divided by the number of payments made in a year, which in our case is 12 because we required monthly amortization. In the event of quarterly payments, we can divide by 4 and so on. b. For the Nper, we had to multiply the number of years by 12 months in order to get the number of payment periods. In our example, five years times 12 payments in a year makes a total of 60 payment periods. c. For PV, we still had to use –B2 in order to get a logical amortization answer.. In the loan amortization table. The point is to highlight that at the 60th (last) payment period, the monthly amortization payment is equal to the interest due plus the principal at the beginning of the period. Thus, the loan would have been fully paid.

49. An extension of this simple example is when the client is given the option to either pay at the end of the period or at the beginning of the period. Basically, the choice is whether the client makes the first payment a month from now or today. The only change that has to be made is by adding 1 to the Type value, which essentially adjusts the calculation to reflect that the first payment was made at the beginning of the period.

54. Modified Internal Rate of Return (MIRR)