1. LECTURE 2 and 3 MBA FINANCIAL MANAGEMENT 1 Lecturer: Chara Charalambous

2. AGENTA Basic principle of finance: Time Value of Money Introduction to Present Value and Future Value Annuities Foundations of the Net Present Value Rule What is Capital Budgeting? 2 Lecturer: Chara Charalambous AGENTA

3. Lecturer: Chara Charalambous 3 Which would you prefer – $10,000 today or $10,000 ten years from today?

4. Answer: Common sense tells us to take the $10,000 today because we recognize that there is a time value of money. The immediate receipt of $10,000 provides us with the opportunity to put our money to work and earn interest. In a world in which all cash flows are certain, the rate of interest can be used to express the time value of money. Interest: Money paid (earned) for the use of money. 4 Lecturer: Chara Charalambous

5. 5 “Money doesn’t grow on trees.” While this is true, money does make more money, if it collects interest. Interest is money that one pays for the use of someone else’s money. Most people know that if you put money in a bank, you will get more money over time. The bank is paying you to use your money for investments and loans. There are two types of interest: basic interest and compound interest.

6. Definition of 'Time Value of Money - TVM' Lecturer: Chara Charalambous 6 The idea that money available at the present time is worth more than the same amount in the future due to its possible earning capacity. This core principle of finance means that money can earn interest when invested and so any amount of money is worth more the sooner it is received. Basic Finance Rule: ‘A dollar received today worth more than a dollar expected to receive in future’ because the sooner a dollar received the quicker it can be invested to earn a positive return. The time value of money is the central concept in finance theory.

7. Money received sooner rather than later allows one person to use the funds for investment or consumption purposes. This concept is refer to as the TIME VALUE OF MONEY. 7 Lecturer: Chara Charalambous

8. 8 There are two types of interest: basic/simple interest and compound interest. We will also examine the use of these two kinds of interest in the value of money in the present and in the future.

9. 1. Simple interest is interest that is paid (earned) on only the original amount, or principal, borrowed (or lent). The dollar amount of simple interest is a function of three variables: the original amount borrowed (lent), or principal; the interest rate per time period; and the number of time periods for which the principal is borrowed (lent). The formula for calculating simple interest is: SI = P0(i )(n) where SI = simple interest in dollars P0 = principal, or original amount borrowed (lent) at time period 0 i = interest rate per time period n = number of time periods 9 Lecturer: Chara Charalambous

10. 10 For example, you may lend $100 to a friend and ask for 10% (0.1) interest every year until you are repaid. If your friend pays you back in two years, your friend will owe you $120.

11. 2. Present and Future Value Present Value: Value today of a future cash flow. Future Value: Amount to which an investment will grow after earning interest. For example, assume that you deposit $100 in a savings account paying 8 percent simple interest and keep it there for 10 years. At the end of 10 years, the amount of interest accumulated is determined as follows: $80 = $100(0.08)(10) To find the future value of the account at the end of 10 years (FV10), we add the interest earned on the principal only to the original amount invested. Therefore: FV10 = $100 + [$100(0.08)(10)] = $180 11 Lecturer: Chara Charalambous

12. 12 So the equation for the future value can be written as: FV=100(1+0.08*10)= $180 FV= PV(i+1) FV = Future Value PV = Present Value – the money invested - the capital i = the interest rate or r = the rate of return on the money invested

13. Lecturer: Chara Charalambous 13 3. Compound Interest : Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent or invested). It is this interest-on-interest, or compounding. Some people have called compound interest the greatest of human inventions. Compound interest can be used to solve a wide variety of problems in finance.  If you choose to invest the amount of $10,000 at a simple annual rate of 4.5%, the future value of your investment at the end of the first year is $10,450: Future value of investment at end of first year: = ($10,000 x 0.045) + $10,000 = $10,450 Can be written as: $10,000 x [(1 x 0.045) + 1] => 10,000*(0.045+1)= 10,450

14. Lecturer: Chara Charalambous 14 If the $10,450 left in your investment account at the end of the first year is left untouched and you invested it at 4.5% for another year, how much would you have? To calculate this, you would take the $10,450 and multiply it again by 1.045 (0.045 +1). At the end of two years, you would have $10,920: Future value of investment at end of second year: = $10,450 x (1+0.045) = $10,920.25 The above calculation, then, is equivalent to the following equation: Future Value = $10,000 x (1+0.045) x (1+0.045) The equation can be represented as the following:

15. Lecturer: Chara Charalambous 15 If we were investing our money for 3 years the equation would be: 10,000*(1+0.045) = $11,411.66 So the equation for the future value can be written as FV= PV(i+1) FV = Future Value PV = Present Value – the money invested-the capital i = the interest rate n = the number of years or periods I have invested my money n The process of going from today’s values, or present values (PV), to future values (FV) is called compounding. 3

16. Present Value Basics If you received $10,000 today, the present value would of course be $10,000 because present value is what your investment gives you now if you were to spend it today. If $10,000 were to be received in a year, the present value of the amount would not be $10,000 because you do not have it in your hand now, in the present. To find the present value of the $10,000 you will receive in the future, you need to pretend that the $10,000 is the total future value of an amount that you invested today. In other words, to find the present value of the future $10,000, we need to find out how much we would have to invest today in order to receive that $10,000 in the future. In order to calculate present value, or the amount that we would have to invest today, we are going to use the FV equation but this time the unknown number it will be the PV. So we will follow the steps below : Original equation : FV= PV(i+1) => PV = FV (i+1) Lecturer: Chara Charalambous 16 n n The factor 1 is called the discounting factor or present value factor (i+1) n US termin ology

17. Remember, the $10,000 to be received in three years is really the same as the future value of an investment So, here is how you can calculate today's present value of the $10,000 expected from a three-year investment earning 4.5%: PV = FV = 10,000 = $8762.97 (i+1) (0.045+1) Lecturer: Chara Charalambous 17 n3

18. Discount Factors and Rates Discount rate: Interest rate used to compute present values of future cash flows. The rate used is the rate of return offered by equivalent investment alternatives in the capital market. It is also called opportunity cost of capital because it is the return foregone by investing in the project rather than investing in securities of comparable risk. Discount Factor :Present value of a $1 future payment. Definition: opportunity cost is the potential benefit that is given up when one alternative is selected over another 18 Lecturer: Chara Charalambous

19. Discount Factor = DF = PV of $1 Discount Factors can be used to compute the present value of any cash flow. DF= 1 (1+r) PV=DF x C 1 t n 19 Lecturer: Chara Charalambous

20. Time Lines One of the most important tools in time value of money analysis is the time line, which is used to help us picture what is happening in a particular situation. Time 0 is today, Time 1 is one period from today (e.g. one year), Time 2 is two periods from today 20 Lecturer: Chara Charalambous TIME:

21. Time Lines Here the interest rate if I invest my money for each of the four periods is 5%. A cash outflow is a payment of cash for investments and is made at Time 0: because is money given out of my pocket it has a minus sign. At Time 4 I have a cash inflow : a receipt of cash from an investment. The inflow is unknown to me and I have to find it thus I symbolize it with ? And is a positive amount (+) because I will receive money in my pocket. Note that no cash flows occur at Time 1,2 and 3. 21 Lecturer: Chara Charalambous -100 Cash outflow: Cash inflow: + ? 5% TIME:

22. Interest Tables Lecturer: Chara Charalambous 22 These tables, called (appropriately) future value interest factor (or terminal value interest factor) tables and PV interest factor tables, are designed to be used with Equation of FV and PV (slide 16).Tables following are one example covering various interest rates ranging from 1to 5 percent. For example, the future value interest factor at 3 percent for five years (FVIF3%,5) is located at the intersection of the 3% column with the 5-period row and equals 1.1593.

23. Interest Tables  The Future Value Interest Factor for i and n is defined as (1 + i), and these factors can be found using a table: Period 1% 2% 3% 4% 5% 6% 1 1.0100 1.0200 1.0300 1.0400 1.0500 1.0600 2 1.0201 1.0404 1.0609 1.0816 1.1025 1.1236 3 1.0303 1.0612 1.0927 1.1249 1.1576 1.1910 4 1.0406 1.0824 1.1255 1.1699 1.2155 1.2625 5 1.0510 1.1041 1.1593 1.2167 1.2763 1.3382 Lecturer: Chara Charalambous 23 n

24. Interest Tables The Present Value Interest Factor for i and n is defined as 1/(1 + i), and these factors can be found using a table: Period 1% 2% 3% 4% 5% 6% 1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 2 0.9803 0.9612 0.9426 0.9246 0.9070 0.8900 3 0.9706 0.9423 0.9151 0.8890 0.8638 0.8396 4 0.9610 0.9238 0.8885 0.8548 0.8227 0.7921 5 0.9515 0.9057 0.8626 0.8219 0.7835 0.7473 Lecturer: Chara Charalambous 24 n

25. Annuity An annuity represents series of equal payments (or receipts) occurring for a specified number of equity distant periods. Ordinary Annuity Ordinary Annuity: Payments or receipts occur at the end of each period. Annuity Due Annuity Due: Payments or receipts occur at the beginning of each period Lecturer: Chara Charalambous 25

26. Examples of Annuities Student Loan Payments Car Loan Payments Insurance Premiums Mortgage Payments Retirement Savings Pensions 26 Lecturer: Chara Charalambous

27. Parts of an Annuity 0 1 2 3 $100 $100 $100 (Ordinary Annuity) End End of Period 1 End End of Period 2 Today Equal Equal Cash Flows Each 1 Period Apart End End of Period 3 27 Lecturer: Chara Charalambous

28. Parts of an Annuity 0 1 2 3 $100 $100 $100 (Annuity Due) Beginning Beginning of Period 1 Beginning Beginning of Period 2 Today Equal Equal Cash Flows Each 1 Period Apart Beginning Beginning of Period 3 28 Lecturer: Chara Charalambous Or Annuity in Advance

29. What is the difference between an ordinary annuity and an annuity due? Ordinary Annuity PMT 0123 i% PMT 0123 i% PMT Annuity Due 29 Lecturer: Chara Charalambous

30. Example 1 :If I deposit $1000 at the end of each year for 3 years in a saving account that pays 7% interest per year, how much will I have at the end of the 3 years? Lecturer: Chara Charalambous 30

31. FVA 3 $3,215 FVA 3 = $1,000(1.07) 2 + $1,000(1.07) 1 +$1,000(1.07) 0 = $1,145 +$1070 +$1000= $3,215 Example of an Ordinary Annuity -- FVA $1,000 $1,000 $1,000 3 0 1 2 3 4 $3,215 = FVA 3 7% $1,000 $1,145 Cash flows occur at the end of the period 31 Lecturer: Chara Charalambous $1,070

32. FVA = PMT(1+i) + PMT(1+i) +…+ R(1+i) +PMT(1+i) => FVA = PV (1+i) – 1 i Lecturer: Chara Charalambous 32 0 n-1 n n n n-2 1

33. Example 2 :If I deposit $1000 at the beginning of each year for 3 years in a saving account that pays 7% interest per year, how much will I have at the end of the 3 years? Lecturer: Chara Charalambous 33

34. FVAD3 = $1,000(1.07) + $1,000(1.07) + $1,000(1.07) = $1,225 + $1,145 + $1,070 = $3,440 = $1,225 + $1,145 + $1,070 = $3,440 Example of an Annuity Due -- FVAD $1,000 $1,000 $1,000 $1,070 3 0 1 2 3 4 $3,440 = FVAD 3 7% $1,225 $1,145 Cash flows occur at the beginning of the period 3 2 1

35. FVAD n => FVAD n = R(1+i) n + R(1+i) n-1 +... + R(1+i) 2 + R(1+i) 1 => FVA = PV (1+i) – 1 * (1+i) i Lecturer: Chara Charalambous 35 n

36. Example 3: you are offered a 3-year annuity with payments of $ 1000 at the end of each year. So you have to deposit the payments in a saving account that pays 7% interest per year. How much you have to deposit today? Lecturer: Chara Charalambous 36

37. PVA 3 PVA 3 = $1,000 / (1.07) 1 + $1,000 / (1.07) 2 + $1,000 / (1.07) 3 = $934.58 + $873.44 + $816.30 $2,624.32 = $2,624.32 Example of the Present Value of an Ordinary Annuity $1,000 $1,000 $1,000 3 0 1 2 3 4 $2,624.32 = PVA 3 7% $934.58 $873.44 $816.30 Cash flows occur at the end of the period

38. PVA n PVA n = R/(1+i) 1 + R/(1+i) 2 +... + R/(1+i) n => PVA n PVA n =FV 1-1/(1+i) i Lecturer: Chara Charalambous 38 n

39. Example 3: you are offered a 3-year annuity with payments of $ 1000 at the beginning of each year. So you have to deposit the payments in a saving account that pays 7% interest per year. How much you have to deposit today? Lecturer: Chara Charalambous 39

40. PVAD n $2,808.02 PVAD n = $1,000/(1.07) 0 + $1,000/(1.07) 1 + $1,000/(1.07) 2 = $2,808.02 Example of an Annuity Due -- PVAD $1,000.00 $1,000 $1,000 3 0 1 2 3 4 $2,808.02 PVAD n $2,808.02 = PVAD n 7% $ 934.58 $ 873.44 Cash flows occur at the beginning of the period

41. PVA n PVA n = R/(1+i) 0 + R/(1+i) 1 +... + R/(1+i) n-1 => PVA n PVA n =FV 1-1/(1+i) * (1+i) i Lecturer: Chara Charalambous 41 n

42. Net Present Value and Other Investment Criteria Lecturer: Chara Charalambous 42

43. 1.Net Present Value (NPV) Net present value (NPV): The present value of an investment project’s net cash flows minus the project’s initial cash outflow. C is usually a negative number, since it refers to the invested amount of money, i.e. it is an outflow. NPV= - C+ C (1+r) Acceptance Criterion. If an investment project’s net present value is zero or more, the project is accepted; if not, it is rejected. Another way to express the acceptance criterion is to say that the project will be accepted if the present value of cash inflows exceeds the present value of cash outflows. o o 1 43 Lecturer: Chara Charalambous AN INVESTMENT CRITERION

44. Net Present Value Rule Accept investments that have positive net present value Example : Suppose we can invest $50 today and receive $60 in one year. Should we accept the project given a 10% expected return? NPV = -50 + 60 = $4.55 1.10 44 Lecturer: Chara Charalambous

45. Valuing an Office Building  Step 1: Forecast cash flows Cost of building = C = 370,000 Sale price in Year 1 = C = 420,000  Step 2: Estimate opportunity cost of capital If equally risky investments in the capital market offer a return of 5%, then Opportunity Cost of capital = r = 5%=required rate of return The opportunity cost of capital is the expected rate of return forgone by not choosing other potential investment activities. It is a rate of return that investors could earn in financial markets making equally risky investments. The cost of an alternative that must be forgone in order to pursue a certain action. Put another way, the benefits you could have received by taking an alternative action. o 1 45 Lecturer: Chara Charalambous

46. Step 3: Discount future cash flows PV= 420000 = 400000 (1+0.05)  Step 4: Go ahead if PV of payoff exceeds investment NPV= -370000+400000=30000 NPV= -C + C (1+r) 0 1 46 Lecturer: Chara Charalambous

47. 2nd Basic Principle in Finance “A safe dollar is worth more than a risky one.” 47 Lecturer: Chara Charalambous

48. 2.Risk and Present Value  Basic Principle n Finance “A safe dollar is worth more than a risky one.”  Higher risk projects require a higher rate of return  Higher required rates of return cause lower PVs PV of C = $420000 at 5% PV= 420000 = 400000 (1+0.05) PV of C = $420000 at 12% PV= 420000 = 375000 (1+0.12) NPV= -370000+375000=5000 1 48 Lecturer: Chara Charalambous 1

49. 3.Rate of Return Rule Acceptance Criterion: Accept investments that offer rates of return in excess of their opportunity cost of capital Return = profit investment Example: In the project of previous example, the foregone investment opportunity is 12%. Should we do the project? 420000-370000 =0.135 or 13.5% 3700000 49 Lecturer: Chara Charalambous

50. 50 4.Internal Rate of Return Rule It is an interest rate This is the most important alternative to NPV It is often used in practice and is instinctively attractive It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere

51. 51 IRR – Definition and Decision Rule Definition: IRR is the return that makes the NPV = 0 NPV= - C + C = 0 r=? I have to find it (1+r) Decision Rule: Accept the project if the IRR is greater than the required return. Because it means It is giving us more than we have claimed. 0 1

52. Example: If an investment may be given by the series of the following cash flows : Lecturer: Chara Charalambous 52 YearCash Flow 0 -123400 1 36200 2 54800 3 48100 Then the IRR ( r ) is given as follows: In this case, the answer is 5.96% (in the calculation, that is, r =.0596).

53. 53 Computing IRR For the Project If you do not have a financial calculator, then this becomes a trial-and-error process. NPV vs. IRR NPV and IRR will generally give us the same decision

54. Goals of the Corporation Shareholders desire wealth maximization. This is achieved if the financial managers choose projects with positive NPV. The goal of the financial manager is NOT to maximize the profits. But to maximize shareholders wealth. 54 Lecturer: Chara Charalambous

55. 55 NPV Decision Rule If the NPV is positive, accept the project A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners. Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal. So NPV is one of the tools that Financial Managers use.

56. ALL THE PREVIOUS KNOWLEDGE STUDIED FOR THE PURPOSE OF CAPITAL BUDGETING: Financial Managers have to know all the previous materials in order to do capital budgeting. Lecturer: Chara Charalambous 56 What is 'Capital Budgeting‘?. The process in which a business determines whether projects such as building a new plant or extending an existing plan or investing in a long-term venture are worth pursuing. Many times a forthcoming project's lifetime cash inflows and outflows are assessed in order to determine whether the returns generated meet a sufficient target benchmark. In other words is the process of making and managing expenditures on long-term assets, Also known as "investment appraisal." Ideally, businesses should pursue all projects and opportunities that enhance shareholder value. However, because the amount of capital available at any given time for new projects is limited, management needs to use capital budgeting techniques to determine which projects will yield the most return over an applicable period of time. Popular methods of capital budgeting include net present value (NPV), internal rate of return (IRR), discounted cash flow (DCF) and payback period. One of the primary goals of capital budgeting investments is to increase the value of the firm to the shareholders.

57. Lecturer: Chara Charalambous 57 THANK YOU