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Financial markets and time value of money

Learn about financial markets, the cost of capital, and the time value of money. Discover how to calculate present value and understand the relationship between inflation, interest rates, and investments.

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Financial markets and time value of money

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  1. Financial markets and time value of money Some important concepts FIn 351: Lecture 2

  2. Learning objective • Understand financial markets and their functions • Understand the concept of the cost of capital and the time value of money • Learn how to draw cash flows of projects • Learn how to calculate the present value of annuities • Learn how to calculate the present value of perpetuities • Inflation, real interest rates and nominal interest rates, and their relationship

  3. (2) (1) (4a) (4b) (3) (1) Investors buy shares with cash (2)Cash is invested (3) Operations generates cash (4a) Cash reinvested (4b) Cash returned to investors Financial markets and investors Investors Firm's Financial operations Manager (stockholders save and invest in closely held firm.) Real assets (timberland)

  4. Financial markets • A financial market • Securities are issued and traded • The classification of the financial market • By seasoning of claim • Primary market • Secondary market • By nature of market • Debt market • Equity market

  5. Financial markets (continue) • By maturity of claim • Money market • Capital market

  6. The functions of financial markets • Conducting exchange • Providing liquidity • Pooling money to fund large corporations • Transferring money across time and distance • Risk management (hedge, diversify) • Providing information • Providing efficient allocation of money

  7. Conducting exchange • What does it mean ? • Examples

  8. Providing liquidity • What does this mean? • Examples

  9. Pooling money to fund large corporation investments • What does this mean? • Examples

  10. Transferring money across time and distance • What does this mean? • Examples

  11. Risk management • What does this mean? • Examples

  12. Providing information • What does this mean? • Examples

  13. Providing efficient allocation of money • What does this mean? • Examples

  14. The cost of capital • The cost of capital is a very important concept in capital budgeting. • It links investment opportunities in financial markets and investment opportunities in real assets markets.

  15. What is the cost of capital? Cash Investment opportunity (real asset) Investment opportunities (financial assets) Firm Shareholder Invest Alternative: pay dividend to shareholders Shareholders invest for themselves

  16. Financial choices • Which would you rather receive today? • TRL 1,000,000,000 ( one billion Turkish lira ) • USD 652.72 ( U.S. dollars ) • Both payments are absolutely guaranteed. • What do we do?

  17. Financial choices • We need to compare “apples to apples” - this means we need to get the TRL:USD exchange rate • From www.bloomberg.com we can see: • USD 1 = TRL 1,186,899 • Therefore TRL 1bn = USD 843

  18. Financial choices with time • Which would you rather receive? • $1000 today • $1200 in one year • Both payments have no risk, that is, • there is 100% probability that you will be paid • there is 0% probability that you won’t be paid

  19. Financial choices with time (2) • Why is it hard to compare ? • $1000 today • $1200 in one year • This is not an “apples to apples” comparison. They have different units • $100 today is different from $100 in one year • Why? • A cash flow is time-dated money • It has a money unit such as USD or TRL • It has a date indicating when to receive money

  20. Present value • In order to have an “apple to apple” comparison, we convert future payments to the present values • this is like converting money in TRL to money in USD • Certainly, we can also convert the present value to the future value to compare payments we get today with payments we get in the future. • Although these two ways are theoretically the same, but the present value way is more important and has more applications, as to be shown in stock and bond valuations.

  21. Present value (2) • The formula for converting future cash flows or payments: = present value at time zero = cash flow in the future (in year t) = discount rate for the cash flow in year t

  22. Example 1 • What is the present value of $100 received in one year (next year) if the discount rate is 7%? • Step 1: draw the cash flow diagram • Step 2: think ! PV<?> $100 • Step 3: PV=100/(1.07)1 = $100 PV=? Year one

  23. Example 2 • What is the present value of $100 received in year 5 if the discount rate is 7%? • Step 1: draw the cash flow diagram • Step 2: think ! PV<?> $ • Step 3: PV=100/(1.07)5 = $100 PV=? Year 5

  24. Example 3 • What is the present value of $100 received in year 20 if the discount rate is 7%? • Step 1: draw the cash flow diagram • Step 2: think ! PV<?> $ • Step 3: PV=100/(1.07)20 = $100 Year 20 PV=?

  25. Present value of multiple cash flows • For a cash flow received in year one and a cash flow received in year two, different discount rates must be used. • The present value of these two cash flows is the sum of the present value of each cash flow, since two present value have the same unit: time zero USD.

  26. Example 4 • John is given the following set of cash flows and discount rates. What is the PV? • Step 1: draw the cash flow diagram • Step 2: think ! PV<?> $200 • Step 3: PV=100/(1.1)1 + 100/(1.09)2 = $100 $100 PV=? Year one Year two

  27. Example 5 • John is given the following set of cash flows and discount rates. What is the PV? • Step 1: draw the cash flow diagram • Step 2: think ! PV<?> $350 • Step 3: PV=100/(1.1)1 + 200/(1.09)2 + 50/(1.07)3 = $100 $200 $50 PV=? Yr 1 Yr 2 Yr 3

  28. Projects • A “project” is a term that is used to describe the following activity: • spend some money today • receive cash flows in the future • A stylized way to draw project cash flows is as follows: Expected cash flows in year one (probably positive) Expected cash flows in year two (probably positive) Initial investment (negative cash flows)

  29. Examples of projects • An entrepreneur starts a company: • initial investment is negative cash outflow. • future net revenue is cash inflow . • An investor buys a share of IBM stock • cost is cash outflow; dividends are future cash inflows. • A lottery ticket: • investment cost: cash outflow of $1 • jackpot: cash inflow of $20,000,000 (with some very small probability…) • Thus projects can range from real investments, to financial investments, to gambles (the lottery ticket).

  30. Firms or companies • A firm or company can be regarded as a set of projects. • capital budgeting is about choosing the best projects in real asset investments. • How do we know one project is worth taking?

  31. Net present value • A net present value (NPV) is the sum of the initial investment (usually made at time zero) and the PV of expected future cash flows.

  32. NPV rule • If NPV > 0, the manager should go ahead to take the project; otherwise, the manager should not.

  33. Example 6 • Given the data for project A, what is the NPV? • Step1: draw the cash flow graph • Step 2: think! NPV<?>10 • Step 3: NPV=-50+50/(1.075)+10/(1.08)2 = $50 $10 -$50 Yr 1 Yr 2 Yr 0

  34. Example 1 • John got his MBA from SFSU. When he was interviewed by a big firm, the interviewer asked him the following question: • A project costs 10 m and produces future cash flows, as shown in the next slide, where cash flows depend on the state of the economy. • In a “boom economy” payoffs will be high • over the next three years, there is a 20% chance of a boom • • In a “normal economy” payoffs will be medium • over the next three years, there is a 50% chance of normal • In a “recession” payoffs will be low • over the next 3 years, there is a 30% chance of a recession • In all three states, the discount rate is 8% over all time horizons. • Tell me whether to take the project or not

  35. Cash flows diagram in each state • Boom economy • Normal economy • Recession $3 m $8 m $3 m -$10 m $7 m $2 m $1.5 m -$10 m $6 m $1 m $0.9 m -$10 m

  36. Example 1 (continues) • The interviewer then asked John: • Before you tell me the final decision, how do you calculate the NPV? • Should you calculate the NPV at each economy or take the average first and then calculate NPV • Can your conclusion be generalized to any situations?

  37. Calculate the NPV at each economy • In the boom economy, the NPV is • -10+ 8/1.08 + 3/1.082 + 3/1.083=$2.36 • In the average economy, the NPV is • -10+ 7/1.08 + 2/1.082 + 1.5/1.083=-$0.613 • In the bust economy, the NPV is • -10+ 6/1.08 + 1/1.082 + 0.9/1.083 =-$2.87 The expected NPV is 0.2*2.36+0.5*(-.613)+0.3*(-2.87)=-$0.696

  38. Calculate the expected cash flows at each time • At period 1, the expected cash flow is • C1=0.2*8+0.5*7+0.3*6=$6.9 • At period 2, the expected cash flow is • C2=0.2*3+0.5*2+0.3*1=$1.9 • At period 3, the expected cash flows is • C3=0.2*3+0.5*1.5+0.3*0.9=$1.62 • The NPV is • NPV=-10+6.9/1.08+1.9/1.082+1.62/1.083 • =-$0.696

  39. Perpetuities • We are going to look at the PV of a perpetuity starting one year from now. • Definition: if a project makes a level, periodic payment into perpetuity, it is called a perpetuity. • Let’s suppose your friend promises to pay you $1 every year, starting in one year. His future family will continue to pay you and your future family forever. The discount rate is assumed to be constant at 8.5%. How much is this promise worth? C C C C C C PV ??? Yr2 Yr3 Yr4 Yr5 Time=infinity Yr1

  40. Perpetuities (continue) • Calculating the PV of the perpetuity could be hard

  41. Perpetuities (continue) • To calculate the PV of perpetuities, we can have some math exercise as follows:

  42. Perpetuities (continue) • Calculating the PV of the perpetuity could also be easy if you ask George

  43. Calculate the PV of the perpetuity • Consider the perpetuity of one dollar every period your friend promises to pay you. The interest rate or discount rate is 8.5%. • Then PV =1/0.085=$11.765, not a big gift.

  44. Perpetuity (continue) • What is the PV of a perpetuity of paying $C every year, starting from year t +1, with a constant discount rate of r ? C C C C C C Yr0 t+2 t+3 t+4 T+5 Time=t+inf t+1

  45. Perpetuity (continue) • What is the PV of a perpetuity of paying $C every year, starting from year t +1, with a constant discount rate of r ?

  46. Perpetuity (alternative method) • What is the PV of a perpetuity that pays $C every year, starting in year t+1, at constant discount rate “r”? • Alternative method: we can think of PV of a perpetuity starting year t+1. The normal formula gives us the value AS OF year “t”. We then need to discount this value to account for periods “1 to t” • That is

  47. Annuities • Well, a project might not pay you forever. Instead, consider a project that promises to pay you $C every year, for the next “T” years. This is called an annuity. • Can you think of examples of annuities in the real world? C C C C C C PV ??? Yr2 Yr3 Yr4 Yr5 Time=T Yr1

  48. Value the annuity • Think of it as the difference between two perpetuities • add the value of a perpetuity starting in yr 1 • subtract the value of perpetuity starting in yr T+1

  49. Example for annuities • you win the million dollar lottery! but wait, you will actually get paid $50,000 per year for the next 20 years if the discount rate is a constant 7% and the first payment will be in one year, how much have you actually won (in PV-terms) ?

  50. My solution • Using the formula for the annuity

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