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

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

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

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

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

The functions of financial markets 1. Conducting exchange 2. Providing liquidity 3. Pooling money to fund large corporations 4. Transferring money across time and distance 5. Risk management (hedge, diversify) 6. Providing information 7. Providing efficient allocation of money

Conducting exchange What does it mean ? Examples

Providing liquidity What does this mean? Examples

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

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

Risk management What does this mean? Examples

Providing information What does this mean? Examples

Providing efficient allocation of money What does this mean? Examples

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.

What is the cost of capital? Cash Investment opportunity (real asset) FirmShareholder Investment opportunities (financial assets) InvestAlternative: pay dividend to shareholders Shareholders invest for themselves

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

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

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

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

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.

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

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 = Year one $100 PV=?

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 = Year 5 $100 PV=?

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 = Year 20 $100 PV=?

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.

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) /(1.09) 2 = Year one $100 PV=? $100 Year two

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) /(1.09) /(1.07) 3 = Yr 1 $100 PV=? $50 Yr 3Yr 2 $200

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: Initial investment (negative cash flows) Expected cash flows in year one (probably positive) Expected cash flows in year two (probably positive)

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).

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?

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.

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

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 = Yr 0 Yr 1Yr 2 $10$50 -$50

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

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

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?

Calculate the NPV at each economy In the boom economy, the NPV is / / / =$2.36 In the average economy, the NPV is / / / =-$0.613 In the bust economy, the NPV is / / / =-$2.87 The expected NPV is 0.2* *(-.613)+0.3*(-2.87)=-$0.696

Calculate the expected cash flows at each time At period 1, the expected cash flow is C 1 =0.2*8+0.5*7+0.3*6=$6.9 At period 2, the expected cash flow is C 2 =0.2*3+0.5*2+0.3*1=$1.9 At period 3, the expected cash flows is C 3 =0.2*3+0.5* *0.9=$1.62 The NPV is NPV= / / / =-$0.696

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? PV ??? CCCCCC Yr1 Yr2Yr3Yr4Yr5Time=infinity

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

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

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

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.

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 ? CCCCCC t+1 t+2t+3t+4T+5Time=t+infYr0

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 ?

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

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? PV ??? CCCCCC Yr1 Yr2Yr3Yr4Yr5Time=T

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

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) ?

My solution Using the formula for the annuity

FIn 351: Lecture 3 Example You agree to lease a car for 4 years at $300 per month. You are not required to pay any money up front or at the end of your agreement. If your opportunity cost of capital is 0.5% per month, what is the cost of the lease?

Solution

Lottery example Paper reports: Today’s JACKPOT = $20mm !! paid in 20 annual equal installments. payment are tax-free. odds of winning the lottery is 13mm:1 Should you invest $1 for a ticket? assume the risk-adjusted discount rate is 8%

My solution Should you invest ? Step1: calculate the PV Step 2: get the expectation of the PV Pass up this this wonderful opportunity

Mortgage-style loans Suppose you take a $20,000 3-yr car loan with “mortgage style payments” annual payments interest rate is 7.5% “Mortgage style” loans have two main features: They require the borrower to make the same payment every period (in this case, every year) The are fully amortizing (the loan is completely paid off by the end of the last period)

Mortgage-style loans The best way to deal with mortgage-style loans is to make a “loan amortization schedule” The schedule tells both the borrower and lender exactly: what the loan balance is each period (in this case - year) how much interest is due each year ? ( 7.5% ) what the total payment is each period (year) Can you use what you have learned to figure out this schedule?

My solution yearBeginning balance Interest payment Principle payment Total payment Ending balance $20,000 13,809 7,154 $1,500$6,191$7,691$13,809 1,0366, ,1547,6910 7,154

Future value The formula for converting the present value to future value: = present value at time zero = future value in year t = discount rate during the t years

Manhattan Island Sale Peter Minuit bought Manhattan Island for $24 in Was this a good deal? Suppose the interest rate is 8%.

Manhattan Island Sale Peter Minuit bought Manhattan Island for $24 in Was this a good deal? To answer, determine $24 is worth in the year 2003, compounded at 8%. FYI - The value of Manhattan Island land is well below this figure.

Inflation What is inflation? What is the real interest rate? What is the nominal interest rate?

Be consistent in how you handle inflation!! Use nominal interest rates to discount nominal cash flows. Use real interest rates to discount real cash flows. You will get the same results, whether you use nominal or real figures Inflation rule

Example You own a lease that will cost you $8,000 next year, increasing at 3% a year (the forecasted inflation rate) for 3 additional years (4 years total). If discount rates are 10% what is the present value cost of the lease?

Inflation Example - nominal figures

Inflation Example - real figures