Starting our journey through the Corporate Finance world Starting with an application: $1M Some “big picture” ideas Starting Chapter 4 Application ◼ ◼ How has the value of $1 million changed over the last three decades? Core ideas: Discounting and Inflation ◼ We will talk about inflation in more detail later Americans have been lured to the term “millionaire” ◼ ◼ ◼ ◼ Having a million dollars has caught the attention of Americans for decades However, inflation has decreased the value of $1,000,000 The lowered value of $1,000,000 has led to many game shows that offer a $1,000,000 prize Some examples ◼ ◼ ◼ Survivor Who Wants to Be a Millionaire? Jeopardy! Million Dollar Masters Tournament The $1,000,000 Chance of a Lifetime ◼ One of the first shows to offer a Million Dollar prize ◼ ◼ Aired from 1986-1987 Initially, 3 wins each against another couple and a bonus round paid $1,000,000 as follows ◼ ◼ $40,000 per year for 25 years A winner in 1986 should have received final payment in 2010 Why not give $1,000,000 all at once? ◼ $1,000,000 in June 1986 = $2,237,032 in June 2017 (based on CPI) ◼ ◼ This is a lot of money What is a way to lower the obligation? ◼ ◼ Pay out over time Payments made in the future are worth less than those made today Source: http://www.bls.gov/data/inflation_calculator.htm, July 22, 2017 Begin Unit 1 ◼ Introduction; valuation tools under certainty ◼ ◼ Note that we are generally in a world without risk in Unit 1 Uncertainty will be introduced in Unit 2 ◼ Today ◼ An introduction ◼ ◼ ◼ ◼ Firm types Cash flow Timing of cash flows Start Chapter 4 ◼ Probably the most important chapter in this course An introduction ◼ Types of firms ◼ ◼ Sole proprietorships and partnerships Corporations ◼ ◼ ◼ LLCs Cash flow issues ◼ ◼ Note double taxation When are firms constrained by available cash? Timing of cash flows ◼ Under what conditions do you take more money in the future? The “big picture” to remember ◼ ◼ There are different firm types In all types of business, we are trying to maximize the value of existing owners’ equity ◼ Many issues must be addressed to do this Timing of outflows vs. inflows ◼ ◼ Sometimes, a contract is signed such that a firm provides a good or service first and then the consumer pays for it This creates some issues that must be dealt with ◼ ◼ ◼ Accounting issues Cash availability Depreciation of cash Accounting issues ◼ Accountants view income from a sale when an agreement is made ◼ ◼ Sales versus costs The financial view deals with money flows ◼ ◼ Income is cash inflow minus outflow ◼ Accountants look at promised payments and promised money flows Financial person looks at actual money that changes hands Accounting issues ◼ Since this is a finance class, we will look at cash flows ◼ ◼ ◼ When do they occur? How do we value future payments versus the same payment made today? How do we incorporate risk of not receiving future payments? Cash availability ◼ ◼ ◼ ◼ Suppose you are in charge of a firm’s finances dealing with one contract Current cash on hand: $10 million You currently must pay $5 million in costs before you receive payment of $20 million in 1 year Should you accept more contracts? ◼ Maybe Cash availability ◼ Possible new contract ◼ $125 million paid over 5 years ◼ ◼ $20 million in costs must be paid each year ◼ ◼ $25 million/year (paid at the end of each year) Note that each year’s costs must be paid before receiving the payment at the end of the year Should you accept the contract? Cash availability ◼ Note cash availability of the firm ◼ ◼ Note current obligation over the next year ◼ ◼ $10 million $5 million Note obligation over the next year if the new contract is signed ◼ ◼ $25 million Not enough given the current cash availability What can you do to get the new contract? ◼ You can raise more money… ◼ ◼ ◼ Issue more stock Sell bonds …but you need to be careful ◼ ◼ Make sure you do not decrease the value of stock to current shareholders When cash flow is tight, beware of potential cost overruns Depreciation of cash ◼ ◼ As mentioned before, cash currently not invested loses its value over time Cash not needed in the short run can be safely invested ◼ ◼ Example: Government bonds Return is often low in short-term safe government bonds ◼ Rate of return is often about the same rate as inflation ◼ Exception: Since 2008, the rate has usually been significantly below the rate of inflation Timing of cash flows ◼ Sometimes, a firm must choose between less money today or more money in the future ◼ ◼ Which is best? We will deal with this issue over the next two weeks An example: Timing of cash flows ◼ ◼ Suppose you are about to sign a contract Your customer offers you two payment options ◼ ◼ ◼ $1,000 per year for each of the next 10 years A one-time payment of $12,000 five years from now Which is best? ◼ It depends on how much your value of money decreases on a yearly basis Future value of money for firms with bad cash flow ◼ Suppose that there are two firms that are the same in every respect except… ◼ ◼ …one firm has good cash flow practices (A) …one firm has bad cash flow practices (B) ◼ Firm B is more reliant on current payments to keep the amount of cash on hand to be positive ◼ ◼ ◼ Firm B values current payments much more than future payments Firm B has a higher discount rate Firm B is more likely to pass up good long-run investment opportunities Putting it all together ◼ ◼ There are different firm types In all types of business, we are trying to maximize the value of existing owners’ equity ◼ Many issues must be addressed to do this Issues to maximizing owners’ equity ◼ Can we trust a manager to make decisions that are in the best interest of the firm’s stockholders? ◼ ◼ ◼ ◼ Is a manager’s goal the same as the stockholders’ goals? Can we compensate managers to act in a firm’s best interest? Insider trading? We will address these issues in this course Idea of discounting ◼ ◼ The more you value money paid to you in the future, the less you “discount” it Example ◼ Suppose I value a $100 payment a year from now as equal to $98 today ◼ ◼ My annual discount rate is about 2% What if my value today is $97 ◼ My annual discount rate is about 3% Idea of discounting ◼ Given a $100 payment a year from now, note that the higher the discount rate, the less you value future payments ◼ ◼ 2% discount rate ➔ ~$98 present value 3% discount rate ➔ ~$97 present value Main concept of Chapter 4: What is r ? ◼ The letter r can be thought of in multiple ways ◼ Interest rate ◼ ◼ ◼ If I invest $1 today, I will have $(1 + r) in the next time period Rate of return Discount rate ◼ If I receive $1 in the next time period, it is 1 worth $ today 1+ r A two-period example ◼ ◼ ◼ Suppose that you are in charge of selling an unused building that your company owns Your company has established that the rate of return for your firm is 10% per year Simple world: The only relevant years for this analysis is “this year” (year 0) and “next year” (year 1) A two-period example ◼ You receive three offers for a building ◼ ◼ ◼ ◼ $100,000, to be paid in year 0 $95,000, to be paid in year 0 $107,800, to be paid in year 1 Should you accept the biggest dollar amount? ◼ Maybe → PV analysis What are the PVs of the three offers? ◼ ◼ ◼ $100,000 $95,000 $98,000 ◼ Derived from $107,800 paid in year 1 ◼ Which offer should you take? ◼ ◼ $100,000, paid in year 0 In this case, the highest dollar amount offered is NOT accepted DO NOT DISCOUNT BY MULTIPLYING BY 1 – r!!!!! Expanding from the twoperiod case ◼ In the real world, we may get much more complicated offers for the building ◼ ◼ ◼ ◼ ◼ ◼ ◼ $40,000 per year in years 0-2 $21,000 every six months in years 0-2 $15,000 per year in years 0-14 $12,000 per year forever, starting in year 0 $5,900 every six months forever, with the first two payments in year 0 Assume that r = 10% We will examine this problem in more detail in upcoming lectures For simplicity, we will assume that… ◼ ◼ ◼ …yearly payments are made on January 1 …twice-a-year payments are made on January 1 and July 1 …present value is calculated on January 1 of year 0 Before we solve the PV of the offers… ◼ ◼ …we must determine how to calculate interest earned when there are multiple periods of interest earned Two ways to calculate interest ◼ ◼ Simple interest Compound interest ◼ ◼ Used the most in this class We will use examples of bank deposits Interest ◼ ◼ ◼ How to calculate simple interest How to calculate compound interest Include example: $100 for 3 years @ 10% Back to our bank example ◼ The difference for 3 years between compound interest & simple interest ◼ ◼ 3r 2 + r 3 is 0.031, or 3.1%, when r = 10% The difference between the two methods gets bigger very fast as the number of years grows ◼ ◼ ◼ 1% difference with two years compounding (left to student to figure) 6.41% for four years (left to student to figure) 59.37% for 10 years (left to student to figure) Early earnings and compounding ◼ ◼ If you are in debt after college, you may realize that you will have sizable payments to make once you start your “career” job However, if you can afford to earn a high interest rate in your retirement fund early in your career, you will get the benefits of compounding for decades ◼ Some companies will partially match your investments The longer the compounding, the bigger the difference ◼ ◼ Invest $100 for 40 years at 5% Simple interest ◼ ◼ Compound interest ◼ ◼ $300 at the end of 40 years $704 at the end of 40 years The difference is even bigger at 10% ◼ $500 vs. $4525.93 More to come… ◼ Compounding is a very useful tool for growing your money for retirement ◼ ◼ We will talk more about compounding in the next lecture ◼ ◼ Example: $1 invested at 10% turns into $45.26 in 40 years You may want to spend some time practicing compounding between now and the next lecture We will also start our analysis of the buildingfor-sale example in the next lecture Working backwards: Discounting ◼ ◼ If we multiply by (1 + r )T to compound interest by T years, we must divide by (1 + r )T to discount future cash flows by T years Present value of an investment ◼ CT PV = (1 + r )T Application: NBA Basketball on TV ◼ ◼ ◼ 9-year extension for 2016-2025 $2.6B annually Note that these types of reported numbers are typically in nominal terms ◼ i.e. undiscounted Source: http://chicago.cbslocal.com/2014/10/06/nba-extendstelevision-rights-with-espn-tnt-in-monster-new-deal/ A note about the next lecture ◼ ◼ ◼ The next lecture builds on what we learned today The next lecture presents tools that will be necessary to know for the following three lectures A task for you for the next lecture ◼ If you earn 1% interest every month on a $100 investment over the next year, how much will you have in 12 months (use compound interest) Would you ever work again if you won $100,000 per year for 25 years? More on present value analysis How do we discount multiple times within the same year? More tools for the building-for-sale example Warm up application: Negative amortization loans ◼ ◼ Pause this video and watch the video at http://www.youtube.com/watch?v=StfaAMIQj7Y Good for… ◼ ◼ Cyclical jobs When there are good investment opportunities ◼ ◼ Be careful to think about risk here Why aren’t there many Neg Am loans out there? ◼ “Underwater” Negative amortization loans: An example ◼ ◼ $80,000 loan on a house valued at $100,000 Stated annual interest rate is 6%, compounded monthly ◼ ◼ 0.5% per month Minimum payment required per month is 0.3% of the loan ◼ Notice that the minimum payment (0.3%) is less than the monthly interest rate (0.5%) Negative amortization loans: An example ◼ The first month’s interest ◼ ◼ The first month’s minimum payment ◼ ◼ $80,000  0.005 = $400 $80,000  0.003 = $240 The minimum payment adds $160 to the principal after the first month ◼ New balance is $80,160 Negative amortization loans: An example ◼ The second month’s interest ◼ ◼ The second month’s minimum payment ◼ ◼ $80,160  0.005 = $400.80 $80,160  0.003 = $240.28 New balance after 2 months: $80,320.52 ◼ Notice that the balance is increasing at an increasing rate When does the bank get its money back? Main goals for today ◼ ◼ We want to continue our understanding of interest and discounting There are many subtleties that we need to know how to deal with Recall: Our building-for-sale example ◼ In the real world, we may get much more complicated offers for the building ◼ ◼ ◼ ◼ ◼ ◼ $40,000 per year in years 0-2 $21,000 every six months in years 0-2 $15,000 per year in years 0-14 $12,000 per year forever, starting in year 0 $5,900 every six months forever, with the first two payments in year 0 Assume that r = 10% What if we compound interest more than once a year? ◼ ◼ ◼ Banks typically compound interest for loans and deposits on a monthly or daily basis How does it do it? If annual interest rate is r, then monthly interest rate is r /12 and daily rate is r /365 in a non-leap year ◼ Notice that interest within the same year is compounded when this happens ◼ Without any repayment, $100 loaned today leads to an amount owed one year from now of… ◼ …$100  (1 +0.01)12 = $112.68 EAIR ◼ The effective annual interest rate (EAIR) is the annual rate of return once compounding has been accounted for ◼ ◼ Also sometimes referred to as EAR or APY When $100 turns into $112.68 a year from now, the EAR is 12.68% ◼ ◼ How many of you did this? Recall that the stated annual interest rate (SAIR) is 12% (or 1% per month) ◼ SAIR is also sometimes referred to as SAR or APR Can we reach annual interest rate of infinity? ◼ ◼ Can we compound more and more frequently to get an EAR of infinity? No ◼ ◼ The use of limits tells us what the greatest EAR is, given a SAIR Continuous compounding m r  lim m→ 1 +  = exp( r ) m  Exponential functions ◼ ◼ If we continued to increase the frequency of compounding forever, we eventually get to “continuous” compounding If exp(·) represents the exponential Note: function, then exp(1), m r  lim m→ 1 +  = exp( r ) m  or e 1, is about 2.718 Back to the building problem ◼ What is the present value of the following payment streams? ◼ ◼ $40,000 per year in years 0-2 $21,000 every six months in years 0-2 $40,000 per year in years 0-2 ◼ $40,000 in year 0 has a PV of… ◼ ◼ $40,000 in year 1 has a PV of… ◼ ◼ $40,000/(1.1) = $36,363.64 $40,000 in year 2 has a PV of… ◼ ◼ $40,000 (no discounting) $40,000/(1.1)2 = $33,057.85 Total NPV for 3 payments: $109,421.49 What is our discount rate every six months here? ◼ We need to figure out the discount rate every six months to get an effective annual rate of 10% per year ◼ ◼ Square root of 1.1 is 1.0488 When compounding every six months, we must use a stated discount rate of 4.88% every six months ◼ Essentially, a stated annual interest rate of 9.76% if we are compounding twice per year, compounded twice a year, with an effective annual interest rate of 10% Good article to read if you are still confused: http://www.investopedia.com/articles/basics/04/102904.asp#axzz1n3HpdCmr We want the effective rate to be 10% per year ◼ When compounding every six months, we must use a discount rate of 4.88% every six months ◼ Essentially, a stated annual interest rate of 9.76% if we are compounding twice per year, with an effective annual interest rate of 10% ◼ We need the effective rate to be the same for all calculations or else we do not have correct calculations for comparison $21,000 every six months in years 0-2 ◼ PV of six payments (try this on your own) ◼ ◼ ◼ ◼ ◼ ◼ ◼ $21,000 $20,022.71 $19,090.91 $18,202.47 $17,355.37 $16,547.70 Total PV of six payments: $112,219.16 Which to choose? ◼ If we could only receive $40,000 per year in years 0-2 or $21,000 every six months in years 0-2, which would we choose? ◼ The latter ◼ $112,219.16 > $109,421.49 Are there shortcut formulas to help with the other offers? ◼ ◼ Yes, given a constant percentage rate of increase or decrease Perpetuities ◼ ◼ A payment stream that goes on forever Annuities ◼ A payment stream that has a finite end date Perpetuities ◼ Sometimes, an asset can offer a stream of cash flows forever ◼ ◼ Example: A bond that pays $100 per year forever How much is this stream of cash flows worth? ◼ Is it infinite? Perpetuities ◼ If someone receives C dollars each year forever (starting one year from now), the present value (PV) is C C C PV = + + + ... 2 3 1 + r (1 + r ) (1 + r ) ◼ PV = C / r ◼ Intuition? Recall that we assume a discount rate r Example ◼ ◼ ◼ Mrs. Jones is set to receive $5,000 per year from Crowes, Inc., starting next year Her discount rate is 8% How much is the present value of this stream of payments? ◼ PV = $5,000 / 0.08 = $62,500 What if first payment is made today ? Growing perpetuity ◼ Sometimes, perpetuities are more complicated ◼ ◼ The annual payment starts at C, but increases by fraction g each subsequent period Example of growing perpetuity ◼ First payment in one year is $100, and increases by 3% each year ◼ Here, g = 3% = 0.03 Growing perpetuity ◼ Similar to a regular annuity, a growing annuity’s present value can generally be expressed as C C  (1 + g ) C  (1 + g ) 2 C  (1 + g ) N −1 PV = + + + ... + + ... 2 3 N 1+ r (1 + r ) (1 + r ) (1 + r ) ◼ PV = C / (r – g) if r > g ◼ What if r is not greater than g? Example ◼ ◼ ◼ ◼ Charlie Scream is due to earn $50,000 in royalties next year Every year thereafter, the amount of royalty payments increases by 20% Charlie’s yearly discount rate is 25% How much is this stream of payments worth? ◼ Plug into PV = C / (r – g) Annuities: Like perpetuities? ◼ An annuity is a constant stream of payments made for a fixed time period ◼ ◼ Example: The CA lottery has a game in which you can be “Set For Life” with a top prize is $100,000 per year for 20 years How can we easily figure out how much this is worth? ◼ Assume in this case that the first payment is made in one year How to figure out how much an annuity is worth ◼ We can calculate how much the 20 payments are worth by taking the difference of the following two values ◼ Payments in year 1 (one year from now) to infinity ◼ ◼ A perpetuity worth $1.25 million in PV terms Payments in years 21 to infinity ◼ ◼ A perpetuity that we have to discount by 20 years $1.25 million, divided by 1.0820, or $268,165 Assume r = 0.08 in this example Formula for PV of annuity ◼ The general form of what we did on the last slide is C C 1  PV = r −  T  r  (1 + r )  Alternate ways for PV of an annuity 1  1 PV = C  − T   r r (1 + r )  1  1 − (1 + r )T PV = C  r        or The term in brackets is often referred to as the “annuity factor” Growing annuity ◼ Finite number of payments that grows each year at growth rate g  1 + g   1 −  1+ r    PV = C  r−g   T       Back to payment streams ◼ We will analyze these payment streams now We will also analyze this payment stream, but pay careful attention In the real world, we may get much more complicated offers for the building ◼ ◼ ◼ ◼ ◼ $40,000 per year in years 0-2 $21,000 every six months in years 0-2 $15,000 per year in years 0-14 $12,000 per year forever, starting in year 0 $5,900 every six months forever, with the first two payments in year 0 $15,000 per year in years 0-14 ◼ Annuity (starting in year 1) with an additional payment in year 0 ◼ ◼ ◼ Recall r = 0.1 1   1 − (1 + 0.1)14  PV = 15,000 + 15,000  0.1     PV = $125,500.31 $12,000 per year forever, starting in year 0 ◼ Perpetuity (starting in year 1) with an additional payment in year 0 ◼ ◼ PV = C + C / r = 12,000 + 12,000 / 0.1 PV = $132,000 $5,900 every 6 months forever, with the first two payments in year 0 ◼ ◼ Recall: Square root of 1.1 is 1.0488 PV of two payments in year 0 ◼ ◼ 5,900 + 5,900 / 1.0488 = 11,525.48 Payment of $5,900 at the beginning of the year and a payment of $5,900 six months later is equivalent to a single payment of $11,525.48 at the beginning of the year $5,900 every 6 months forever, with the first two payments in year 0 ◼ ◼ ◼ We will now treat this problem as equivalent to a payment of $11,525.48 per year forever (starting in year 0) PV = $11,525.48 + $11,525.48 / 0.1 PV = $126,780.28 Determining the best offer to accept for the building ◼ $40,000 per year in years 0-2 ◼ ◼ $21,000 every six months in years 0-2 ◼ ◼ PV = $125,500.31 $12,000 per year forever, starting in year 0 ◼ ◼ PV = $112,219.16 $15,000 per year in years 0-14 ◼ ◼ PV = $109,421.49 PV = $132,000 $5,900 every six months forever, with the first two payments in year 0 ◼ PV = $126,780.28 Loan amortization ◼ Four types of loans to consider ◼ Unless mentioned otherwise, assume that the payments are made yearly in these examples ◼ ◼ ◼ ◼ Principal reduced by the same amount each year Payments are the same each year Loans with a “balloon” payment Negative amortization loans ◼ We started looking at this earlier Principal paid back is the same each year ◼ Simple to calculate for a T year loan ◼ ◼ ◼ Pay 1 /T of the principal each year Example: $3,000 loan to be paid back over 3 years, r = 20% Let’s do this on the board Payments are the same each year ◼ Many loans you will receive from banks will require you to pay back the same amount of money each month ◼ ◼ Personal loans Mortgages ◼ If you loan more than 80% of the value of the house, you may also need to pay private mortgage insurance (PMI) until you have 20% equity in the house Example: $3,000 loan, paid back over 3 years, r = 20% ◼ We have to figure out how a stream of payments will be worth $3,000 today ◼ ◼ ◼ ◼ ◼ 1  1 PV = C  − T   r r (1 + r )  Plug in values that we know ◼ ◼ Annuity formula: PV = $3,000 r = 0.2 T=3 Annuity factor: 2.10648 C = $1,424.18 Recall: The term in brackets is often referred to as the annuity factor Loan with a “balloon” payment ◼ Some loans will let you pay less than the amount required to reach a zero balance at the end of the loan ◼ ◼ ◼ The extra amount is a “balloon” payment that is due at the end of the loan A new loan is often made to pay off the “balloon” payment How do we do this? Example: $3,000 loan, paid back over 3 years, r = 20% ◼ Partial amortization loan ◼ ◼ Some of the principal gets paid back In this case, we assume a 10-year amortization ◼ ◼ If we paid all of the principal back over 10 years, we would need to pay $715.57 per year (calculation left to student) What is the balloon payment after 3 years? ◼ Note: The balloon payment is the payment that is made above the regular payment Example: $3,000 loan, paid back over 3 years, r = 20% ◼ ◼ Pay $715.57 per year Year 1 ◼ ◼ ◼ ◼ Pay $715.57 $600 in interest Reduce principal by $115.57 New balance is $2884.43 ◼ Year 2 ◼ ◼ ◼ ◼ $576.89 in interest Reduce principal by $138.68 New balance is $2745.75 Year 3 ◼ New balance is $2579.33 Example: $3,000 loan, paid back over 3 years, r = 20% Year # 1 2 3 Totals Beginning Total balance payment $3,000.00 $715.57 $2,884.43 $715.57 $2,745.75 $715.57 Interest paid $600.00 $576.89 $549.15 Principal paid $115.57 $138.68 $166.42 $2,146.71 $1,726.04 $420.67 Ending balance $2,884.43 $2,745.75 $2,579.33 Example: $3,000 loan, paid back over 3 years, r = 20% ◼ 3-year loan based on a 10-year amortization ◼ ◼ Yearly payment of $715.57 An additional $2,579.33 is due at the end of three years (balloon payment) ◼ ◼ Reminder: Unless mentioned otherwise, the balloon payment is defined for this class as the amount ABOVE the regular payment that is made at the end of the loan We also have an alternate way of calculating the balloon payment Balloon payment calculation ◼ ◼ We can calculate how much the remaining payments are worth three years from now, using the annuity formula We calculate the value in “Year 3” dollars ◼ Loan balance = $715.57  [1 – (1/1.27)]/0.2 = $715.57 3.60459 = $2579.34 We are off by a penny due to rounding of yearly payment Have a great day Firm and investment valuation How much is a firm worth? Calculating net present value Payback period methods Other investment rules people typically use Case study application: The Las Vegas Strip Payback periods ◼ ◼ Many investments claim something like “pays for itself in less than ten years” Payment claims are typically undiscounted ◼ Sometimes, not discounting can make seemingly good decisions into bad decisions Payback example ◼ ◼ ◼ Another hot summer day You have to water the grass for an hour (again) just to keep it green I wish there was another way ◼ There is! Artificial turf Payback example ◼ Artificial turf with a 20-year life ◼ Initial cost of $5000 to cover a 1000 square foot area ◼ Yearly benefits ($650) ◼ No mowing ◼ ◼ No watering ◼ ◼ $300 $200 Other savings ◼ $150 Payback example ◼ What the turf company tells you ◼ ◼ ◼ ◼ $5000 cost $650 in cost savings per year “It pays for itself in less than eight years” What does economic analysis tell you? ◼ Let’s see… Payback example ◼ Assume we get the benefits at the end of each year ◼ ◼ If r = 15%, a 20-year annuity, paying $650 per year is worth $4068.57 today Even if we move the first year’s benefit to be undiscounted, the PV is $4678.85 Payback example ◼ Although the payback method tells us when we “get our money back,” it ignores discounting ◼ ◼ Proper discounting practices should always be used More on this soon Suppose we use the “Payback period method” ◼ ◼ If we naïvely believe that we invest in anything that gets “paid back” within a certain number of years, we can make bad investments Let’s look at another example ◼ Our building-for-sale example ◼ Suppose a three-year window (years 0-2) Five offers for a building for sale ◼ ◼ What if we wanted to get a payback of $110,000 within three years Which offers get us there? ◼ ◼ ◼ ◼ ◼ $40,000 per year in years 0-2 $21,000 every six months in years 0-2 $15,000 per year in years 0-14 $12,000 per year forever, starting in year 0 $5,900 every six months forever, with the first two payments in year 0 ◼ Assume that r = 10% Suppose we only look at a three-year window ◼ ◼ We look at years 0-2 to determine if we should sell the piece of property Some offers look good (> $110,000) ◼ ◼ ◼ $40,000 per year in years 0-2 $21,000 every six months in years 0-2 Some do not ◼ All other offers pay $45,000 or less in the first three years What was really the best offer? ◼ $40,000 per year in years 0-2 ◼ ◼ $21,000 every six months in years 0-2 ◼ ◼ PV = $125,500.31 $12,000 per year forever, starting in year 0 ◼ ◼ PV = $112,219.16 $15,000 per year in years 0-14 ◼ ◼ PV = $109,421.49 PV = $132,000 $5,900 every six months forever, with the first two payments in year 0 ◼ PV = $126,780.28 What does a three-year window really do? ◼ ◼ It assumes a 0% discount rate in the three-year window After the three-year window, it assumes an infinite discount rate ◼ Anything after the three-year window has a net present value of 0 Why we should not use the payback period method ◼ It can be very costly, especially with highvalue decisions ◼ Timing not accounted for; example: Which would you prefer? ◼ ◼ ◼ ◼ ◼ $600 in year 1, $600 in year 2, and $500 in year 3 $100 in year 1, $100 in year 2, and $1500 in year 3 Wrong discounting Arbitrary periods Why use it? Firm value ◼ ◼ Many companies try to find small businesses to buy Which businesses are worth buying? ◼ ◼ ◼ First, determine the appropriate discount rate Second, find net present value of the firm Third, determine if there are any other constraints NPV calculation ◼ ◼ ◼ ◼ NPV = –(PV of costs) + PV of benefits If NPV is positive, you should make the investment If NPV is negative, you should not make the investment Exceptions: Constrained world ◼ ◼ Example: Limited amount of money to invest Other constraints? NPV example ◼ Suppose that you are considering buying a machine that will produce corporate finance books for the next two years ◼ ◼ ◼ Asking price for company: $20,000, paid in year 0 r = 10% Value of books produced What is ◼ Year 1: $11,000 ◼ ◼ PV = $10,000 Year 2: $14,278 ◼ PV = $11,800 the NPV? Constrained NPV example ◼ ◼ $50,000 available to invest Three projects with upfront cost and positive NPV ◼ ◼ ◼ Project 1: $20,000 needed to invest, NPV is $1,800 Project 2: $30,000 needed to invest, NPV is $4,000 Project 3: $50,000 needed to invest, NPV is $5,500 Investing when there are multiple choices ◼ Suppose that there are multiple options of investment to produce a good or service ◼ Example: Manufacturing record players ◼ One machine costs $5,000 ◼ ◼ Lasts 5 years Another costs $7,500 ◼ Lasts 6 years All costs are in real dollars Comparing the two machines: Maintenance costs ◼ ◼ We assume that all maintenance costs below are made at the end of each year in this example Machine 1: Costs $5,000 in Year 0 ◼ ◼ Machine 2: Costs $7,500 in Year 0 ◼ ◼ $2,000 in yearly maintenance for 5 years $1,600 in yearly maintenance for 6 years Which one do we invest in? ◼ We use a technique called equivalent annual cost This technique assumes that we can make comparable investment decisions in the future Equivalent annual cost ◼ Step 1 ◼ ◼ Find the present value of the outflow of each project Step 2 ◼ Determine the equivalent annual cost by finding an annuity payment so that we get the same present value ◼ Step 1 ◼ Machine 1’s present value ◼ ◼ $13,424.73 (5 years) Machine 2’s present value ◼ $15,367.72 (6 years) Step 2: Think “rental rate” ◼ Machine 1 ◼ ◼ ◼ Annuity factor for 5 years at 6% is 4.2124 ◼ ◼ Machine 2 ◼ Annuity factor for 6 years at 6% is 4.9173 Machine 1 ◼ Solve $13,424.73 = C  4.2124 C = $3,186.96 Machine 2 ◼ ◼ Solve $15,367.72 = C  4.9173 C = $3,125.24 Valuing information ◼ ◼ Information is valuable However, information is costly to gather ◼ ◼ Note costs could be in terms of money and/or time How much information should be gathered? ◼ Also, who should gather the information? The economics of information ◼ ◼ Information is valuable for high-price transactions, since even a 5% difference in NPV can be a lot of money Outside consultants are often helpful here ◼ They are knowledgeable about a market, which is valuable Some examples of MC and MB curves of information The internal rate of return ◼ ◼ The internal rate of return (IRR) is the rate of return for a project such that the NPV is zero Simple example ◼ ◼ ◼ Invest $500 today Receive $600 one year from now IRR is 20% ◼ 0 = –$500 + $600 / (1.2) Internal rate of return ◼ Let ρ be the internal rate of return to be solved B1 − C1 B2 − C2 BT − CT B0 − C0 + + + ... + =0 2 T 1+  (1 +  ) (1 +  ) A more complicated example ◼ ◼ ◼ ◼ ◼ You invest $3000 today You will receive $1650 in one year You will receive $1815 in two years What is the IRR? We need to solve for 1650 1815 − 3000 + + =0 2 1 +  (1 +  ) Solving ◼ ◼ ◼ 1650 1815 − 3000 + + =0 2 1 +  (1 +  ) Multiply both sides by (1 + ρ)2 ➔ –3000(1 + ρ)2 + 1650(1 + ρ) + 1815 = 0 The above equation is equivalent to –3000ρ2 – 4350ρ + 465 = 0 Use the quadratic formula to solve ◼ ◼ ◼ − b  b 2 − 4ac →x = 2a Generic form: ax 2 + bx + c = 0 a = –3000, b = –4350, and c = 465 ρ = –155% or 10% More than 2 payback periods ◼ ◼ The mathematics become difficult when there are more than two payback periods Methods we can use ◼ ◼ Guess, check, and re-guess until we solve Use a computer to solve ◼ ◼ Excel spreadsheet (see textbook for more) Make a program to solve Problems with IRR method ◼ ◼ Difficult to calculate IRR by hand with more than 2 positive cash flows We can get multiple IRRs (See Section 5.5 for more details) ◼ ◼ We always ignore negative IRRs, however As with the payback period method, the IRR method does not always tell us which projects are BEST to invest in ◼ Suppose we have two projects (X and Y) and we can only invest in one project You can invest in one project: Which one? ◼ ◼ Project X has the higher internal rate of return Project Y has the higher present value ➔ Do Y Project Year 0 Year 1 ρ PV Invest? X -$100 $110 10% 3.77 NO Y -$1,000 $1,080 8% 18.87 YES If we can only do one project, we say that X and Y are mutually exclusive projects Assume 6 percent discount rate in calculating PV, and that all other invested money has a return with PV = 0 Which project to invest in? ◼ Comparing two projects ◼ ◼ ◼ R&D project Advertising project Choice depends on interest rate (see bolded #s) Annual Net Return PV Year R&D Advertising r= R&D Advertising 0 -$1,000 -$1,000 0 $150 $200 1 600 0 0.01 $128 $165 2 0 0 0.03 $86 $98 3 550 1,200 0.05 $46 $37 0.07 $10 -$21 When NOT to invest ◼ ◼ Same project with some different discount rates Note that once r is above 7.549%, neither project should be invested in ◼ ◼ 7.549% is IRR for R&D project Negative NPV for both projects at higher discount rates Annual Net Return PV Year R&D Advertising r= R&D Advertising 0 -$1,000 -$1,000 0.05 $46 $37 1 600 0 0.06 $28 $8 2 0 0 0.07 $10 -$21 3 550 1,200 0.07549 $0 -$35 0.08 -$8 -$47 Why use IRR? ◼ Despite the problems with IRR, many people use it for simplicity ◼ ◼ Mid-level managers want to justify to their bosses that investments get “enough” return IRR can be useful when there are differing opinions on what the discount rate is The profitability index ◼ ◼ ◼ ◼ The profitability index (PI) is also called the benefit-cost ratio Useful in cases when an investment is made at Year 0 and benefits are received over time PI = PVs of cash flow after investment Initial investment Note that PI > 1 ➔ NPV > 0 PI example ◼ ◼ ◼ You invest $100,000 in a business You are guaranteed $15,000 per year (starting next year) forever Your discount rate is 12.5% ◼ ◼ ◼ The PV of the money you receive is $120,000 Your initial investment is $100,000 Your PI is 120,000 / 100,000, or 1.2 Moving on: A case study application ◼ We will look at some recent changes to the Las Vegas strip ◼ ◼ ◼ ◼ I use the Las Vegas strip because it gives us some good examples for making sound financial decisions The Las Vegas Strip of old “Sahara closes after 59 years” “Echelon remains partly built…” ◼ Why? Think IRR decrease after the 2008 financial meltdown Where was this? When? The answer is coming soon Sahara closes after 59 years ◼ The Las Vegas strip loses 1,720 rooms ◼ ◼ A sample of past performers ◼ ◼ ◼ ◼ ◼ ◼ Closed May 16, 2011 Abbott and Costello Frank Sinatra Sammy Davis Jr. Bill Cosby George Carlin Why did it close? Picture source: http://www.flickr.com/photos/mrak75/987349729/; Performer source: Wikipedia (http://en.wikipedia.org/wiki/Sahara_Hotel_and_Casino) What will happen to the Sahara? ◼ Just as is often the case in Las Vegas, it is out with the old, in with the new ◼ Past example on 1 site on the strip ◼ ◼ ◼ ◼ ◼ Tally-Ho, 1963 King’s Crown The Aladdin The New Aladdin Planet Hollywood ◼ 2014-2019 ◼ ◼ SLS Las Vegas August 2019 ◼ During ongoing renovations, renamed Sahara Las Vegas Picture source: http://vintagelasvegas.com/post/102026474949/tally-holas-vegas-strip-1963-the-hotel-became, via https://twitter.com/classiclasvegas The great recession: Echelon remains partly built ◼ Echelon was to replace the land of the Stardust and other nearby properties ◼ ◼ ◼ ◼ Hotels 750,000 sq. ft. convention center 400,000 sq. ft. shopping center 140,000 sq. ft. casino Picture source: http://www.vegastodayandtomorrow.com/echelon_place.htm Timeline for Echelon ◼ ◼ ◼ Construction began in 2007 Initial opening was planned for 2010 Construction was suspended in 2008 ◼ ◼ What do we have instead? ◼ ◼ Construction now resumed “Viva McDonald’s” Compare to CityCenter ◼ See https://en.wikipedia.org/wiki/CityCenter for more details Picture source: http://www.yelp.com/biz_photos/1Vww5khNocAe9rRDyPIJX A?select=wFrJe7-Qvp9u9Lvtepdm2Q → New ownership ◼ The Echelon project has been scrapped ◼ ◼ Resorts World Las Vegas broke ground in 2015, and is now scheduled to open in summer 2021 ◼ ◼ Note sunk costs This is about three years later than originally planned at the groundbreaking ceremony Sahara/Resorts World/New convention center (old Riviera site): Revitalization for the North Strip? Two more issues today ◼ Incorporating risk into discounting ◼ ◼ The higher the risk, the higher the discount rate How long will it take for our investment to reach a certain dollar value? ◼ $62,500 to $1,000,000: How long if EAIR is 7%? ◼ ◼ Formally: t is about 41 years Rule of 70: t is about 40 years ◼ Only an approximation Usefulness of Rule of 70 ◼ ◼ This is a very useful tool for the real world, due to ease of calculation From a former student ◼ “(I)n a 5 hour interview with a wealth management firm, one question was (no calculators permitted): ‘If a client comes to you with $10,000 today, what would you tell them about their worth 20 years from now assuming a 14.5% annual interest rate?’ The interviewer was surprised when I asked how often the money is compounded but he answered yearly. Without writing down anything and about 20 seconds later I told him $160,000, which really impressed him.” Why is what we are doing important ◼ Next lecture, we will continue to build off of today’s lectures ◼ ◼ ◼ We will use these tools to help us with more complicated cash flows Can we value an annuity? Can we value a perpetuity? What are you going to invest in? “You must risque to win” --- Andrew Jackson 7th US president Nicknames: King Mob, Old Hickory, The Hero of New Orleans Wrapping up decision making An introduction to risk More on costs Spillovers Introducing the housing bubble What is risk? Applications of risk Cost allocation ◼ For profit maximizing purposes, we will allocate costs to a project if the cost is needed to complete the project ◼ ◼ ◼ Note that other parts of the company can sometimes benefit, however We will incorporate these benefits into the calculation Example: Adding a computing system to a building also requires AC Opportunity cost ◼ ◼ Another issue that needs to be taken into account when investing is opportunity cost Anytime an investment means forgoing other revenue, this is an added cost ◼ ◼ Opportunity cost Example: 10 hours per week for work ◼ ◼ Building widgets, which sell for $1 each Working at an I.V. coffee shop for $10/hr. Widget production function Hours of widget production Total number of widgets built 0 0 Additional widgets built 15 1 15 13 2 28 11 3 39 9 4 48 How many widgets should I build? ◼ ◼ ◼ ◼ You should build widgets for 3 hours/week, earning $39 from widgets You should work 7 hours/week, earning $70 from work Total earnings: $109/week Marginal analysis ➔ Maximize earnings Side effects in business ◼ Erosion ◼ ◼ A new product or service introduced leads to a reduction in sales of products or services already on the market Synergy ◼ A new product or service introduced leads to an increase in sales of products or services already on the market Examples ◼ RAZR ◼ ◼ Erosion of other clubs More golf ball sales ◼ A tennis racquet breakthrough ◼ ◼ ◼ Should we develop the RAZR? Erosion of other racquet models More tennis ball sales Golf = $$$ ◼ R&D costs for the RAZR ◼ ◼ Projected NPV of direct profits from the RAZR ◼ ◼ $16 million Projected increase in golf ball profits (in NPV) ◼ ◼ $20 million Projected loss of profits (in NPV) from lost sales of other clubs ◼ ◼ $5 million in year 0 $4 million Invest: $24M in benefits > $21M in costs What if there are past sunk costs? Inflation ◼ How does inflation affect the tools we have used to date? ◼ ◼ So far, we have made decisions in the absence of factoring inflation in What do we need to do to account for inflation? ◼ The nominal interest rate is how much you are quoted to earn ◼ ◼ Example: You are quoted a yearly interest rate of 12% The real interest rate discounts the nominal interest rate by the inflation rate Nominal versus real interest rates ◼ Suppose that a bag of chips sells for $1 today and goes up by the rate of inflation each year ◼ ◼ Assume that inflation is 5% per year in this example $100 buys you 100 bags of chips this year Nominal versus real interest rates ◼ Let’s see how many bags of chips we can buy if we invest our $100 for one year ◼ ◼ ◼ $100 ➔ $112 in one year Price of chips goes from $1 ➔ $1.05 $112/$1.05 = 106.67 ◼ Real interest rate is 6.67% ◼ Your real dollar amount goes from $100 to $106.67 in one year Calculating the real interest rate, in general ◼ ◼ Inflation erodes our nominal interest rate in the sense that our purchasing power only goes up by the amount of the real interest rate How much is the real interest rate? ◼ Real interest rate = 1 + Nominal interest rate 1 + Inflation rate ◼ – 1, or 1 + Nominal interest rate = (1 + Real interest rate)  (1 + inflation rate) Alternate approximation: Additive effect How should we discount? ◼ Whether or not you account for inflation, you need to make sure you are consistent in your calculations ◼ ◼ ◼ Use ALL nominal cash flows OR Use ALL real cash flows Once you decide, you must be consistent on your method of choice Example… Amelia’s Plumbing ◼ ◼ Amelia starts her own plumbing company today (year 0) Her expected cash flow (nominal terms) ◼ ◼ ◼ ◼ ◼ ◼ ◼ Year Year Year Year 0: 1: 2: 3: – $30,000 $120,000 $150,000 $160,000 Nominal discount rate: 13% Rate of inflation: 4% Real discount rate: 1.13/1.04 – 1 = 8.6538% Nominal cash flow: NPV ◼ Discounted cash flows (in $1000s) ◼ ◼ ◼ ◼ ◼ Year Year Year Year 0: 1: 2: 3: –30 120 150 160 (no discounting) / 1.13 = 106.19 / 1.132 = 117.47 / 1.133 = 110.89 Total net cash flow (in $1000s) ◼ 304.55 Real cash flow: NPV (All numbers are in $1000s) ◼ Real cash flows ◼ ◼ ◼ ◼ Year 0: –30 (no discounting) Year 1: 120 / 1.04 = 115.38 Year 2: 150 / 1.042 = 138.68 Year 3: 160 / 1.043 = 142.24 ◼ Discounted cash flows (note that real discount rate is 8.6538%) ◼ ◼ ◼ ◼ Notice that we get the same discounted cash flows by either method Year 0: –30 (no discounting) Year 1: 115.38 / 1.086538 = 106.19 Year 2: 138.68 / 1.0865382 = 117.47 Year 3: 142.24 / 1.0865383 = 110.89 This wraps up Unit 1 ◼ Before we leave today, I want you to introduce risk, along with some real-life applications of risky situations What is risk? ◼ ◼ A dictionary will define risk as potential for loss We will think of risk differently ◼ Think of risk in this class as two or more outcomes possible ◼ Example: Option A with probability p and Option B with probability (1 – p) Thinking about simple risks ◼ A “fair” roulette wheel ◼ ◼ ◼ You bet $10 ◼ ◼ ◼ Half of the numbers are red Half of the numbers are black Either you win $10 or you lose $10 Each with probability 0.5 What about real-world problems? ◼ What is our best guess? Thinking about a real-life application of risk Source: http://mysite.verizon.net/vzeqrguz/housingbubble/ ◼ We will analyze the housing bubble of the 2000s at times throughout the rest of the quarter  in the housing market ◼ In most cases, the employees estimating the possible scenarios did not include the ACTUAL outcome in their estimates ◼ For example, in Las Vegas (Feb. 2012)… ◼ ◼ …three-quarters of homes for sale were vacant …housing prices were at their lowest in 25 years Source: http://www.lvrj.com/business/housing-market-sales-rise-13percent-nationwide-140120293.html, Feb. 23, 2012 ◼ Recent example of a house sale ◼ 6248 Dundee Port Avenue, Las Vegas NV 89110 (built in 1998) ◼ ◼ ◼ ◼ ◼ ◼ ◼ ◼ ◼ ◼ ◼ Originally sold for $121,500 4 bedrooms 2 bathrooms 1,560 sq. ft. house 7,405 sq. ft. lot Sold June 2008 for $315K Sold Sept. 2012 for $95K July 2013 value: $108,501 Oct. 2016 value: $202,724 July 2017 value: $221,081 July 2020 value: $280,448 Source: http://www.zillow.com/homedetails/6248Dundee-Port-Ave-Las-Vegas-NV-89110/7029918_zpid/, July 2013, Oct. 2016, July 2017, and July 2020 What happened? ◼ ◼ The Great Recession is something that has not been seen in the United States since the 1930s Many people underestimate outcomes with very low probabilities ◼ ◼ Most people have difficulty incorporating lowprobability events into cost-benefit analysis Memory is also an issue 2006: POP! Source: http://mysite.verizon.net/vzeqrguz/housingbubble/ Before moving on… ◼ ◼ Some products are in fact very successful Many toys are very risky, but some are wildly successful ◼ ◼ ◼ ◼ Tickle Me Elmo Zhu Zhu pets Cabbage Patch Kids How are toys manufactured/transported? What is risk? ◼ ◼ A dictionary will define risk as potential for loss We will think of risk differently ◼ Think of risk in this class as two or more outcomes possible ◼ ◼ Example: Option A with probability p and Option B with probability (1 – p) I am presenting 7.1 differently than the textbook Simple example ◼ You are developing the next wonder drug ◼ ◼ Unfortunately, one of your competitors is also developing a drug that will do the same thing Whoever develops the drug first makes much higher profits The numbers ◼ R&D costs to develop the drug are the same no matter what ◼ ◼ If you develop the drug first, the NPV numbers are… ◼ ◼ ◼ $6 million in NPV Direct drug production costs of $10 million Revenue from the drug of $20 million If you develop the drug second, the NPV numbers are… ◼ ◼ Direct drug production costs of $5 million Revenue from the drug of $6 million Assigning probabilities: 50/50 Calculating the expected profit ◼ Expected costs (in millions of dollars) ◼ ◼ Expected benefits (in millions of dollars) ◼ ◼ (20 + 6) / 2 = 13 Expected profit in NPV ◼ ◼ 6 + (10 + 5) / 2 = 13.5 -$500,000 Investing quickly/first breakthrough Another example ◼ ◼ ◼ ◼ ◼ You have spent $200,000 (NPV) developing a new product Depending on market conditions, you could sell 300 units, 500 units, or 900 units of the product If you sell 300 units, your average cost (AC) to produce the good is $500 and the price you sell the good for is $800 500 units… AC is $400… price is $1000 900 units… AC is $600… price is $1200 Potential profits ◼ 300 unit case ◼ ◼ ◼ ◼ ◼ Loss of $110,000 500 unit case (next line is in $1000s) ◼ ◼ ◼ $200,000 in development costs Additional costs: $500  300 = $150,000 Revenue: $800  300 = $240,000 –200 – 0.4  500 + 1  500 Gain of $100,000 900 unit case (left to student) ◼ Gain of $340,000 Calculating expected profits ◼ Assume that… ◼ ◼ ◼ ◼ …the 300 unit case occurs with probability 0.15 …500 unit case… probability 0.65 …900 unit case… probability 0.2 The expected profit of this project is (in $1000s) ◼ 0.15  (–110) + 0.65  (100) + 0.2  (340) = 116.5 What is your risk tolerance?
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