Managerial Finance FINC 474 Session 2 Present and future value Dr. Michael Kinsman Welcome to week 2 of FINC 474 Last week we Discussed what you learned in accounting Talked about and used ratio analysis FINC474 Week 2 2 This is a great time to ask questions about last week This is a great time to ask the question only you have about last week s material! Please don t ask about this week we ll get there! FINC474 Week 2 3 FINC474, Week 2 1
Plan for tonight Tonight, we are going to talk about present value and future value. We will do the Seal Best case FINC474 Week 2 4 A balance sheet view of finance The balance sheet Decisions about working capital and solvency Net working capital The capital Long term liabilities structure and Long term assets Equity dividend decisions The investing decision (capital budgeting) This week we are doing FINC474 Week 2 5 Interest rates Both in your personal investing and in your business life, interest rates are important. They provide cash outflows because you pay interest and they help determine the value of investments because of what we will see later tonight--the time value of money. FINC474 Week 2 6 FINC474, Week 2 2
Interest rates In essence, the interest rate is the cost of money--the higher the cost of money, the more a dollar today is worth relative to a dollar to be received in the future. One way of looking at that relationship is the yield curve. FINC474 Week 2 7 The yield curve The yield curve is the relationship between the cost of debt and time to maturity. There are three relationships that we might observe in yield curves Normal yield curves Downward sloping yield curves Humped yield curves FINC474 Week 2 8 Normal yield curves Normal yield curves occur over 95 percent of the time, and reflect a long term rate higher than short term rates: Interest rate Time to maturity FINC474 Week 2 9 FINC474, Week 2 3
Normal yield curves The reasons that long term rates are higher than short term are several in number, but probably the most important is that there is less certainty about our forecasts out 30 years than those out 1 year. FINC474 Week 2 10 Downward sloping yield curves During a period of high inflation, there is a belief that interest rates will come down: Interest rate Time to maturity FINC474 Week 2 11 Humped yield curves Humped yield curves, which include a downward sloping curve, happen when something is holding down rates now: Interest rate Time to maturity FINC474 Week 2 12 FINC474, Week 2 4
What s money worth? I have a problem. As you know, my family sometimes comes over after class for dinner. My wife, old fashioned as she is, wants me to pay for dinner. Unfortunately, I forgot my wallet and have no money. So, the deal is this: How much will you give me today for my promise to give you back $20 in a month? FINC474 Week 2 13 It s nice to have friends! Interest rate = 11.11% = $2 $18 Interest Principal Per month! That s an annual rate of 133.33% FINC474 Week 2 14 What does that 133% consist of? Historically, since the time of Christ, Freidman and Schwarz discovered that the interest rate just for giving up your money is 2 to 4 percent. ❶ Rate for giving up the money 2 to 4% FINC474 Week 2 15 FINC474, Week 2 5
What does that 133% consist of? In addition, you need a return because you face a world of inflation if inflation were 25 percent, you would not loan money at 3 percent! ❶ Rate for giving up the money 2 to 4% ❷ Rate for inflation 2% FINC474 Week 2 16 What does that 133% consist of? Taken together, those two are called the risk free rate, usually thought of as the rate on 90 government treasury bills. ❶ Rate for giving up the money 2 to 4% ❷ Rate for inflation 2% Risk free rate 4 to 6% FINC474 Week 2 17 What does that 133% consist of? Everything else is a premium for the risk you take. In this case, the total return for risk is what s left over 127 to 129 percent per annum. This is low for a Pepperdine prof! ❶ Rate for giving up the money 2 to 4% ❷ Rate for inflation 2% ❸ Premium for risk 127 to 129% Total 133% FINC474 Week 2 18 FINC474, Week 2 6
Note that all risk is in the rate! Included in the rate you used to calculate return on investment was the risk of inflation and the risk of the project, as well as an amount just for giving up your money. It must be so in all rates you use, or you ve goofed and aren t being appropriately compensated for use of your money. FINC474 Week 2 19 Calculator setup Please do not get ahead of us, but do feel free to give or get help if needed. You need to set your calculator up right--see your calculator cheat sheet download: Be sure your calculator is in end mode (it should not have begin in the window). Except for 12c users, set your calculator for one period per year. To check this, enter 2 into n, 5 into I, 1000 into FV, 0 into payment, and calculate PV. Answer should be $907.03. FINC474 Week 2 20 Check digits In the questions, I will give you check digits--the two digits surrounding the decimal point. For example, 321.72 will give you 1.7 as check digits. FINC474 Week 2 21 FINC474, Week 2 7
Helpful hint to avoid frustration! If you are practicing these problems, please be sure you have set number of periods per year to 1 ( standard is 12). See the calculator cheat sheet for how. If your answers are incorrect (generally too low) and you have your calculator in end mode, this is likely your problem. FINC474 Week 2 22 Problem 1 Suppose you have $1000 that you want to invest at 8 percent interest for five years. How much will that money be worth at the end of the fifth year? The check digits are 9.3 FINC474 Week 2 23 This is a future value problem Amount 1,000 8% How do we know? The problem asks what the amount is going to be worth in the future. FINC474 Week 2 24 FINC474, Week 2 8
Answer 1 The answer is $1,469.33 As you can see, the check digits are the two digits surrounding the decimal point. If you have them right, you are pretty sure you have the answer right and don t have to say it out loud that gives everybody a chance to figure it out, not just the first person to get it. I ll give you check digits for many problems. FINC474 Week 2 25 What s an annuity precisely defined? Equal payment equally spaced through time. FINC474 Week 2 26 What kinds of annuities are out there? There are two types: Ordinary annuity, where the first payment is a period from now. This problem is solved with your calculator in the end mode. Annuity due, where the first payment is paid now. This problem is solved with your calculator in the begin mode. FINC474 Week 2 27 FINC474, Week 2 9
Problem 2 Let s turn our earlier example around. Someone promises you $1000 in five years. Using an interest rate of 7 percent, how much is that money worth today? The check digits are 2.9 FINC474 Week 2 28 This is a present value problem Amount 1,000 712.99 7% How do we know? The problem asks what the money is worth today. FINC474 Week 2 29 Problem 3 What if you are promised a series of even payments of $400 per year for five years. Let s suppose that the market rate of interest is 8 percent. How much is that series of payments worth today that is to say, how much would you take in cash today for it? Check digits: 7.0 FINC474 Week 2 30 FINC474, Week 2 10
This is a present value of an annuity problem. Amount 400 400 400 400 400 1597.08 How do we know it s a present value problem? What s the money worth today is the question. How do we know it s an annuity? Look for the words per year with a repeated amount. FINC474 Week 2 31 Problem 4 Suppose that you decide to deposit a constant amount of $100 per year into an account each year at the end of the year. How much will be in your savings account at the end of the third year if you earn 9 percent on the account annually? Check digits: 7.8 FINC474 Week 2 32 Future value of an annuity Amount 100 100 100 327.81 Notice that you get no interest on the money deposited at year 3! This is a future value of an annuity problem because we have an annuity and we ask what it will be worth. FINC474 Week 2 33 FINC474, Week 2 11
Problem 4 slightly modified Suppose that you decide to deposit a constant amount of $100 per year into an account each year at the beginning of the year. How much will be in your savings account at the end of the third year if you earn 9 percent on the account annually? Check digits: 7.3 FINC474 Week 2 34 Future value of an annuity Amount 100 100 100 357.31 Notice that you get interest on the money deposited at year 3! This is a future value of an annuity using an annuity due problem because we have an annuity and we ask what it will be worth. To solve it you must set your calculator to begin mode. FINC474 Week 2 35 Problem 5 Suppose that I have a choice: Suppose that I am promised $5,000 in four years, or $4,000 today. If my interest rate is six percent, which should I take? FINC474 Week 2 36 FINC474, Week 2 12
Problem 5 Oh my, what is the problem? It is a real life problem! It can be done in many ways: As a future value problem Amount 4,000 As a present value problem Compare to $5000 Amount 5,000 Compare to $4000 FINC474 Week 2 37 Or even by comparing interest rates! What interest rate makes the two amounts equal. (Remember one of them has to be a negative number for this to work!) Amount (4,000) 5,000 FINC474 Week 2 38 Problem 6 What if the amount I am promised is an uneven series? What s this series worth today? Use a 7 percent interest rate. (Check digits: 0.5) Amount 5 20 50 10 FINC474 Week 2 39 FINC474, Week 2 13
Problem 7 Can we use our calculator to calculate the loan amortization schedule for our loan suppose our loan is $15,000, four years, with an interest rate of 10 percent. First, what is the annual payment on that loan? Check digits: 2.0 FINC474 Week 2 40 Now set up your table Beg. Ending Year Prin. Payment Interest Principal Prin. 1 15,000.00 4,732.06 2 3 4 Go to your calculator cheat sheet to see how to fill out the rest of the table. FINC474 Week 2 41 The finished amortization Beg. Ending Year Prin. Payment Interest Principal Prin. 1 15,000.00 4,732.06 1,500.00 3,232.06 11,767.94 2 11,767.94 4,732.06 1,176.79 3,555.27 8,212.67 3 8,212.67 4,732.06 821.27 3,910.79 4,301.88 4 4,301.88 4,732.06 430.19 4,301.87 0.01 FINC474 Week 2 42 FINC474, Week 2 14
Seal Best Without any analysis, tell me a little about Seal Best who are the players, what is the situation? What did you do to analyze Seal Best? FINC474 Week 2 43 Seal Best Ratios Seal Best, Inc. Ratios Industry 1972 1973 1974 Quick (times) 1.0 2.1 1.0 0.6 Current (times) 2.7 4.2 2.6 1.8 Inventory turnover (times/year) 7.0 8.7 5.4 3.5 Average collection period (days) 32.0 33.0 36.0 49.0 Fixed asset turnover (times) 13.0 11.6 10.7 12.4 Total asset turnover (times) 2.6 3.2 2.6 1.9 Debt ratio (percent) 50.0 23.0 33.0 48.0 Return on total assets (percent) 9.0 12.1 6.5 2.8 Return on net worth (percent) 18.0 15.7 9.7 5.4 Profit margin on sales (percent) 3.5 3.8 2.6 1.4 FINC474 Week 2 44 Percentage Income Statement Seal Best Percentage Income Statement (Also called Common Sized Income Statement) 1972 1973 1974 Net sales 2,210.0 100.00 2,295.0 100.00 2,380.0 100.00 Cost of goods sold 1,768.0 80.00 1,836.0 80.00 1,904.0 80.00 Gross profit 442.0 20.00 459.0 20.00 476.0 20.00 Administrative and selling expense 170.0 7.69 187.0 8.15 204.0 8.57 Depreciation 68.0 3.08 85.0 3.70 102.0 4.29 Miscellaneous expense 34.0 1.54 71.4 3.11 102.0 4.29 Total operating expense 272.0 12.31 343.4 14.96 408.0 17.14 Net income before taxes 170.0 7.69 115.6 5.04 68.0 2.86 Taxes (50%) 85.0 3.85 57.8 2.52 34.0 1.43 Net income 85.0 3.85 57.8 2.52 34.0 1.43 FINC474 Week 2 45 FINC474, Week 2 15
Data for Cash Flow Statement Seal Best Balance sheet (used as data) Difference 1972 1973 1974 1972-1973 1973-1974 Cash 51,000 23,800 17,000 (27,200) (6,800) Accounts receivable 204,000 231,200 323,000 27,200 91,800 Inventory 255,000 425,000 688,500 170,000 263,500 Property (net) 190,400 214,200 192,100 23,800 (22,100) Notes payable bank 85,000 238,000 85,000 153,000 Accounts payable 81,600 129,200 255,000 47,600 125,800 Accrued expenses 40,800 47,600 64,600 6,800 17,000 Long term debt 37,400 34,000 30,600 (3,400) (3,400) Net worth 540,600 598,400 632,400 57,800 34,000 FINC474 Week 2 46 Cash Flow Statement Operating From operations: From customers Sales 2,295,000 2,380,000 Minus accounts receivable change (27,200) (91,800) Net from customers 2,267,800 2,288,200 To suppliers Minus cost of goods sold (1,836,000) (1,904,000) Minus change in inventory (170,000) (263,500) Plus accounts payable change 47,600 125,800 Minus operating expense (187,000) (204,000) Minus miscellaneous expense (71,400) (102,000) Minus provision for taxes (57,800) (34,000) Plus accrued expense 6,800 17,000 Net to suppliers (2,267,800) (2,364,700) Net from operations 0 (76,500) FINC474 Week 2 47 Cash Flow Statement Investing and Financing Activities From investing Minus depreciation (went into new property) (85,000) (102,000) Minus change in property (23,800) 22,100 Net from investing (108,800) (79,900) From financing Notes payable, bank 85,000 153,000 Long term debt (3,400) (3,400) Net from financing 81,600 149,600 Change in cash (27,200) (6,800) Beginning cash 51,000 23,800 Ending cash 23,800 17,000 FINC474 Week 2 48 FINC474, Week 2 16
Statement of Cash Flows Reconciliation of Net Income to Cash Flows from Operations Reconciliation of net income to cash flow from operations Net income 57,800 34,000 Add back depreciation 85,000 102,000 Change in accounts receivable (27,200) (91,800) Change in inventory (170,000) (263,500) Change in accounts payable 47,600 125,800 Accrued expenses 6,800 17,000 Net cash flow from operations 0 (76,500) FINC474 Week 2 49 FINC474, Week 2 17