Introduction to Financial Management FIN 102 – Week 4a

1. Introduction to Financial ManagementFIN 102 – Week 4a Dr. Andrew L. H. Parkes “A practical and hands on course on the valuation and financial management of corporations”

2. The Time Value of MoneyContinued • Annuities • Ordinary vs. Annuities Due • Future Value • Present Value • Payments • Amortizing a Loan Two Basic Topics: Annuities are often used for retirement and called a nest egg. Intro. to Financial Managment-Week 4a

3. Types of Annuities • Ordinary Annuity: Payments or receipts occur at the end of each period. • Annuity Due: Payments or receipts occur at the beginning of each period. • An Annuity represents a series of equal payments (or receipts) occurring over a specified number of equidistant periods. Intro. to Financial Managment-Week 4a

4. Examples of Annuities • Student Loan Payments • Car Loan Payments • Insurance Premiums • Mortgage Payments • Retirement Savings Intro. to Financial Managment-Week 4a

5. Parts of an Annuity - A End of Period 2 (Ordinary Annuity) End of Period 1 End of Period 3 0 1 2 3 $100 $100 $100 Equal Cash Flows Each 1 Period Apart Today Intro. to Financial Managment-Week 4a

6. Parts of an Annuity - B Beginning of Period 2 (Annuity Due) Beginning of Period 1 Beginning of Period 3 0 1 2 3 $100 $100 $100 Equal Cash Flows Each 1 Period Apart Today Intro. to Financial Managment-Week 4a

7. FVAn = R(1+i)n-1 + R(1+i)n-2 + ... + R(1+i)1+ R(1+i)0 Overview of an Ordinary Annuity -- FVA Cash flows occur at the end of the period 0 1 2 n n+1 . . . i% R R R R= Periodic Cash Flow FVAn Intro. to Financial Managment-Week 4a

8. FVA = $1,000(1.07)2 + $1,000(1.07)1 + $1,000(1.07)0 = $1,145 + $1,070 + $1,000 = $3,215 Example of anOrdinary Annuity -- FVA Cash flows occur at the end of the period 0 1 2 3 4 7% $1,000 $1,000 $1,000 $1,070 $1,145 $3,215 = FVA Intro. to Financial Managment-Week 4a

9. Ordinary annuities • Henry saves $600 each half year and invests it at 13% (convertible semi annually) How much money has Henry got after 10 years? Intro. to Financial Managment-Week 4a

10. The answer • Time Line:After a half year Henry puts in his first $600 and so forth every half year • Starting today the first $600 will stay in the account 9.5 years …on the time line! • The second amount of $600 for 9 years. • The third amount 8.5 years etc. • The last amount of $600 will have no time to gather any interest • Let us use EXCEL!! – see the Function key Intro. to Financial Managment-Week 4a

11. FVADn = R(1+i)n + R(1+i)n-1 + ... + R(1+i)2+ R(1+i)1 = FVAn (1+i) Overview View of anAnnuity Due Cash flows occur at the beginning of the period 0 1 2 3 n-1 n . . . i% R R R R R FVADn Intro. to Financial Managment-Week 4a

12. FVAD3 = $1,000(1.07)3 + $1,000(1.07)2 + $1,000(1.07)1 = $1,225+$1,145+$1,070=$3,440 Example of an Annuity Due Cash flows occur at the beginning of the period 0 1 2 3 4 7% $1,000 $1,000 $1,000 $1,070 $1,145 $1,225 $3,440 = FVAD3 Intro. to Financial Managment-Week 4a

13. Ordinary versus Annuities Due • There is one extra interest period that accrues. • So we multiply the ordinary annuity by (1+i). • THAT IS ALL! Spencer Platt / Getty Images Traders on the floor of the New York Stock Exchange watch the news of a bigger-than-expected rate cut from the Federal Reserve. Intro. to Financial Managment-Week 4a

14. The Power of Compound Interest A 20-year-old student wants to start saving for retirement. She plans to save $3 a day. Every day, she puts $3 in her drawer. At the end of the year, she invests the accumulated savings ($1,095) in an online stock account. The stock account has an expected annual return of 12%. How muchmoney will she have when she is 65 years old? – Set up the problem! Intro. to Financial Managment-Week 4a

15. Solving for FV:Savings problem • If she begins saving today, and sticks to her plan, she will have ______________ when she is 65. • $1,487,261.89 Intro. to Financial Managment-Week 4a

16. Solving for FV:Savings problem, if you wait until you are 40 years old to start • If a 40-year-old investor begins saving today _____________at age 65. This is $1.3 million less than if starting at age 20. • $146,000.59 • Lesson: It pays to start saving early. Intro. to Financial Managment-Week 4a

17. Solving for PMT:How much must the 40-year old deposit annually to catch the 20-year old? • To find the required annual contribution, enter the number of years until retirement and the final goal of $1,487,261.89, and solve for PMT. 11,154.42!! PER YEAR! Intro. to Financial Managment-Week 4a

18. PVAn = R/(1+i)1 + R/(1+i)2 + ... + R/(1+i)n Present Value of anOrdinary Annuity -- PVA Cash flows occur at the end of the period 0 1 2 n n+1 . . . i% R R R R= Periodic Cash Flow PVAn Intro. to Financial Managment-Week 4a

19. PVA3 = $1,000/(1.07)1 + $1,000/(1.07)2 + $1,000/(1.07)3 = $934.58 + $873.44 + $816.30 = $2,624.32 Example of an Present Value of an Ordinary Annuity Cash flows occur at the end of the period 0 1 2 34 7% $1,000 $1,000 $1,000 $ 934.58 $ 873.44 $ 816.30 $2,624.32 = PVA3 Intro. to Financial Managment-Week 4a

20. Calculate the Present Values… • For each of the following ordinary annuities: • $500 payment, compounded every 6 months, for 12 years at 9.5% interest • $1000 payment, compounded annually, for 8 years at 10.8% • $250 payment, compounded monthly, for 10 years, at 8% • $500 payment, compounded quarterly, for 8 years at 9.8% Intro. to Financial Managment-Week 4a

21. The Present Value answers • There are 24 (2x12) periods of $500 payments at 4.75% (9.5/2) interest: $ 7070.27. • There are 8 yearly payments of $1000 discounted at 10.8% or $ 5183.03. • There are 120 payments of $250 at .067% (8/12) so $20,569.52 is the answer. • There are 32 payments (8 years and 4 times per year) of $500; at 0.0245% (9.8%/4) thus $11,001.81 is the answer. Intro. to Financial Managment-Week 4a

22. PVADn = R/(1+i)0 + R/(1+i)1 + ... + R/(1+i)n-1= PVAn (1+i) Overview of an Annuity Due Cash flows occur at the beginning of the period 0 1 2 n-1 n . . . i% R R R R R: Periodic Cash Flow PVADn Intro. to Financial Managment-Week 4a

23. PVADn = $1,000/(1.07)0 + $1,000/(1.07)1 + $1,000/(1.07)2 = $2,808.02 Example of an Annuity Due Cash flows occur at the beginning of the period 0 1 2 3 4 7% $1,000.00 $1,000 $1,000 $ 934.58 $ 873.44 $2,808.02 = PVADn Intro. to Financial Managment-Week 4a

24. Steps to Solve Time Value of Money Problems 1. Read problem thoroughly 2. Determine if it is a PV or FV (or PMT) problem 3. Create a time line 4. Put cash flows and arrows on time line 5. Determine if solution involves a single CF, annuity stream(s), or mixed flow 6. Solve the problem 7. Check (or solve) with Excel 8. Recheck work – does it make sense? Intro. to Financial Managment-Week 4a

25. Used Car • A used car sells for $10,000 in cash OR: • $2000 deposit plus 6 instalments of $1400 per month for 6 months • What is the implied interest in the instalment plan? Intro. to Financial Managment-Week 4a

26. The Interest Rate answer • 10,000 = 2,000 + 1400/(1+i/12) + 1400/(1+i/12)^2 + 1400/(1+i/12)^3+…+1400/(1+i/12)^6 • OR 8,000 = 1,400*(1/(1+i/12)+…+1/(1+i/12)^6) • In Excel, use the rate function: • PV = 8000, NPER = 6, PMT = 1400, … • Excel will solve it; I =1.41% per month OR i=16.945% annually! • Note that you must put in PMT or PV as a negative number. One is a pay OUT the other is paid IN. Intro. to Financial Managment-Week 4a

27. Steps to Amortizing a Loan 1. Calculate the payment per period. 2. Determine the interest in Period t. (Loan balance at t-1) x (i% / m) 3. Compute principal payment in Period t. (Payment - interest from Step 2) 4. Determine ending balance in Period t. (Balance - principal payment from Step 3) 5. Start again at Step 2 and repeat. Intro. to Financial Managment-Week 4a

28. Amortizing a Loan Example Julie Miller is borrowing $10,000 at a compound annual interest rate of 12%. Amortize the loan if annual payments are made for 5 years. First calculate the Payment: $10,000 = C (PVIFA 12%,5) $10,000 = C (3.605) C = $10,000 / 3.605 = $2,774 Intro. to Financial Managment-Week 4a

29. Amortizing a Loan Example [Last Payment Slightly Higher Due to Rounding] Intro. to Financial Managment-Week 4a

30. Solving for the Payment The result indicates that a$10,000loan that costs12%annually for 5 years and will becompletely paid offat that time will require $2,774.10 in annual payments. • You are to amortize a loan of $125,000. Make sure to follow the example, use a 9% interest rate and 20 years. In Excel, total the interest payments, total payments and principal as in the exmple on the previous slide. (5 pts) Intro. to Financial Managment-Week 4a

31. Homework Assignment • Chose a company from the Value Line documents (See my website, this is a Dow Jones 30 company). • Read the Value Line document and take a look at the financials. • Now calculate Free Cash Flow (FCF) = (NOPAT + depreciation +/- change in Working Capital - Capital Spending) • Do this for all the years available on the Value Line document. • Assume that the Cost of Capital (WACC%)=10% • Forecast the FCF for FY 2006 etc. years (assume an endless stream of FCF’s) • Now calculate the Present Value and use the WACC% as discount factor (i) • The present value you have calculated is an estimate for the value of the company you have chosen • Do it in Excel…and save time… Have fun! Intro. to Financial Managment-Week 4a

32. These are calculation techniques you need to master… • We will use them in the near future to calculate the present values of future cash flows of companies • Next week we will discuss Risk and Return (Chapter 5) We want to be aligned in the same direction… Intro. to Financial Managment-Week 4a