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473.32 6 Winter 2014

CF. 473.32 6 Winter 2014. Discounted Cash Flow Valuation. ch 6. Multiple Cash Flows  FV. you have: bank account that earns 8% interest $7,000 in bank now you: deposit $4,000 at end of each of next 3 years How much at the end of 3 years?. Multiple Cash Flows  FV. -7,000.00.

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473.32 6 Winter 2014

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  1. CF 473.32 6 Winter 2014

  2. Discounted Cash Flow Valuation ch 6

  3. Multiple Cash Flows  FV • you have: • bank account that earns 8% interest • $7,000 in bank now • you: • deposit $4,000 at end of each of next 3 years • How much at the end of 3 years?

  4. Multiple Cash Flows  FV • -7,000.00 • -4,000.00 • -4,000.00 • -4,000.00 • PV0 = -7,000.00 • t0 = • 3 • ? • PV1 = -4,000.00 • t1 = • 2 • FV0+FV1+FV2+FV3 • PV2 = -4,000.00 • t2 = • 1 • PV3 = -4,000.00 • t3 = • 0

  5. Multiple Cash Flows  FV • -7,000.00 • -4,000.00 • -4,000.00 • -4,000.00 • PV0 = -7,000.00 • t0 = • 3 • FV • PV1 = -4,000.00 • t1 = • 2 • PV2 = -4,000.00 • t2 = • 1 • PV3 = -4,000.00 • t3 = • 0

  6. Multiple Cash Flows  FV • you have: • mutual fund that earns 9% interest • invest $500 now • another $600 in 1 year • How much at the end of 2 years? • What if you leave it in for 5 years?

  7. Multiple Cash Flows  FV • How much at the end of 2 years? • PV0 • PV1 • -500.00 • -600.00 • 0 • 1 • 2 • FV

  8. Multiple Cash Flows  FV • How much at the end of 5 years? • PV0 • PV1 • -500.00 • -600.00 • 0 • 1 • 2 • 3 • 4 • 5 • FV • FV

  9. Multiple Cash Flows  FV • you have: • account the earns 8% interest • invest $100 at year 1 • another $300 at year 3 • How much at the end of 5 years?

  10. Multiple Cash Flows  FV • r =.08 • PV0 • PV1 • -100.00 • -300.00 • 0 • 1 • 2 • 3 • 4 • 5 • FV

  11. Multiple Cash Flows  PV • you are offered an investment that pays • $200 at year 1 • another $400 at year 2 • another $600 at year 3 • another $800 at year 4 • you can earn 12% on similar investments • How much is this investment worth today?

  12. Multiple Cash Flows  PV • r =.12 • PV0 • 0 • 1 • 2 • 3 • 4 • $200.00 • $400.00 • $600.00 • $800.00 • FV1 • FV2 • FV3 • FV4

  13. Multiple Cash Flows  PV • You are considering an investment that pays • $1,000 at year 1 • another $2,000 at year 2 • another $3,000 at year 3 • If you want to earn 10% on your money, how much should you be willing to pay?

  14. Multiple Cash Flows  PV • r =.10 • PV0 • 0 • 1 • 2 • 3 • $1,000.00 • $2,000.00 • $3,000.00 • FV1 • FV2 • FV3

  15. Multiple Cash Flows  PV • you’re CEO of small printing company • you want to make profits at least 10%. • your staff tell you • if you buy a used printing machine for $5,000 • it will make profits of: • $1,000 at the end of year 1 • another $2,000 at the end of year 2 • another $3,000 at the end of year 3 • machine will be worthless after year 3 • Should you buy the machine?

  16. Multiple Cash Flows  PV • r =.10 • PV0 • 0 • 1 • 2 • 3 • $1,000.00 • $2,000.00 • $3,000.00 • FV1 • FV2 • FV3 • $5,000?

  17. Multiple Cash Flows  PV • your staff have a new idea: • buy a machine for $100,000 • will make • $40,000 profit at the end of year 1 • $75,000 profit at the end of year 2 • after year 2 • again, machine value = $0 • this is a lot of money, so you want • 15% return

  18. Multiple Cash Flows  PV • r =.15 • PV0 • 0 • 1 • 2 • $40,000.00 • $75,000.00 • FV1 • FV2 • $100,000?

  19. Fri

  20. Saving For Retirement • simplify • you are offered opportunity to put some money away for retirement • you will receive • 5 annual payments • $25,000 each • beginning in 40 years • How much would you be willing to invest today if you desired an interest rate of 12%?

  21. Saving For Retirement • simplify • chart • 5 annual payments • $25,000.00 each • beginning in 40 years • interest rate of 12% • how much willing to invest?

  22. FV41 • FV42 • FV44 • FV40 • FV43 • 25,000.00 • 25,000.00 • 25,000.00 • 25,000.00 • 25,000.00 Saving for Retirement • chart • r =.12 • PV0

  23. Perpetuities & Annuities • payments at regular intervals • Annuity • a finite series • ordinary annuity • payment at end of each period • annuity due • payment at beginning of each period • Perpetuity • an infinite series

  24. What?Co. preferred stock $500.00 dividend every year interest rate of comparable investment 8.00% PV = present price = ? c = dividend every period = 500.00 r = interest = .0800 Perpetuity  PV

  25. What?Co. wants to issue preferred stock desired price $100.00 dividend of ? Why?Co. has a preferred stock current price $40.00 dividend of $1.00 every quarter Perpetuity  PV • c= $2.50/quarter • r = 2.50%/quarter

  26. Growing Perpetuity  PV • What?Co. • preferred stock • $500.00 dividend every year • dividend grows every year • 6.00% • comparable interest • 8.00%

  27. Annuities • Present Value annuity factor • Future Value annuity factor

  28. Annuity  PV • PV • PV = $1,243.43 • r = 10% • FV2 • FV3 • FV1 • 500.00 • 500.00 • 500.00

  29. Annuity  PV • Cadillac Escalade • loan payments • $632.00/month • bank terms • 1%/month • 48 months • How much can you borrow? • PV = $23,999.54

  30. Annuity  PV • Publishers Clearinghouse • $10 million prize • paid • 30 equal annual installments • $333,333.33 each • if PC can borrow money at 5% • how much does it actually cost them? • PV = $5,124,150.29

  31. Annuity  c • Finding the Payment • want to borrow $20,000 • 8% per year • compounded monthly • 4-year loan • c = -$488.26

  32. Annuity  t • borrow • $2,000.00 • at 5.00% • annual payments • $734.42 • How long before you pay off the loan? • solving for t • t = 3.00

  33. Annuities  FV • Saving for retirement • $2,000.00/year • 7.50% interest rate • How much will you have in 40 years?

  34. Growing Annuity  PV

  35. Growing Annuity  PV • $50,000-a-year job • increase by 5.00%/year • retire in 40 years • 8.00% interest rate • What is the present value of this job?

  36. EAR • m = # times interest compounded during the year • Effective Annual Rate • Which savings account is better? • 15.0% • compounded daily • 15.5% • compounded quarterly • 16.00% • compounded annually

  37. APR

  38. CorpFi Applications • Annuities • capital spending • “rational” price • lease or buy • Printing machine • $1,000.00 profit/year for 10 years • What should we pay?

  39. CorpFi Applications • Annuities • capital spending • “rational” price • lease or buy • Printing machine • which is better • buy for $6,000.00? • lease for $800.00/year?

  40. CorpFi Applications • Growing Annuities • What should my company be worth? • “rational” price • Profit • this year made • $16,000 • growing at 3%/year • alternative: 7.5%/year

  41. CorpFi Applications • Annuities • “rational” price • stock • common • preferred • bonds

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