FIN 300 Session

1. FIN 300 Session Ryerson SOS

2. Agenda • Recap Time Value of Money (TVM) • Bonds • Shares and Dividends • Capital Budgeting • Portfolio Theory

3. Time Value of Money TVM • APR – Interest rate as if it was compounded once a year • Does not consider compounding • Also known as the “Nominal Rate”

4. Time Value of Money TVM • Effective Annual Rate (EAR) – Adjusted annualized interest rate that considers compounding. EAR = (1+APR/n)n – 1 • N = Number of compounding per year.

5. Time Value of Money TVM • Effective Periodic Rate (EPR) – Interest rate that considers compounding and the number of payments per year. EPR = (1+EAR)t - 1 • T = (1 / Number of payments per year)

6. Using the P/Y & C/Y Calculator Function • If we use the P/Y & C/Y function, there is no need to convert the annual rate into EPR. • P/Y – Payments per year • C/Y – Compounding per year

7. Example: TVM • If SOS invests $100 per month for 2 years at 10% compounded semiannually, how much will it have at the end of 2 years? • EAR = 10.25 EPR = .8165 • N=24 I/Y=.8165 C/Y P/Y=1 PV=0 PMT=100 • FV= 2,639

8. Example: TVM • If SOS invests $100 Per month for 2 years at 10% compounded semiannually, how much will it have at the end of 2 years? • N=24 I/Y=10 C/Y = 2 P/Y=12 PV=0 PMT=100 FV= 2,639

9. Valuing Perpetuities • Perpetuity – Annuity in which the cash flows continue forever. • Formula:

10. Valuing Growing Perpetuities • Formula • Example: • Homer promises to give you $100 every year forever. Homer promises to pay you a 10% return compounded annually. Homer also states that the $100 will grow at a rate of 4%. What is the present value of Homers offer? • = (100) / (.10-.04) --> $1666.67

11. Mortgages • Mortgages = Annuities • Example: You get a $200,000, 30 Year mortgage. SOS Bank offers you a 10% loan compounded weekly. You agreed to make weekly payments. How much are the mortgage payments?

12. Mortgage Example • N= (30 X 52)  1,560 I/Y= 10% P/Y = 52 C/Y= 52 PV = $200,000 FV = 0 Payment = $404.83 • OR • N = 1,560 I/Y= .19231% P/Y = 1 C/Y= 1 PV = $200,000 FV = 0 Payment = $404.83

13. Mortgage Example • How much do you owe SOS Bank after 2 years (104 payments)? • N= (28 X 52)  1,456 I/Y= 10% P/Y = 52 C/Y= 52 FV = $0 PMT= 404.83 Present Value = $197,674 • OR • N = 1,456 I/Y= .19231% P/Y = 1 C/Y= 1 FV = 0 PMT= 404.83 Present Value = $197,674

14. Bonds • What is a bond? • A bond is an IOU issued by a corporation, government, or governmental agency. • As a bondholder, you are a creditor.

15. Bonds • Key Terms: • Coupon Rate – Stated interest payments made on a bond. • Yield to Maturity (YTM) – Also known as the market rate. • This is the rate we use to discount the coupons and the face value of the bond.

16. Bond Valuation Example 1 • You purchased a SOS 9% bond with 10 years to maturity. The bond makes semiannual payments and it has a YTM of 9%. What is the value of the bond today? • N= (10x2)  20 I/Y= 9% P/Y = 2 C/Y=2 FV = $1,000 PMT= 45 (9% x $1,000 / 2) Present Value = $1,000

17. Bond Valuation Example 2 • You purchased a SOS 9% bond with 10 years to maturity for $1060. The bond makes semiannual payments. What is the YTM of the bond? • N= (10x2)  20 P/Y = 2 C/Y=2 FV = $1,000 PMT= 45 (9% x $1,000 / 2) PV= ($1,060) APR (I/Y) = 8.11%

18. Bond Valuation Example 3 • You purchased a SOS bond with 10 years to maturity for $920. The bond makes semiannual payments and it has a YTM of 10%. Compute your semiannual coupon payments • N= (10x2)  20 I/Y = 10% P/Y = 2 C/Y=2 FV = $1,000 PV= ($920) Payments = 43.58 or 8.72%

19. Remember… • When the coupon rate is HIGHER than the YTM, the bond will sell at a premium. (above par). • When the coupon rate is EQUAL to the YTM, the bond will sell at par. • When the coupon rate is LOWER than the YTM, the bond will sell at a discount (bellow par).

20. Zero Coupon Bonds • Also called stripped Bond • A bond that makes no coupon payments • Sells at a deep discount • This type of bonds sell at a deep discount

21. Zero Coupon Bonds… Example • Suppose SOS issues a $1000 face value, 10 year strip bond. What is the price of the bond today if the YTM is 10%? • N= 10 I/Y= 10% P/Y = 1 C/Y=1 FV = $1,000 PMT= 0 Present Value = $653.32 • The bond sell at a deep discount because there is no coupon payments.

22. Chapter 8Stock Valuation • TVM is used in the dividend discount model • Required rate of return • Types of dividends • Constant • Growing • Supernormal growth

23. Chapter 8Stock Valuation • Required rate of return • return the market requires from this investment • Different than risk-free rate because equity investment is more risky • Consider this the same as “r” in TVM formulas

24. Chapter 8Stock Valuation • You should have a solid grasp of TVM and cash flows by now, so focus on how to apply this knowledge to stock valuation

25. Zero Growth Dividend • Dividend does not change • Think of this as a perpetuity with ‘D’ being the cash flow and ‘r’ being the rate of interest

26. Zero Growth Dividend • Dividend does not change • Think of this as a perpetuity

27. Zero Growth Dividend • Example: SOS Common will be paying a dividend of $3 forever. The rate of return required for SOS Common stock is 12%. What should you pay for SOS?

28. Zero Growth Dividend • Example: The price of RSOS common stock is $30 and the required rate of return is 10%. What constant dividend is RSOS paying?

29. Constant Growth Dividend • The dividend keeps growing at a constant rate forever • This is the same as a constant growth perpetuity: ‘D’ is the cash flow, ‘r’ is the rate and ‘g’ is the growth rate • Note the difference between D0 and D1_

30. Constant Growth Dividend • Also called dividend growth model • P0 is the current stock price • D0 is the current dividend • D1 is the next dividend • g is the growth rate of the dividend • r is the required return from the equity

31. Constant Growth Dividend • You may also see the formula in the form below • Pt is the price at time ‘t’ • Dt is the dividend at time ‘t’

32. Constant Growth Dividend • Example: SOS common stock will pay a dividend of $2 next year. The dividend will increase by 5% a year after that. Required rate of return is 15%. What is the value of SOS today? What is the value of the stock in five years? • D1 = $2, g=.05, r=.15 • P0=???, P5=???

33. Constant Growth Dividend • D1 = $2, g=.05, r=.15 • P0=??? • We now have to find the price in five years

34. Constant Growth Dividend • D1 = $2, D5 = ???, g=.05, r=.15 • P5=??? • What will the dividend be in five years? • We now have to find the price in five years

35. Non-Constant Growth Dividend • In real life dividends often vary from quarter to quarter and year to year • Need a way to price these equities with non-constant growth dividends • The solution: use TVM and the dividend pricing formulas • Already know how to discount cash flows back to PV and that is what this process does

36. Non-Constant Growth Dividend • The best way to show this process is to do an example • SOS common stock’s dividend has been growing at 50% and will continue to grow at this rate for the next five years. After five years the dividend will only grow at the rate of 5% per year. What is the price of the stock now?

37. Non-Constant Growth Dividend • SOS common stock’s dividend has been growing at 50% and will continue to grow at this rate for the next two years. After two years the dividend will only grow at the rate of 5% per year forever. Required return for this stock is 10%. If they just paid a dividend of $1, what is the price of the stock now? • D0 = $1, g1=50%, g2=5%, r=10% • P0=???

38. Non-Constant Growth Dividend • D0 = $1, g1=.50, g2=5%, r=.10 • P0=??? • Find first two dividends (1+g1)=1.50 • D1=($1*1.50)=$1.50 • D2=($1.50*1.50)=$2.25 • Now we have to find price for the constant growth period

39. Non-Constant Growth Dividend • D2 = $2.25, g1=.50, g2=5%, r=.10 • Discount all cash flows to t0 to find price of stock

40. Common and Preferred Stock • Common Stock • Right to share proportionally in dividends • Right to share assets after liabilities have been paid i.e. bond and debt holders • Right to vote on matters of great importance e.g. merger • Sometimes have preemptive right to by new stock sold first

41. Common and Preferred Stock • Preferred Stock • Preference over dividend payment • Must receive dividend before common shareholders • Preference over division of assets if company gets liquidated • Usually have no voting privileges

42. Dividends • Some legal stuff about them • Not a liability unless declared by the board of directors • Not a business expense • Not tax deductible for corporation • Paid out of after tax profits • Dividends are sheltered in Canada by a tax credit

43. Chapter 8Stock Valuation • Tricks: • Prof may ask an “over or under question” • Give a stock price and information to find price and ask if stock is over or undervalued • Remember to discount cash flows properly with supernormal growth dividends • Pay attention to which dividend you are given or required to solve for i.e. D0 or D1 • Pay attention to which price you are given or required to solve for i.e. P0 or Pt • Know the difference between required rate of return and risk free rate

44. Chapter 8Stock Valuation • Study tips: • Do supernormal growth questions in text book

45. Capital Budgeting • The process of planning and managing a firm’s investment in long term assets. • Methods: • Net Present Value (NPV) • Internal Rate of Return (IRR) • Payback Period • Profitability Index

46. NPV and IRR • NPV and IRR use the discounted cash flow methods to make a decision and rank projects. • IRR is the discount rate that makes the NPV of an investment “ZERO” • If the NPV > 0, Then accept project. • If IRR is > required rate return, then accept project.

47. Capital Budgeting Example: Computethe NPV and IRR of the above cash flows. Assume a 15% required rate of return. NPV = $37,980 IRR= 37.42%

48. Capital Budgeting Cont… • Use only incremental cash flows only. • Sunk costs (Costs that have already been incurred) are not considered in an investment decision. • Cost of old equipment.

49. Net Present Value…The List Approach • Capital Cost • PV of Salvage • Initial Net Working Capital (NWC) • Change in NWC • PV of Operating Cash Flows • PVCCATS – Loss CCATS due to Salvage Value

50. List Approach Example: • 3 Year Project • $1,000,000 Initial Investment, with a salvage of $576,000 after 3 years. • The project also requires a $100,000 investment in NWC. • After Tax incremental income = $240,000 • Tax rate: 40% Rate of Return (After Tax): 10% • CCA Rate: 20%