Chapter 5 Introduction to Valuation Time Value of Money Present Value earlier money on a time line Future Value later money on a time line Interest Rate exchange rate between earlier money and later money Discount Rate Cost of Capital Opportunity Cost of Capital Required Return Discounting finding the present value of some future amount Chapter 6 Discounting Cash Flow Valuation Annuity finite series of equal payments that occur at regular intervals Ordinary Annuity an annuity where the first payment occurs at the end of the period Annuity Due an annuity where the first payment occurs that the beginning of the period Effective Annual Rate EAR the actual rate paid or received after accounting for compounding that occurs during the ear Annual Percentage Rate APR annual rate quoted by law periodic rate times the number of periods per year Nominal Rate Quoted Rate Stated Rate Periodic Rate Continuous Compounding occurs when investments or loans are perpetuities Chapter 7 Interest Rates and Bond Valuation Bond an interest only loan Par Value the principal amount of a bond that is repaid at the end of the term Face Value Coupon Rate the annual coupon divided by the face value of a bond Coupon Payment the stated interest payment made on a bond Maturity Date the specified date on which the principal amount of a bond is paid Yield or Yield to Maturity YTM the rate required in the market on a bond YTM Current Yield Capital Gains Yield Current Yield Annual Coupon Price Bond Value PV of coupons PV of par value Bond Value PV of annuity PV of lump sum Coupon Bond Repayment of Bonds x Par Value Last Coupon Payment After Tax Cash Outflow of Bonds x Coupon Payment x 1 Tax Rate As interest rates increase present values decrease As interest rates decrease present values increase Lower discount rate more valuable the coupon payments are today YTM coupon rate Par Value Bond Price YTM coupon rate Par Value Bond Price YTM coupon rate Par Value Bond Price Discount Bond a bond that has a price below par value which provides a yield above the coupon rate Premium Bond a bond that has a price above par value which provides a yield below the coupon rate Price Risk change in price due to changes in interest rates Long term bonds have more price risk than short term bonds Low coupon rate bonds have more price risk than high coupon rate bonds Reinvestment Rate Risk uncertainty concerning rates at which cash flows can be reinvested Short term bonds have more reinvestment rate risk than long term bonds High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds Not an ownership interest Creditors do not have voting rights Excess debt can lead to financial distress and bankruptcy Interest is considered a cost of doing business and is tax deductible Debt Equity Ownership interest Common stockholders vote for the board of directors and other issues Dividends are not considered a cost of doing business and are not tax deductible Dividends are not a liability of the firm and stockholders have no legal recourse if dividends are not paid An all equity firm cannot go bankrupt merely due to debt since it has no debt Bond Indenture contract between the company and the bondholders that includes Total amount of bonds issued Basic terms of the bonds A description of property used as security if applicable Sinking fund provisions Call provisions Details of protective covenants Government Bonds Treasury Securities o Federal government debt o T bills pure discount bonds with original maturity of one year or less o T notes coupon debt with original maturity between one and ten years o T bonds coupon debt with original maturity greater than 10 years Municipal Securities o Debt of state and local governments o Varying degrees of default risk rated similar to corporate debt o Interest received is tax exempt at the federal level Zero Coupon Bond a bond that makes no periodic interest payment coupon rate 0 The entire YTM comes from the different between purchase price and the par value Cannot sell for more than par value Deep Discount Bonds Original Issue Discount Bonds More risk than a comparable coupon bond Examples are Treasury Bills and principal only Treasury strips P FV 1 Required Return n Zero Coupon Bond Repayment of Bonds x par value After Tax Cash Outflow of Bonds x P1 P0 x Tax Rate Factors Affecting Bond Yields Default risk premium remember bond ratings Taxability premium remember municipal vs taxable Liquidity premium bonds that have more frequent trading will generally have lower required returns Anything else that affects the risk of the cash flows to the bondholders will affect the required returns Holding Period Yield The rate of return when you sell a bond before it matures Find the present value of the bond using the number of years until the bond matures as n Find the HPY using the price you paid as the present value and the present value of the bond at the time as the future value with the number of years you had the bond Chapter 8 Stock Valuation Constant Dividend No growth The firm will pay a constant dividend forever The price is computed using the perpetuity formula Price decreases when the rate of return increases Example Preferred Stock Constant Dividend Growth Constant Growth Model Gordon Model The firm will increase the dividend by a constant percent every period Long term growth is never greater than the required return rate Dividend Yield D1 P0 Capital Gains Yield P1 P 0 P 0 R Dividend Yield Capital Gains Yield g Capital Gains Yield Supernormal Growth Multistep growth Dividend growth is not consistent initially but settles down to a constant growth eventually Step 1 Compute the dividends until the growth levels off Step 2 Find the expected future price of the last year that uses the first growth rate Step 3 Find the present value of the expected future cash flows Features of Common Stock Voting rights Proxy votes Classes of Stock Share proportionally in declared dividends Share proportionally in remaining assets during liquidation Preemptive right first shot at new stock issue to maintain proportional ownership if desired Chapter 9 Net Present Value and Other Investment Criteria NPV Decision Rule of the owners If the NPV is positive accept the project Positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth Our goal is to increase owner wealth so NPV is a direct measure of how well this project will meet our goal NPV increases