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Valuation of Money, Stock; and Bonds The Time Value of Money • Simple and compound interest • Future Values and Compound Interest mT r fvm ,T 1 m • As m approaches infinity, the factor 1 m r r e m where e = 2.71828 The Time Value of Money • Given continuous compounding, the future value of a dollar n periods hence is rT fvT e The Time Value of Money The Time Value of Money • Annually Compounded Interest Rates (Effective Interest Rate) (EIR) = (1+ i/m)m -1 Vs Annual Percentage Rates (i) = Monthly rate X 12 = Quarterly rate X4 The Time Value of Money Present Values Pv = Future Value After “t” Periods (1+r)t DF is always <1 and keeps decreasing with increasing “t” The Time Value of Money Compounding m Interest EIR Period per (1+i/m)m % period % 1 year 1 6 (1.06)1 6.00 Semiannually 2 3 (1.03)2 6.0900 Quarterly 4 1.5 (1.015)4 6.134 Monthly 12 0.5 (1.005)12 6.1678 Weekly 53 0.11538 (1.0011538)52 6.1800 Daily 365 0.01644 (1.0001644)365 6.1831 Continuous ∞ Almost 0 (2.718)0.06 6.1837 Calculating Present Value Present Value for Single Period: PV = C X DF = C / (1+r) Present Value for Several Periods of Varying Amounts: PV (A+B+C+D….) = C1 + C2 + C3 + C4 +… (1+r) (1+r)2 (1+r)3 (1+r)4 = E [ Ct] ( 1+ r)t The Time Value of Money Annuity Fv = C[(1+ r/m)nm -1] r/m Pv = C[(1+ r/m)nm -1] = 1 - 1 r/m (1+ r/m)nm r r (1+r)t Growing Annuities = C1 + C1 (1 + g) + C1(1 + g)2 …. + C1 (1 + g) t-1 + (1+ r) (1 +r)2 (1 +r)3 (1 + r)t = C1 1 - (1 + g)t (r - g) (r - g) (1 + r)t Types of Annuities Ordinary Annuity Annuity Due PV Annuity Due = PV Ordinary Annuity for (t-1) Payments + Initial Payment Annuity Deferred PV Annuity Deferred = PV Ordinary Annuity (1 + r)n-1 Where n = No. of years annuity delayed General Annuity – when compounding periods and payment periods do not coincide There are two ways that we can do it: 1) Convert the interest rate to the effective rate for the payment period 2) Convert the payments to EACs that correspond with the compounding periods Convert the interest rate to the effective rate for the payment period R=100 per month for 03 years i = 14% pa, being compounded daily Effective daily rate = .14/365 =0.0003836 or 0.03836% (For 28 days a month and for calendar months?) Effective monthly rate = (1+ 0.0003836)28 -1 = 0.010796 = 1.0796% PV of loan = 100 1 - 1 0.010796 0.010796(1+ 0.010796)39 = 3169.28 Convert the payments to EACs that correspond with the compounding periods R=100 i = 14% pa, being compounded daily Effective daily rate = .14/365 =0.0003836 or 0.03836% EAC =? 100 =EAC 1 - 1 0.0003836 0.0003836(1+ 0.0003836)28 EAC = 3.553 per day PV of loan =3.353 1 - 1 0.0003836 0.0003836(10.0003836)1092 = 31169.28 Relationship between Present Value, Future Value and Equivalent Annuity Cash Flows Multiply EAC by Multiply PV by present value PV inverse of present annuity factor value annuity factor EAC EAC FV Multiply EAC by Multiply FV by Future value inverse of Future annuity factor value annuity factor Perpetuities Pv of Perpetuity = C/r Pv of Growing Perpetuity = C1 C2 (1 + g) C3(1 + g)2 + + …. (1 +r) (1 + r)2 (1+ r)3 + = C1 (r - g) Declining Discount Factor? Basis of Capital Market • A dollar tomorrow has value lower than a dollar today • There is no money machine (arbitrage) The Time Value of Money Net Present Value of Project = Pv of Cash flows out – Required Investment Remember: A risky dollar is worth less than a safe one Other Names: Present Value or just Pv Discounted Value Market Price Market Value The Time Value of Bonds Bonds and Notes • Bond (10% bonds of 22 etc.) • Coupon • Face Value/Par Value/ Maturity Value (US$1000) • Coupon Rate (%age of par value) • Current Yield • Yield to Maturity (equates bond’s price to present value) • Rate of Return on Bonds – The %age rate of actual income upon investment by holding a bond for a specific period Effects of interest rates on bond’s market values/Prices PV of bond payments Interest rate, % The Time Value of Bonds Reading the Financial Pages Treasury Bonds Maturity Ask Rate Mo/Yr Bids Ask Chg Yld 7 June 93n 100:10 100:12 -1 2.08 111/2 Nov 95 116:17 116:21 - 3 4.27 Note It is in YTM of Coupon It is quoted in 32nds Investor 32nds Rate p.a Prices are 100 + 10/32 = 100.315% of Face value (Spread of 2/32) & 116+ 17/32 = 116.375% of Face value (Spread of 4/32) The Time Value of Bonds Reading the Financial Pages Other Bonds Cur. Net Bonds Yld Vol Close Chg AT&T 81/8 22 7.7 84 105 ¼ 1/4 Year of maturity Coupon 105 ¼ of the face ¼ of 1 % of Rate p.a. value face vale Interest income as percentage of the Bond’s price Interest income =81.25 (8 1/8% of 1000) How to show price Bond’s Price =1052.50 below par value? Cur. Yld = 81.25/1052.50 = 0.077 =7.7% The Time Value of Bonds • Bond Price as %age of its face value e.g. 115.87% [ A 5- year 9% Bond with prevailing interest rate @ 5.3%- 15.87% above the face value] • Yield to Maturity – Internal rate of return – The discount rate that makes the present value of a bond’s payments equal to its price (Diff in face value and present value of bonds) • Bonds Rating • Investment Bonds and Junk Bonds (Bbb/BBB & above and Ba/BA& below) • Coupon rate and rate of return Moody’s Standard & Poor’s The Term Structure of Interest Rates (Relationship between time to maturity and yield to maturity) YTM % Abnormal Yield Curve Normal Yield Curve Maturity Period The Term Structure of Interest Rates Short term yield is lower than long term yield Why not the investors go for only long term bonds? Nominal and Real Interest Rate (Inflation and The Time Value of Money) Consumer Price Index %age increase in CPI is the measurement of Inflation Current or nominal dollar and constant or Real dollar US CPI 1947-1993 Purchasing 800 Power Index (1947=100) Consumer Price 600 adjusted value 400 of dollar 200 Series1 0 Years Years (1947-1992) Real Future value of investment = Investment X (1+ nominal interest rate) (1+ Inflation rate) Real rate of interest Rate at which the purchasing power = (1+ nominal interest rate) - 1 of an investment (1+ inflation rate) increases Approximately it is the diff of NIR and IR if Nos. are small Real Cash Flow = Nominal Cash Flow (1+Inflation rate) Current cash flows to be discounted by the nominal interest rate and the real cash flows by the real interest rate • Price of the bond and its valuation Price/PV (Bond)= PV (Coupon Payments)+ PV (Principal) = (coupon X n-years annuity factor) + (final payment X n- year discount factor) Example: A 07 years 7.5% annual Coupon rate treasury bond with face value of $1000 {Suppose the prevailing rate on a similar risk security (TB) is 5.41%} Price/ Market value /PV= 75 1 - 1 0.0541 0.0541 (1.0541)7 = 427.60 + 691.56 = $1119.56 What if the required rate of return is different in different years? Valuation of Common Stock • Common Stock and Preferred Stock • Primary and Secondary markets • Stock Exchange Working • Reading The Stock Market Listing • Dividend • Price Earning Ratio Valuation of Common Stock • Book Value and Market Value • Liquidation Value • Going Concern Value – The diff. between Book value and liquidation value- Can be traced to: Extra Earning Power Intangible assets; and Value of Future Investments Valuing Common Stock • Valuing Common Stock Pay offs to owners comes in two ways a) Cash Dividend b) Capital Gains or Losses Hence: Expected Return = r = DIV1 + ( P1 – P0) P0 = Expected Dividend + Expected Capital Yield appreciation Today’s Price = P0 = DIV1 + P1 1+ r Valuing Common Stock P1 is dependent upon all future cash flows P1 = P2 + DIV2 1+ r P2 = P3 + DIV3 (1+r)2 ….. P0 = DIV1 + DIV2 + DIV3 +…..+ DIVH + PH (1+r) (1+r)2 (1+r)3 (1+r)H The Dividend Discount Model Valuing Common Stock • Dividend dependent upon: a) EPS b) Dividend Policy The present value of all dividends = PD0 = DIV1 + DIV2 + DIV3 +….. + DIVt 1+ r (1+ r)2 (1+ r)3 (1+ r)t If constant dividend: PD0 = DIV 1 + 1 + 1 + ………+ 1 1+ r (1+ r)2 (1+ r)3 (1+ r)t If t ∞ PD0 = DIV r Valuing Common Stock The Dividend Discount Model with No Growth (100% Dividend Pay out Ratio ) If the company pays a constant dividend – a Perpetuity… PD0 = DIV1 r PD0 = EPS1 r Valuing Common Stock The Dividend Discount Model with Constant Growth (Gordon Growth Model) DIV1 = 3 DIV2 = 3(1+ g) = 3 (1+.08) = 3.24 (Suppose g = 8%) DIV3 = 3(1+g)2 = 3 (1+.08)2= 3.50 PD0 = D1 + D1(1+g)2 + D1(1+g)3 +……. = DIV1 1+r (1+r)2 (1+r)3 r–g = DIV0 + DIV1 (If the immediate dividend is included) r–g = DIV0 (1+g) (Because DIV1 = DIV0 X g) r-g Provided: a) g is constant b) g < r c) Dividend is paid d) There is no loss Valuing Common Stock The expected rate of return PD0 = DIV1 = r–g r = DIV1 + g = The Market Capitalization rate PD0 = Dividend Yield + Growth Rate DIV1 + g = r = Expected rate of return offered by other, equally risky stocks PD0 Given DIV1 and g So that subject company offers an Investors set the stock Price adequate expected rate of return r Valuing Common Stock Growth Stocks and Income Stocks o Payout Ratio EPS/BVPS 1-POR o Plowback Ratio (b) o g = Return on Equity X Plowback ratio o Present Value of Growth opportunities (PVGO) o Sustainable Growth Rates (g) o Methods to alter Profits Depreciation Methods Inventory Evaluation Methods Treating R&D Expense as current rather than Investment Methods of Reporting Tax Liabilities Some Warnings about Constant-Growth Model • r is only for a single share . A large number of equal risk securities may be taken into account • Resist applying it to firms with high current rates of growth – Difficult to sustain these rates • Avoid using it in inflationary period • Do not use simple constant-growth formula to test whether the market is correct in its assessment of share’s value. You may be making poor dividend forecast Remember: There are no mechanical rules to forecasting future

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posted: | 7/7/2010 |

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valuation of bonds and other inventories

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