8 - 1 Copyright © 2002 by Harcourt, Inc.All rights reserved. Chapter 2: DCF Applications Application 1: Capital budgeting Application 2: Bond Valuation Application 3: Investment Performance Analysis Application 4: Equity / stock valuations

8 - 2 Copyright © 2002 by Harcourt, Inc.All rights reserved. What is capital budgeting? Analysis of potential additions to fixed assets. Long-term decisions; involve large expenditures. Very important to firm’s future.

8 - 3 Copyright © 2002 by Harcourt, Inc.All rights reserved. Steps 1. Estimate CFs (inflows & outflows). 2. Assess riskiness of CFs. 3. Determine k = WACC (adj.). 4. Find NPV and/or IRR. 5. Accept if NPV > 0 and/or IRR > WACC.

8 - 4 Copyright © 2002 by Harcourt, Inc.All rights reserved. NPV:Sum of the PVs of inflows and outflows.

8 - 5 Copyright © 2002 by Harcourt, Inc.All rights reserved. What is Project L’s NPV? % Project L: = NPV L NPV S = $19.98.

8 - 6 Copyright © 2002 by Harcourt, Inc.All rights reserved. Calculator Solution Enter in CFLO for L: CF 0 CF 1 NPV CF 2 CF 3 I = = NPV L

8 - 7 Copyright © 2002 by Harcourt, Inc.All rights reserved. Rationale for the NPV Method NPV= PV inflows – Cost = Net gain in wealth. Accept project if NPV > 0. Choose between mutually exclusive projects on basis of higher NPV. Adds most value.

8 - 8 Copyright © 2002 by Harcourt, Inc.All rights reserved. Internal Rate of Return: IRR 0123 CF 0 CF 1 CF 2 CF 3 CostInflows IRR is the discount rate that forces PV inflows = cost. This is the same as forcing NPV = 0.

8 - 9 Copyright © 2002 by Harcourt, Inc.All rights reserved. NPV: Enter k, solve for NPV. IRR: Enter NPV = 0, solve for IRR.

Copyright © 2002 by Harcourt, Inc.All rights reserved. What’s Project L’s IRR? IRR = ? PV 3 PV 2 PV 1 0 = NPV Enter CFs in CFLO, then press IRR: IRR L = 18.13%.IRR S = 23.56%.

Copyright © 2002 by Harcourt, Inc.All rights reserved IRR = ? Find IRR if CFs are constant: -100 Or, with CFLO, enter CFs and press IRR = 9.70% % INPUTS OUTPUT NI/YRPVPMTFV

Copyright © 2002 by Harcourt, Inc.All rights reserved. Rationale for the IRR Method If IRR > WACC, then the project’s rate of return is greater than its cost--some return is left over to boost stockholders’ returns. Example:WACC = 10%, IRR = 15%. Profitable.

Copyright © 2002 by Harcourt, Inc.All rights reserved. IRR Acceptance Criteria If IRR > k, accept project. If IRR < k, reject project.

Copyright © 2002 by Harcourt, Inc.All rights reserved. Bonds and Their Valuation Key features of bonds Bond valuation Measuring yield Assessing risk

Copyright © 2002 by Harcourt, Inc.All rights reserved. Key Features of a Bond 1.Par value: Face amount; paid at maturity. Assume $1, Coupon interest rate: Stated interest rate. Multiply by par to get $ of interest. Generally fixed.

Copyright © 2002 by Harcourt, Inc.All rights reserved. 3.Maturity: Years until bond must be repaid. Declines. 4.Issue date: Date when bond was issued.

Copyright © 2002 by Harcourt, Inc.All rights reserved. Financial Asset Values  PV= CF 1+k... + CF 1+k 1n k n. 012n k CF 1 CF n CF 2 Value

Copyright © 2002 by Harcourt, Inc.All rights reserved. The discount rate (k i ) is the opportunity cost of capital, i.e., the rate that could be earned on alternative investments of equal risk. k i = k * + IP + LP + MRP + DRP.

Copyright © 2002 by Harcourt, Inc.All rights reserved.  V kk B dd  $100$1, $ k d = $ $ $ = $1, % ,000 V = ?... What’s the value of a 10-year, 10% coupon bond if k d = 10%?

Copyright © 2002 by Harcourt, Inc.All rights reserved NI/YR PV PMTFV -1,000 The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10: $ $1, PV annuity PV maturity value PV bond ====== INPUTS OUTPUT

Copyright © 2002 by Harcourt, Inc.All rights reserved. What is the “yield to maturity”? YTM is the rate of return earned on a bond held to maturity. Also called the “promised yield.”

Copyright © 2002 by Harcourt, Inc.All rights reserved. What’s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887? k d =? 1,000 PV 1. PV 10 PV M 887 Find k d that “works”!...

Copyright © 2002 by Harcourt, Inc.All rights reserved NI/YR PV PMT FV  V INT k M k B d N d N  INT 1 + k d   kk dd k d, Find k d INPUTS OUTPUT...

Copyright © 2002 by Harcourt, Inc.All rights reserved. If coupon rate < k d, discount. If coupon rate = k d, par bond. If coupon rate > k d, premium. If k d rises, price falls. Price = par at maturity.

Copyright © 2002 by Harcourt, Inc.All rights reserved. Find YTM if price were $1, NI/YR PV PMTFV 7.08 Sells at a premium. Because coupon = 9% > k d = 7.08%, bond’s value > par. INPUTS OUTPUT

Copyright © 2002 by Harcourt, Inc.All rights reserved. Definitions Current yield =. Capital gains yield =. = YTM = +. Annual coupon pmt Current price Change in price Beginning price Exp total return Exp Curr yld Exp cap gains yld

Copyright © 2002 by Harcourt, Inc.All rights reserved. Current yield= = = 10.15%. Find current yield and capital gains yield for a 9%, 10-year bond when the bond sells for $887 and YTM = 10.91%. $90 $887

Copyright © 2002 by Harcourt, Inc.All rights reserved. YTM= Current yield + Capital gains yield. Cap gains yield = YTM – Current yield = 10.91% – 10.15% = 0.76%. Could also find value in Years 1 and 2, get difference, and divide by value in Year 1. Same answer.

Copyright © 2002 by Harcourt, Inc.All rights reserved. Semiannual Bonds 1.Multiply years by 2 to get periods = 2n. 2.Divide nominal rate by 2 to get periodic rate = k d /2. 3.Divide annual INT by 2 to get PMT = INT/2. 2n k d /2 OK INT/2OK NI/YR PV PMTFV INPUTS OUTPUT

Copyright © 2002 by Harcourt, Inc.All rights reserved. 2(10) 13/2 100/ NI/YR PV PMTFV Find the value of 10-year, 10% coupon, semiannual bond if k d = 13%. INPUTS OUTPUT

Copyright © 2002 by Harcourt, Inc.All rights reserved. You could buy, for $1,000, either a 10%, 10-year, annual payment bond or an equally risky 10%, 10-year semiannual bond. Which would you prefer? The semiannual bond’s EFF% is: 10.25% > 10% EFF% on annual bond, so buy semiannual bond.

Copyright © 2002 by Harcourt, Inc.All rights reserved. If $1,000 is the proper price for the semiannual bond, what is the proper price for the annual payment bond? Semiannual bond has k Nom = 10%, with EFF% = 10.25%. Should earn same EFF% on annual payment bond, so: N I/YRPV PMT FV INPUTS OUTPUT

Copyright © 2002 by Harcourt, Inc.All rights reserved. A 10-year, 10% semiannual coupon, $1,000 par value bond is selling for $1, with an 8% yield to maturity. It can be called after 4 years at $1,050. What’s the bond’s nominal yield to call (YTC)? N I/YR PV PMT FV x 2 = 7.137% INPUTS OUTPUT

Copyright © 2002 by Harcourt, Inc.All rights reserved. k Nom = 7.137% is the rate brokers would quote. Could also calculate EFF% to call: EFF% = ( ) 2 – 1 = 7.26%. This rate could be compared to monthly mortgages, etc.

Copyright © 2002 by Harcourt, Inc.All rights reserved. Bond Ratings Provide One Measure of Default Risk Investment GradeJunk Bonds Moody’sAaaAaABaaBaBCaaC S&PAAAAAABBBBBBCCCD

Copyright © 2002 by Harcourt, Inc.All rights reserved. Provisions in the bond contract Secured vs. unsecured debt Senior vs. subordinated debt Guarantee provisions Sinking fund provisions Debt maturity

Copyright © 2002 by Harcourt, Inc.All rights reserved. Dollar-weighted returns Internal rate of return considering the cash flow from or to investment Returns are weighted by the amount invested in each stock Time-weighted returns Not weighted by investment amount Equal weighting Performance Valuations: Dollar- and Time-Weighted Returns

Copyright © 2002 by Harcourt, Inc.All rights reserved. Text Example of Multiperiod Returns PeriodAction 0Purchase 1 share at $50 1Purchase 1 share at $53 Stock pays a dividend of $2 per share 2Stock pays a dividend of $2 per share Stock is sold at $108 per share

Copyright © 2002 by Harcourt, Inc.All rights reserved. PeriodCash Flow 0-50 share purchase 1+2 dividend -53 share purchase 2+4 dividend shares sold Internal Rate of Return: Dollar-Weighted Return

Copyright © 2002 by Harcourt, Inc.All rights reserved. Time-Weighted Return Simple Average Return: (10% %) / 2 = 7.83%

Copyright © 2002 by Harcourt, Inc.All rights reserved. Averaging Returns Arithmetic Mean: Geometric Mean: Text Example Average: ( ) / 2 = 7.81% [ (1.1) (1.0566) ] 1/2 - 1 = 7.83% Text Example Average:

Copyright © 2002 by Harcourt, Inc.All rights reserved. Past Performance - generally the geometric mean is preferable to arithmetic Predicting Future Returns- generally the arithmetic average is preferable to geometric. Geometric has downward bias Comparison of Geometric and Arithmetic Means

Copyright © 2002 by Harcourt, Inc.All rights reserved. 1) Sharpe Index r p - r f p r p = Average return on the portfolio r f = Average risk free rate p = Standard deviation of portfolio return   Risk Adjusted Performance: Sharpe

Copyright © 2002 by Harcourt, Inc.All rights reserved. 2) Treynor Measure r p - r f ß p r p = Average return on the portfolio r f = Average risk free rate ß p = Weighted average  for portfolio Risk Adjusted Performance: Treynor

Copyright © 2002 by Harcourt, Inc.All rights reserved. = r p - [ r f + ß p ( r m - r f ) ] Risk Adjusted Performance: Jensen 3) Jensen’s Measure p p = Alpha for the portfolio r p = Average return on the portfolio ß p = Weighted average Beta r f = Average risk free rate r m = Avg. return on market index port.  

Copyright © 2002 by Harcourt, Inc.All rights reserved. Appraisal Ratio Appraisal Ratio =  p /  (e p ) Appraisal Ratio divides the alpha of the portfolio by the nonsystematic risk Nonsystematic risk could, in theory, be eliminated by diversification

Copyright © 2002 by Harcourt, Inc.All rights reserved. It depends on investment assumptions 1) If the portfolio represents the entire investment for an individual, Sharpe Index compared to the Sharpe Index for the market. 2) If many alternatives are possible, use the Jensen  or the Treynor measure The Treynor measure is more complete because it adjusts for risk Which Measure is Appropriate?

Copyright © 2002 by Harcourt, Inc.All rights reserved. Decomposing overall performance into components Components are related to specific elements of performance Example components Broad Allocation Industry Security Choice Up and Down Markets Performance Attribution

Copyright © 2002 by Harcourt, Inc.All rights reserved. Set up a ‘Benchmark’ or ‘Bogey’ portfolio Use indexes for each component Use target weight structure Process of Attributing Performance to Components

Copyright © 2002 by Harcourt, Inc.All rights reserved. Calculate the return on the ‘Bogey’ and on the managed portfolio Explain the difference in return based on component weights or selection Summarize the performance differences into appropriate categories Process of Attributing Performance to Components