EMGT 502

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EMGT 502

• Thursday
• 1 September 2006

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Today

• Work some FV, PV, and NPV Problems
• Maybe get to financial asset valuation
• Do some initial VB programming in Excel

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PV Problem

• Discuss valuation issues especially bonds
• What is the PV of 200 in 1 year and 100 in 2
  years? (at 15?)
• If the cost of this cash flow stream is 220,
  whats the NPV? IRR?

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PV Problem

• Well, at 15 the NPV is about 29.52. Good
  project?
• At 30 the NPV is about -6.98. Good project?
• What about the IRR?
• How can we decide?
• What if the cash flows are reversed?

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What About the IRR

• There should be only 1 most of the time
• Often we have to solve for the (we hope) unique
  solution iteratively
• Usually built-in function in most programs

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FV Analogy

• The IRR of the simple example with the
  favorable cash flow is 26.77 (.26766).
• That means we could invest the 220 at 26.77 and
  generate the two cash flows.

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Cash Flow Timing

• We can see from the previous graph that timing
  does matter
• Sooner is always better, right? for positive
  cash flows, anyway.
• Suppose the 220 can be paid in two equal
  installments, one now and one in 6 months. What
  then?

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Still More on Timing

• First, note what happened to the PV of the
  outflows in our small example.
• Now, what if inflows can be realized monthly
  for the less-preferred cash-flow stream only.
  Now what?
• What if we can arrange for weekly cash inflows?
  Daily?

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Annuities

• What is the present value of 100 to be received
  annually for the next 20 years if the rate is
  15?
• Depends on the start date suppose its in 1
  year.

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NPV Problem

• Suppose we have a project that will have positive
  annual cash flows of 1m for 5 years beginning 3
  years from now. Initial investment is 2m, with
  1m required in 1 and 2 years. NPV at 20? IRR?

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Interest Rates (k)

• Generally quoted on an annual basis APR
• If we have a non-annual period, we need to adjust
  
• For less than 1 year, with m defined as the
  number of periods/year
• Effective Annual Rate EAR

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Continuous Compounding

• Obviously, as m increases, the gap between EAR
  and APR will also increase
• The limit occurs when we have continuous
  compounding and

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Revisiting our Example

• Whats the NPV if we assume the 1m cash flows are
  realized daily? Hourly?

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Valuation Issues

• The PV, NPV formulas will be used early and often
  in our capital budgeting context
• They also provide the basis for valuation of
  financial instruments

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Arbitrage

• One of the core concepts associated with notions
  about the pricing of financial instruments is
  that of arbitrage
• The idea is a simple one identical cash flow
  streams should be identically priced

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Arbitrage

• The basic idea may be extended to bundles or
  collections of assets that provide similar cash
  flows
• A classic example is in option pricing, where the
  cash flows associated with a call option can be
  duplicated by borrowing and investing at the risk
  free rate

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Arbitrage Idea

• The idea works best when markets are perfect
• No taxes, transaction costs, or other
  restrictions
• Everybody acts in the small
• Efficient markets
• Investors are rational wealth maximizers
• Efficiency implies prices reflect available info

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Markets?

• Are markets efficient?
• Some argue that the answer is yes
• Some argue for a qualified yes
• Are markets perfect?
• No, but
• Imperfections seem to relatively slight in effect
  over the long term

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Price

• The term generally refers to the last price
• The most recent tick
• The closing price
• Could be some sort of average
• Bid/Ask prices and spreads are common
• Often quoted as a rate instead of a number
• May be slightly different for the same asset

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Value

• Refers to the price of an asset in a perfect
  market
• So-called fundamental value
• May be useful in setting k in capital budgeting
  contexts
• So-called Fair Price may be an estimate of
  price in a competitive market

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Bond Valuation

• Application of PV calculation
• Cash flows are usually known with some certainty
• Depends on the quality of the bond
• May depend on lifetime of the bond
• Face value due at the end
• Fixed interest payments

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Bonds

• Government Bonds
• US Treasuries
• Bills
• Notes, Bonds
• Other Governments
• Municipals
• Corporate Bonds
• Quality varies

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Bond Pricing

• Its just the solution to a PV problem
• If we already know the price (the usual case), we
  can calculate r, known as the Yield to Maturity
  (YTM)
• k refers to the periodic (usually 6-month) rate

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Treasuries

• We are interested in the yield for the period in
  question
• We annualize this yield assuming that
• Investors are rational
• The rate of return will remain the same for the
  assumed investment/holding period

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Fixed Income Securities

• Treasuries
• Bills dont pay interest notes and bonds usually
  do, but strips are available
• Municipals
• Revenue or GO
• Corporates
• Indenture specifies call provisions, sinking
  fund, and subordination provisions

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BV Example

• Suppose UI, Inc. Issue a 20-yr Bond with a Face
  Value of 1000 and a semi-annual coupon of 7.
  If the annual rate of return on similar bonds at
  the time of issue is 7.5, whats the BV going to
  be?

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Bond Info

• The Wall Street Journal (WSJ) publishes some bond
  price data
• So do online sources
• Corporate data tend to be incomplete
• Treasury Data are complete

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Corporate Bond Info

• Listed under US Exchange Bonds in WSJ
• Incomplete because it includes bonds traded in
  NYC the previous day only
• http//bond.yahoo.com
• Lets find a bond to check on at the yahoo site

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Corporate Bond Listings

• First of all, we need the coupon rate and the
  maturity date
• Current Yield is just the annual coupon/price
• Current Yield is not YTM
• Can we calclate the YTM on a bond based on the
  info we have?

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Stock Valuation/Pricing

• A bit more nebulous
• Conventionally the PV of the dividend stream
• If its constant its D/k the PV of a
  perpetuity kgt required rate of return
• If its nonconstant, but has a constant growth
  rate, the Gordon formula applies

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Stock Valuation/Pricing

• Not as straightforward as bond pricing
• Issues
• Time horizons
• Information/market efficiency
• Portfolio compositions impact individual
  valuations
• Intangibles

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Using Excel for Calculations

• We can either
• Use the canned formulas
• Write programs in the Visual Basic for Excel
  utility to do the calculations
• With or without the canned formulas

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The Keys

• Figure out what we want to do
• Draw a picture maybe
• Develop the algorithm
• Tell the machine where the data are and/or are to
  go
• Write the code

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VBA Example

• Write a short program to calculate period 2 cash
  flows necessary for the IRR in a 2-period problem
  X(0) -1000
• We need the data in the spreadsheet somewhere
• We need a place to put the final answer and if
  we wish intermediate calculations
• We need to figure our simple algorithm

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VBA Example

• We can either calculate X(2)X(1) ourselves
• Or we can use a program like the one we have for
  today
• Or we can use the canned programs
• Or we can use a program like the one we have
  today to use the canned programs
• Or we could do it all by hand (?)

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Homework 1 Due 9am 8 Sept

• Develop an algorithm to solve a multi-cash flow
  situation for the IRR. Be flexible.
• Submit a short summary of what you did.
• Extra credit write code for your algorithm.

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Homework Guidelines

• Be right
• Be neat
• If you cant be right, be neat
• Professional-type presentation preferred
• email submissions are fine
• 0-10 subjective scale used by me