Loan types
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Pure discount loans
o Simplest form of loan
o A borrower received money today and repays a single lump sum at some time in the
future
o Example: treasury bills (T-bills)
o Example: if a T-bill promises to repay $10000 in 12 months, and the market interest rate
is 7% how much will the bill sell for in the market?
 Answer- $9,345.79
Interest-only loans
o Borrowers pay interest each period and repay the entire principal at some point in the
future
o Example: corporate bonds
o Example: for a 3-year, 10% interest-only loan of $1000, the borrower would pay $100 at
the end of first and second year and at the third year, 1000 along with $100.
 Answer- $1,000
Amortized loans
o The borrowers pay a fixed amount each period (interest and principle), over time,
reducing the balance to zero
o Example: home mortgages, auto loans, business loans etc.
o Example: construct a amortization schedule for a $1000, 10% annual rate loan with 3
equal pay
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Step 1:
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Step 2:
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Step 3:
Interest Rates and Bond valuation
What is a bond?
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Bond is a loan
Firms can issue bonds to raise capital
When you buy a bond, you are lending money to the company who issues it
The company, in turn, promises you to pay periodic interest at specific dates and the principle
when the bond reaches the maturity date
Who issues bonds?
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Government bonds—or treasury bonds, are issued by the federal government
Municipal bonds—or Munis, are issues by the state and local governments
Corporate bonds—are issued by business firms
Why do firms issue bonds?
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Do not want equity dilution (EPS consideration)
Academic papers suggest that seasoned equity offerings (SEO) are often undervalued, and have
to sell at discount
Bond terminologies
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Par value
o Stated face value of the bond
o The amount of money firms repay you on the maturity date
o Generally assumed to be $1,000
Coupon
o Periodic interest payment
o Set at bond issuance and remains in force during the bond’s life
Coupon rate
o Annual coupon payment/par value
o A bond has par value of $1000 and coupon rate 5%, pays coupons $50 per year
Maturity date
o Pre-specified date on which the par value must be repaid
o Most bonds have maturities ranging from 10 to 40 years
Bond Valuation
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The value of any financial assets in the present value of the future cash flows the asset is
generating
Example: What is the value of a 10-year, 10% annual coupon bond, assuming the par value is
1,000 and the discount rate is 10%
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o
Example: what is the price on a 20-year, $1000 par value, 8% annual coupon bond, assuming
that the discount rate is 12%
o N=20, I=12, PMT=80, FV=1000
 PV=-701.22
Interest rate risk
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When interest rate rise, what happens to the value of outstanding bonds?
o All else equal, the longer the time to maturity, the greater the interest rate risk
o All else equal, the lower the coupon rate, the greater the interest rate risk
Interest rates go up, bond prices go down
When interest rates go down, prices go up
o With lower interest rates, newly issued bonds yield less than “old” bonds, so the prices
of these old bonds go up until the yields are the same
Bond valuation cont.
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Coupon rate= market interest rate
o Bond price=par value
o Bond is selling at par
Coupon rate > market interest rate
o Bond price > par value
o Bond is selling at a premium
Coupon rate < market interest rate
o Bond price < par value
o Bond is selling at a discount
Bonds with semiannual coupons
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Although some bonds pay coupons annually, the vast majority make payments semiannually
Example: What is the value of a 10-year, 10% semiannual coupon bond, if rd=13%?
o
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Example: a 25-year bond with a $1000 face value and a 6% coupon rate (with semi-annual
payments) is currently selling for %634.88. What is the yield to maturity on this bond?
o N=50, PV= -634.88, PMT= (6% *1000)/2 = 30, FV=1000, I=5% (semi-annual)
 (annual, convention) Yield=5% *2=10%
Yield to maturity (YTM)
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Unlike the coupon rate, which is fixed, the bond's yield varies from day to day
Yield to maturity is the rate of return we expect to earn if we buy the bond today and hold it to
maturity
Example: what is the YTM on a 10-year, 9% annual coupon, $1000 par value bond, selling for
$887?
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Should YTM go up or down if the Fed raises interest rates?
o Rationale: think of a competitive credit market
Debt vs. Equity
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Debt is not an ownership interest in the firm. Creditors generally do not have voting power
The interest payment on debt is considered a cost of doing business and is fully tax deductible.
Dividend, however, is not tax deductible
Unpaid debt is a liability of the firm. If it is not paid, it can lead to bankruptcy
Bond ratings
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Designed to reflect the probability of a bond issue going into default
Call provisions
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Many corporate and municipal bonds contain a call provision that gives the issuer the right to
call the bonds for redemption
The issuer normally pays a call premium, which often equals one year’s interest
In most cases, bonds are not callable until several years after issue, generally 5-10 years
Companies call bonds when interest rates have declined significantly since bonds were issued
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It reduces their interest expenses
A call privilege is valuable to the firm but detrimental to long-term investors
Callable bonds have a higher interest rate than the non-callable bonds
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Correct answer: E
Inflation and interest rates
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Real vs. Nominal rates
The fisher effect
1 + R = (1 + r) * (1 + h)
o R: nominal rate
o r: real rate
o h: inflation rate
Term structure of interest rates
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Relationship between interest rates (or yields) and maturities
The yield curve is a graph of the term structure
Yield of corporate bonds
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Yield are determined by more factors for bonds issued by corporations
Default risk premium
o The possibility of default/credit risk
Liquidity premium
o A liquid asset can be converted to cash quickly at a “fair market value”
o Liquidity premium can be measured by trading volume
Zero-coupon bond
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Pays no periodic coupons
They often mature in ten or more years
Receive the face value (usually $1000) at maturity
Example: If you want to purchase a zero-coupon bond that has a $1000 face value and matures
in three years, and you would like to earn 10% per year on it, what is maximum price you are
willing to pay?
o $1000/ (1 + 10%) ^3 = $751.3
Chapter 8: Stock Valuation
Common stock
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Represents ownership
Ownership implies control
Stockholders elect directors
Directors elect management
Cash flow from stockholders
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If you buy a share of stock, you can receive cash in two ways:
o The company pays dividends
o You sell your shares
As with bonds, the price of the stock is the present value of these expected cash flow
Discounted Dividend Model
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The value of a stock is the present value of the future dividends expected to be generated by
the stock
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For common stocks, the future cash flows (dividends) are highly uncertain
Example: if g=0 (zero growth)
o If ABC corp. Has a policy of paying a $2 per share dividend every year, what is the stock
price if the discount rate is 13%?
 The dividend stream would be a perpetuity
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Constant growth stock
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A stock whose dividends are expected to grow forever at a constant rate
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If g is constant, the discounted dividend formula converges to
o
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Rs > g
Dividend yield and capital gains yield
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Dividend yield
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D1/ P0
Capital gains yield
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(P1 – P0) / P0
Total return (rs)
o Dividend yield + capital gains yield
Supernormal growth stocks
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What is g=30% for 3 years before achieving long-run growth of 6%?
o Can no longer use just the constant growth model to find stock value
o However, the growth does become constant after 3 years
Non-constant growth stocks
Preferred stock
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Hybrid security
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Like bonds, preferred stockholders receive a fixed dividend that must be paid before dividends
are paid to common stockholders
However, companies can omit preferred dividends payments without fear of pushing the firm
into bankruptcy
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Chapter 9
Capital Budgeting 1: Net present Value and other investment criteria
Capital budgeting
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Use similar valuation techniques to evaluate the investment by a firm in real assets, which we
refer to as projects
Project—any firm decision that involves cash outflows made in order to receive cash inflows
o Example: new product, new software, new plant and machinery
Capital Budgeting Rules
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Given the outflows and inflows, is the project a worthwhile investment? --capital budgeting
decisions
Net present value (NPV)
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The value of a project
Sum of the PVs of all cash inflows and outflows of a project discounted at the cost of capital
(WACC)
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The higher the NPV, the higher the shareholder wealth
Thus, NPV is the best selection criteria
Calc Example
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NPV rules
o If projects are independent, accept if the project NPV >0
o If a project is mutually exclusive, same economic life, accept project with the highest
positive NPV
o Accept one if mutually exclusive, select both if independent
Internal rate of return (IRR)
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Discount rate that makes NPV 0
IRR Rules
o Accept project if IRR > WACC, because the project’s return exceeds its costs and there is
some return left over to boost stockholders’ return
o If projects are independent, accept both projects as both IRR > WACC=10%
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If projects are mutually exclusive, accept S, because IRRS >IRRL
Warning about IRR: Multiple IRRs
o Under certain conditions a project may have more than one IRR
o Cash inflows occur before cash outflows, cash flows change signs more than once
o NPV assumes that project cash flows can be reinvested at WACC
o IRR assumes that project cash flows can be reinvested at IRR
Modified internal rate of return (MIRR)
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The discounted rate that causes the PV of a project’s terminal value (TV) to equal the PV of costs
TV is found by compounding inflows at WACC
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o 0= PV outflow + TV inflow/ (1+ MIRR)^N
MIRR vs NPV
o MIRR is superior to regular IRR as an indicator of a project’s “true” rate of return
o For independent projects, the NPV, IRR and MIRR always reach the same accept/reject
conclusion/ they are equally as good
o For mutually exclusive projects, the NPV is best because it selects the project that
maximizes values
Regular payback period
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Number of years required to recover a project’s cost
The shorter the payback, the better the project
Calculated by adding project’s cash inflows to its cost until the cumulative cash flow for the
project turns positive
Calculating
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Warnings
o An arbitrary decision rule since the critical number is arbitrarily chosen
o Ignore the time value of money. Future cash inflows are directly compared with the
project’s cost without discounting those future cash flows
o Ignores the cash flows that occur after the critical number
Discounted payback period
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