## Corporate FinanceUniversity of Iowa School of Law Miller, Robert T.

CORPORATE FINANCE
MILLER
SPRING 2013

a.       Capital Value
i.      The present value of a series of amounts due is called the capital value of the future receipts. Capital Value: the current price of the rights to the stream (series) of receipts
ii.      Annuity: sequence of annual amounts received at annual intervals. The series of future amounts due is called an annuity
iii.      PV for a sequence of amounts due at future times
1.      Add the present values of each of the future amounts due
2.      The sum is the present value of the whole series of amounts due at future dates
b.      Role of Discounting in Bond Valuation
i.      Holder of bond receives a fixed set of cash payments – an interest payment each year until the bond matures and the face value (or prinicipal) of the bond in addition to the final interest payment on the date of maturity (Stream of Payments
c.       Discounting in Capital Budgeting Decisions
(ie Time Value of \$ in Project Choice)
·         “Capital Budgeting Decision” = evaluation of particular investment projects which are under consideration by the firm’s manager.
·         Three Alternative Methods used in making this determination
1.      Net Present Value Method
2.      Internal Rate of Return Method
3.      Payback Method
·         NPV and IRR are discounted cash flow techniques that reduce future cash receipts to present value in determining the value of the asset giving rise to the payments
1.      IRR solves for the discount rate —the IRR— at which the net present value of the investment is zero: the present value of the cash invested in a project equals the present value of the cash flows from the project. If the internal rate of return exceeds the minimum rate set by the firm as part of its capital budgeting process the project is undertaken
2.      The net present value method discounts to present value each cash outflow (including the original investment) and each cash inflow, using the rate of return available in the market for comparable investments as the discount rate. If NPV is positive, the project is undertaken
·         Argued that the NPV method is preferable because the discount rate chosen is presumably the external cost of capital, a market rate, while the discount rate implicit in the IRR method is the return associated with a particular project, which is less likely to be duplicable on reinvestment.
1.      Net Present Value Method (NPV)
a.
b.      Asset’s (or investment’s) value is the present value of the income it generates over its life
c.       NPV approach entails
i.      Estimating the returns that can be expected to be realized from the investment
ii.      Discounting those projected returns to present value
iii.      Investment is acceptable if the present value of the estimated returns equals or exceeds the cash outlay required to finance it

Or stated differently

NPV = PV of cash inflows – PV of cash outlays that it requires
if NPV > 0 à accept project
1.      Putting money in bank has a NPV of 0, so NPV method involves the desirability of an investment, compared to the alternative of putting money in a bank
d.      Assumption: all intermediate cash flows can be reinvested at the chosen discount rate.
e.       The actual return will match the initial calculation only if opportunities for reinvestment at the discount rate exist when the cash flows are received
2.      Internal Rate of Return (IRR) Method
a.       Establish what rate of discount serves to equate the anticipated cash inflows with the required cash outlay. The result is compared to the required rate of return to determine whether the net yield on investment is positive
b.      Establish the discount rate that equates the present value of the expected cash outflows with the present value of the expected inflows.
c.       ie. The rate that discounts the stream of future cash flows to equal the initial outlay.
d.      Sum of expected cash inflow discounted at IRR minus cost = 0
e.       Solve for r :

n
Σ     [ At  /(1 + r)t ] = 0     .
t = 0
to get IRR, solve for r

f.        Assumption: intermediate cash flows can be reinvested during the life of the project at the same internal rate of return earned from the project
g.       Actual rate of return achieved by a project will equal the internal rate of return calculated only if the intermediate cash flows generated by the project can be reinvested in an equally profitable investment
h.      Fyi: the higher the internal rate of return, the better the investment, other equal
3.     Payback Method
a.       Idea is to calculate the number of periods necessary for cash flows from a project to repay its initial investment. The project will be accepted if this period is shorter than the maximum payback period that the firm sets as part of its capital budgeting process
b.      Payback period: the time necessary to recover the initial investment
i.      Exp: the cash flow, before depreciation, is \$4,500 per year, so it takes two years to recover the initial \$9,000 investment. So payback period is 2 years.
c.       Other things equal, a project whose cash flows come sooner is preferable to one whose cash flows come later
d.     Payback method usually thought to be inadequate because it fails to adequately account for the time value of money – it ignores the need to discount all expected flows. It gives no value to cash flows that are received after the projects initial investment is repaid. Also takes no account of differences in the timing of receipts.
2.   Expected Returns
Ø  Need to determine quantity and duration of the stream of expected returns to be discounted
o   ie the amount to be discounted – referred to as inflows, income, profits, earnings, returns, yield
Ø  With respect to the amount to be discounted –two general questions can be raised:
o   What is (or ought to be) meant by the term “returns” in the context of investment valuation? (what’s the composition of “returns”)
o   Is it appropriate to utilize a single-valued estimate of expected returns, or should the investor or appraiser somehow attempt to take account of the full range of possible outcomes, insofar as they can be foreseen? (probability distributions)
Ø  Expected Return: the sum of all the possible outcomes (Value x Probability) of a project
o   Sum of all outcomes of: (the conditional return if a particular outcome occurs) x (the probability of that outcome occurring)
a.       Intro to Financial Statements
– See my notes
b.      Composition of “Returns”
i.      Accounting Earning, “Owner Earnings,” and Net Cash Flows
1.
c.       Future Returns and Probability Distributions
d.      Outlinedepot and my notes
3.   Risk and Capitalization Rate
·         Most investors are risk-averse
·         No theory to tell us how risk-averse investors ought to be,  nor any reason to think that all investors have the same level of distaste for risk
Risk
a.       Two Measures of Risk:
i.      Measure of TOTAL RISK: standard deviation
ii.      Measure of SYSTEMIC RISK: beta
b.      Expressing Risk: Variance and Standard Deviation

ii.      σp: standard deviation (uncertainty) of rate of return for portfolio
3.      Portfolio Selection
a.       From the Ep (expected return portfolio) and σp (expected risk portfolioà standard deviation ) combinations available investor selects the best based on his preferences
i.      Indifference curves
d.      Reducing (unsystemic) Risk Through Diversification
i.      By splitting investment dollars among a number of different investments (diversification) investors can reduce risk, without reducing expected return, by splitting their invest
ii.      If most investors are diversified, the market price will reflect the value that diversified investors place on risky security. Undiversified investors will bear extra risk, and will not be compensated for bearing that risk
iii.      However, diversifying by buying a large number of different stocks will reduce risk only to some irreducible minimum (bedrock). ie. diversification cannot eliminate all risk, it can only reduce risk to its systemic risk
1.      Some risks are common to many firms across the stock market, though perhaps to differing degrees. These risks affect the profits of all firms, so one cannot eliminate them by buying a portfolio of different stocks.
iv.      Systemic Risk (market risk)
1.      The portion of security’s total risk (standard deviation of return) which cannot be eliminated by combining it with other securities
2.      Base level of stock market risk à ie systemic return is perfectly correlated with the market return
v.      Unsystemic Risk (company-specific or industry specific)
1.      can be reduced by diversifying across firms and across industries
vi.      Risk depends on covariance – extent to which the returns vary together, rather than independently
1.      If move in exactly opposite directions in exactly the same amounts (perfect negative covariance), all risk is eliminate
2.      If move in perfect lock-step (perfect positive covariance)
3.      If independent of each other, they have zero covariance
vii.      Object of diversification is to eliminate independent variability from the portfolio.
1.      Variability of a well-diversified portfolio reflects mainly the covariances of the securities within the portfolio
2.      Diversification will reduce risk as long as the returns from two investments are not perfectly positively correlated
viii.      Even when this is done, however, portfolios will still differ in degree of market risk which accounts for most of the risk of a well-diversified portfolio, and beta of an individual security measures its sensitivity to market movements.
1.      Thus, in a portfolio context, a security’s risk is measured beta