Intermediate Corporate Finance
Chapter 9 - Discounting and valuation
Real investments are expenditures that generate cash in the future, and contrary to financial
investments like stocks and bonds they’re not financial instruments that trade in financial markets.
Plant, Property and Equipment (PPE) are typically real investment decisions, but so are those
involving personnel and marketing, and most other corporate decisions to spend; hiring an
employee is an investment, since as she acquires skills we hope she provides positive net
benefits.
The main premise of this text is that financial managers should use a market-based approach to
value assets, both real and financial. The following chapters show how to combine prices
available in financial markets into a single number so that managers can compare this with
investment costs to evaluate whether a real investment adds net positive value to a firm. This
number is the present value PV which is the market price of a portfolio of traded securities that
tracks the future cash flows of the proposed real investment project we want to value. A project
creates value if the cost of investing is less than the cost of investing in a portfolio of financial
assets with the same future cash flows.
Thus the PV is the worth of a project’s future cash flows now found by looking at the market price
of (nearly) identical future cash flows obtained from financial investments. These cash flows are
discounted, and the mechanics of discounting is the focus of this chapter, which involves
understanding how to compute future cash flows and applying the formulas that derive PV by
applying discount rates to future cash flows.
The cash flows of projects can come directly from the real assets of the project, or indirectly via
financing subsidies; most notably the tax subsidy associated with debt financing (interest rate tax
shield) and relocation subsidies (offered by regions to entice businesses to move). Here however
we consider how to compute cash flows flowing directly from the real assets.
Unlevered cash flows
One first identifies a project’s unlevered cash flows: those generated directly from real assets,
which in a hypothetical world where financing doesn’t affect a project’s operations (through
altering relationships or generating bankruptcy costs) are the cash flows from the project’s assets
under the assumption the project is all-equity financed. Unlevered cash flows are not affected by
financing cash flows which are associated with (1) issuance or retirement of debt and equity, (2)
interest or dividend payments, and (3) any interest-based tax deductions that stem from debt
financing. Unlevered cash flows are derived from forecasts of cash flow statements or from
forecasts of earnings before interest and taxes EBIT.
Deriving unlevered cash flows using accounting cash flow statement
The increase (decrease) in cash reported near the bottom of cash flow statement represents the
difference in the cash and cash equivalents position of the firm from one balance sheet to the
next. This is the accounting cash flow, but doesn’t equal the unlevered cash flow that we discount
for valuation. The accounting cash flow includes cash from financing such as dividends and
interest, and since debt interest usually reduces tax liabilities the reduction in cash flow due to
taxes stated in the cash flow statement is lower than unlevered.
Accounting cash flow statements break the cash flow into (1) operating cash flows, (2) investing
cash flows, and (3) financing cash flows. Operating cash flows refers to cash flowing directly from
operations minus interest and taxes. The interest payment however arises solely from financing,
meaning the interest payment wouldn’t exist in an all-equity financed firm, making operating cash
flow not a proper account for cash flows stemming directly from operations, since they take some
financing into account. In addition, operating cash flows ignore the required capital expenditures
(CapEx) for keeping in operation, while this required reinvestment is included for unlevered cash
flows. This reinvestment only appears in the investing cash flow portion. Many textbooks refer to
unlevered cash flows as operating cash flows, but they are not the same: to obtain unlevered cash
flows from the cash flow statement you take the operating cash inflow, subtract the investing cash
inflow (unless it’s positive but usually we must invest), add interest since we wouldn’t have debt
with unlevered cash flow, but subtract the debt interest tax subsidy (shield).
Unlevered cash flow = Operating cash inflow - Investing cash outflow + Debt interest - Debt
interest tax subsidy. We subtract investment costs and add debt expense net of the tax shield.
,Fast-growing firms tend to have negative unlevered cash flows due to reinvestment, even if they
are very profitable (think of Amazon) since new projects are draining more cash than the mature
projects bring in. When growth opportunities diminish and a firm matures, it’ll become a ‘cash
cow’, and ignoring this stage of a firm will result in significant undervaluation.
Cash flow statements of financial services companies (or units) also tend to have negative
unlevered cash flows since financing activities create wealth, which our unlevered cash flow
valuation methodology ignores: it’s useless for valuing financial firms.
Financing activities per se play no role in the cash flows generated by project assets, so we do
not count them in asset valuation unless there is an obvious and easily measured subsidy
associated with the financing of a real assets, such as tax subsidy, which can be ascribed to the
asset being valued. Other than this exception, for valuing an asset we focus solely on the cash
flows it generates. When the asset being valued does provide a financing-related subsidy we
need to account for this in the asset value, or when the assets themselves are financing activities,
but we focus on this in chapter 13.
Deriving unlevered cash flow from EBIT
So that’s how one may derive unlevered cash flows using the cash flow statement. Option 2 is
using EBIT, which is:
-Reduced by depreciation and amortisation, which affects earnings but not cash flow.
-Not affected by new investment in working capital, which does affect cash flow.
-Not affected by CapEx or sale of assets unless they provide a profit or loss since their value
deviates from what we amortised for, but such CapEx flows are affecting cash flow.
-EBIT is computed before taxes, but the unlevered cash flow is after subtracting taxes.
Unlevered cash flow = EBIT + depreciation and amortisation - ∆working capital - CapEx + Sale of
capital assets - Realised capital gains + Realised capital losses - (EBIT * Tax rate).
The last term translates the pretax cash flow to an unlevered (after-tax) cash flow. Unlevered cash
flow is the pretax cash flow minus EBIT * taxes, not unlevered cash flow before taxes minus taxes
since we pay taxes over EBIT, not over our cash earnings. For tax purposes expenses like
depreciation determine profits, not cash outflows which depend on CapEx and such.
The cash flows that matter are the project’s incremental cash flows: the cash flows of the firm with
the project minus those of the firm if the project were turned down, so the difference. Incremental
cash flows means considering all possible interactions a project might have with the firm, e.g.
using a portion of the factory floor may diminish the production possibilities of another product,
an opportunity cost one must take into account. Alternatively it may enhance other planned
projects’ cash flows: e.g. designing a chassis for one car which is then used for other models.
Creating pro-forma forecasts of financial statements: 4 steps for forecasting FS
Cash flow forecasts are usually derived from FS forecasts, although FS forecasting is useful to
financial managers in its own right and helps predict earnings per share under different financing
alternatives, the amount of cash at year’s end, the additional funding needed, debt-to-equity
ratios in the future, or the effects of a stock buyback on EPS and times interest earned. Here we
consider tips on constructing a usable forecasting model for a typical nonfinancal firms. The
highly leveraged nature of financial firms (e.g. insurance companies) makes them trickier to
forecast. 4 major sections are contained in the forecast spreadsheet: assumptions, income
statement, cash flow statement, and the balance sheet.
1 - assumptions. The most important number in your assumptions list is the sales forecast, since
it drives most others; expenses are typically forecasted as a percentage of sales. Assumed
percentages can be derived from past experience, although a fraction is fixed which won’t differ
as much with sales levels. Most expenses are variable in the long run though, so percentage of
sales method is more accurate the longer the forecasting horizon.
Financing decisions have major impacts on the FS, thus the net amount of debt and equity you
assume a firm will issue is vital. A basic assumption is starting with zero issuance, and additional
financing being used whenever cash levels drop below a certain threshold. Equity being costly,
debt is usually the method to meet funding unless debt exceeds some threshold, which could be
based on Times Interest Earned (EBIT / Interest expense) ratio or Debt/Equity ratio.
,2 - Income statement. Cost of sales is calculated depending on your percentage cost
assumption and forecast assumption, resulting in EBIT which represents the income from
operations before claimants like tax, lenders, and shareholders are paid.
EBIT minus interest is Earnings Before Taxes, for which we must calculate our interest expense, a
function of the expected future average interest rate and expected future debt outstanding.
Earnings After Taxes simply subtracts earnings. Costs such as ‘Other-net’ may be ignored for
forecasting when immaterial, but if they’ve been material in the past one may predict them using
percentage of sales if we’d expect the item to grow with the firm’s size.
3 - Cash flow statement. Once we have the EBIT and earnings after taxes (net income) we can
construct the cash flow statement, which has an operating, investment, and financing cash flow
statement. Net Income is the first item in operating cash flows, to which we add depreciation and
amortisation, as well as other non-cash charges. Investments in working capital are subtracted,
since they’re not expenses but do cost cash. Increases in inventories, accounts receivable, and
other current assets (excluding cash) are subtracted, being cash outflows.
Money spend on PPE or M&As, CapEx in general, are subtracted as investment cash outflows. All
investing cash flows must tie to balance sheet items. New PPE = Old PPE + CapEx - Depreciation
- Asset Sales. So using old and new PPE, and forecasted depreciation, we can find the investing
cash flows easily as the difference. Depreciation used in the investing cash flows exactly offsets
those added in the operating, meaning the assumption about depreciation expense is irrelevant
for the change in total cash position.
Lastly, financing cash flows: paying off debt is a cash outflow, borrowing inflow, and for
forecasting we often focus only on net change in debt. Dividend payments are cash outflows,
stock sales inflows, buybacks outflows.
4 - Balance sheet Assets: accounts receivable, inventories, PPE, and other items.
The cash entry on the balance sheet results directly from the cash flow statement, and when it’s
negative it indicates a need to obtain additional financing, or scaling back asset needs. Firms
prefer to have a minimum of 15 to 30 days of sales around in cash and cash equivalents to
facilitate transactions and buffer for short-term differences in making and receiving payments.
Larger cash reserves may be held in anticipation of spending on planned projects in the future or
against downturns.
After cash the item Accounts Receivable and Inventories follow, the size of both depend on sales
levels. A percentage of sales therefore is usually accurate for AR and Inventory.
Forecasting PPE can be done in one of three ways: (1) Direct method for forecasting PPE can be
used when you can forecast CapEx and asset sales directly, since we simply add CapEx and
subtract depreciation and sales. (2) More of the same method: if the firm has substantial excess
capacity and is not planning on adding any, new PPE is simply old PPE minus depreciation. (3)
percentage of sales may work since the need for PPE usually rises with level of sales.
Other balance sheet items may be goodwill, also referred to as ‘Excess of cost over the market
value of net assets acquired’ when acquiring another company and paying a premium. Goodwill is
usually amortised, so one would forecast the entry to decline in the future unless continued
acquisitions will increase it.
Balance sheet liabilities: Debt, current liabilities, deferred taxes, and other.
New debt is the old plus what’s expected to be issued, simply. Current liabilities like Accounts
Payable and other accused expenses are directly related to sales: percentage of sales method.
Deferred taxes arise from timing differences between reporting taxes and having to pay them,
often the result of differences between book and tax depreciation, meaning it makes sense to
forecast deferred taxes as a function of PPE forecasts.
Other liabilities don’t accrue interest, and are not conventional debt, but rather include things like
a large charge against earnings to establish a reserve for a future restructuring, which we’d expect
to decline in the future. It may also include reserves for contingencies such as accidents or other
liabilities.
The result of the balance sheet forecasts is the balance sheet equity resulting from assets minus
liabilities. The components (such as paid-in-capital and owner’s equity) are usually not forecasted
separately, and forecast is old equity plus increases from net income and stock sales, minus stock
buybacks and cash dividends.
, Chapter 10 - Investing in risk-free projects
For riskless cashflows determining whether a project creates value for shareholders is quite
straightforward: the manager simply examines whether the investment project offers an arbitrage
opportunity. The net present value NPV criterion measures arbitrage profits associated with an
investment project and recommends projects for which they’re positive. A riskless project has
future cash flows that perfectly aligned with a portfolio of riskless bonds with maturities at each
cash flow. Hence arbitrage profits can be created whenever a project’s startup cost is less than
the cost of acquiring the tracking portfolio paying the exact same as the cash flows.
This chapter focuses exclusively on riskless cash flows, allowing us to illustrate some basic
principles required for valuing risky assets too. Difficulties arise with discount rates varying per
cash flow payment or variety constraints such as limited capital and mutually exclusive projects.
With riskless cash flows the NPV equals that obtained using the discounted cash flow DCF
method, which obtains the NPV by discounting all cash flows at the prevalent return.
The NPV/DCF method’s modern equivalent is Economic Value Added EVA, a measure of true
economic profitability but nothing more than NPV really.
We learned in chapter 9 to only focus on incremental cash flows: this means ignoring sunk costs,
since they’ve been incurred regardless of whether or not we choose to adopt a new project.
10.2 - Net Present Value
NPV of an investment portfolio is the project’s Present Value, equaling the value of the tracking
portfolio of financial instruments, minus the cost of implementing the project. With positive NPV, a
project creates value since a future cash flow pattern can be produced more cheaply internally
than externally by investing in financial assets.
With riskless projects perfect tracking is possible since cash flows are known with certainty: the
value created with the project is then pure arbitrage gain achieved by investing in the project and
shorting the tracking portfolio, which pays us the value of the portfolio at the expense of paying
our cash flows to the other side of the short in the future. However, this transforms the project’s
gains to instantaneous value since the PV of the future cash flows is higher than the tracking
portfolio’s NPV, meaning we get a positive amount at time 0: NPV is positive, we have arbitrage
between real assets and financial assets markets. (the implicit assumption is that financial assets
are zero-NPV, assuming no money is made by buying and shorting stocks i.e. no bargains exist,
the world we assume thus corresponds to the Efficient Market Hypothesis).
Discounted cash flow and net present value
Riskless cash flows can be perfectly tracked with a portfolio of default-free bonds (zero-coupon in
this example) with maturity at each cash flow date, and the discount rates of these cash flows
equalling each bond’s yield to maturity YTM. YTM equals the discount rate that equates a bond’s
current market price to its face value (compounded per period). YTM is thus used as cost of
capital.
The discounted cash flow of a project is given by
the formula on the right, where rt is the per period
YTM of a default-free zero-coupon bond maturing
at date t. Today’s cash flow C0 is usually negative,
and is usually omitted in the discounted future cash
flow stream.
Adopting a project at a cost less than the PV of its future cash flows, so positive NPV, means that
financing the project by selling short the tracking portfolio yields surplus cash today: wealth is
created risklessly in the case of riskless cash flows with positive NPV. For riskless projects NPV
and DCF are the same.
Note that ‘shorting’ a portfolio of riskless bonds is simply issuing the bonds: we borrow the
money and use cash flows to repay, and the excess that we can borrow when having to repay
exactly the cash-flows is NPV. In frictionless markets firms can realise arbitrage profits if it
finances a positive NPV real asset through this issuing of bonds or other securities. Without
frictions however, the financing choice won’t affect values and any other option is possible.
Implications of NPV for mutual exclusivity and capital constraints
