Investing is real assets – such as productive machinery, new production facilities, research or a new product line – creates new cash flows that did not previously exist, and thus new wealth that was not there before.
A good investment will produce more wealth than it consumes; a bad investment will do the opposite.
A constant annuity is a set of cash flows that are the same amounts across future time points. The present value of $1 per period for t periods implies a constant cash flow per period, and is therefore an annuity.
PV of $1 for t periods = [(1 + i ) t – 1] / i (1 + i ) t
Future value of $1 for t periods = [(1 + i ) t – 1] / i
A perpetuity is a cash flow stream that is assumed to continue forever. The formula for the present value of a perpetuity is: PV = CF/ i. For example, $100 per period forever at a discount rate of 10 per cent = $100/0.10 = $1,000.
Interest rates that begin at the present and run to some future time point are called spot interest rates .
If interest rates are 5% between t 0 and t 1 , 6% between t 0 and t 2 and 7% between t 0 and t 3 , then the one-period spot rate is 5%, the two-period spot rate is 6% and the three-period spot rate is 7%.
The set of all spot rates is called the term structure of interest rates.
The yield-to-maturity is the rate that discounts a bond’s promised cash flows to equal its market price, analogous to IRR.
A difference in yields between bonds that have been subjected to the same discount rates is the coupon effect on the yield to maturity . It reflects that a greater or lesser portion of the bond’s value derives from the interest payments – because the interest is valued based on the spot discount rate for that period.
The YTM’s are expressing not only the earning rates but also the amounts invested in the bonds across time, i.e., higher interim cash interest payments means that relatively less is invested in the later periods.
The YTM, being a constant per-period average, cannot form the basis of comparison unless the cash flows are identical. Bonds of equal risk must earn the same rates during the same periods.
A forward interest rate is usually noted with the letter f surrounded by a left subscript indicating the rate’s beginning time point and a right subscript indicating the rate’s ending time point, e.g., the interest rate between t 1 and t 2 is noted as 1 f 2 .
The implied forward rate can be calculated by extracting the invested amount and comparing to the payment on that amount.
At t 0 , a market participant may have certain expectations about the rates at t 1 . In the interim, new information may appear that causes the market to revise its cash flow expectations, opportunity costs or both.
The possibility of a rate change can be hedged using interest rate futures.
The value of the futures contract depends on the implicit rate at the time that it is bought or sold. If rates increase, the value of the futures contract decreases.
Free (as in ‘unfettered’) Cash Flow is interpreted to be the amount that could be withdrawn by capital suppliers without impairing the operating expectations. If the amount is negative, it is to be contributed.
The Adjusted Present Value (APV) allows the analyst to incorporate various adjustments to cash flows, but this method requires that their dimensions (rather than proportions) be estimated.
APV will find the same NPV as WACC by: (1) discounting the unleveraged cash flows based on financing completely with equity, (2) then adding the discounted (by the pre-tax rate of interest) interest tax shields.
Sales revenue can be converted to cash receipts by adjusting for the change in accounts receivable, but it is probably preferable to simply adjust for revenues and expenses by adjusting for the change in working capital.
Working capital = current assets – current liabilities
Interest and capital repayment are not cash flows, but merely claims on the cash flows created.
If calculating NPV or IRR, the tax calculation should not include the deduction for interest, since this is already included in the discount rate for NPV, and IRR assumes equity capital only. APV requires an estimate of the tax shields, then discounts at the pre-tax rate.
Overhead allocations are a costing device, and unrelated to the change in cash flows.
The Profitability Index (PI) is very similar to CBR. It has the NPV of all future cash flows in the numerator and the initial cash flow in the denominator. It can only be used when the t 0 cash flow is an outlay.
It will produce the same ratio as the CBR when the only negative outlay in in the t 0 period.
It calculates the NPV of the project per dollar of initial outlay, but is unsuitable for ranking projects because the criterion should be the quantum of wealth increase and not the ratio.
Both IRR and NPV are discounted cash flow methods: IRR calculating a rate (and assuming reinvestment) to get an NPV of 0. The NPV uses the hurdle rate to discount, and assumes reinvestment at that rate, to calculate a change to shareholder wealth.
The IRR is unable to contend with each cash flow having a unique discount rate.
If the sign on the returns changes more than once, the IRR method will calculate a return rate for each additional change in sign.
The most common error in dealing with inflation is in estimating cash flows. The estimates should include the effect of inflation on the cash flows, and then be discounted with nominal rates.
Inflation has the effect of reducing the value of depreciation deductibility for tax. An optimal method might be determined treating these expenses as generating ‘tax shields’, then comparing the present values from the competing methods.
The Security Market Line ( SML ) describes the relationship between risk and return: the higher the risk, the higher the required return. It depicts the set of risk-adjusted returns available in the market (i.e., opportunity costs).
An average expected return (a ‘mean’) on a project can be derived from a probability distribution of returns.
To a capital supplier, risk is best measured by the standard deviation of rates of return for a portfolio of assets (and not those of the assets themselves).
A portfolio will have less risk than the average of the securities in it due to the interactions between them. This is the value of diversification .
To the extent that the returns from securities are correlated (unless perfectly so), their risks will cancel each other out. The correlation coefficient runs in a continuum from +1.0 (perfectly correlated) to 0.0 (independent) to –1.0 (perfectly inversely correlated).
The covariance between a pair of assets is given by the product of the standard deviations and their correlation coefficient.
As an alternative to adding a risk premium to the risk free rate to produce a risk-adjusted discount rate, we could adjust the future cash flows downward according to their risk characteristics, and then discount the (now ‘certain’) cash flow at the risk free rate.
CF ce = CF – [Covariance(CF, r m ) / Variance (r m )] x (E(r m ) – rf)
The future cash flow is reduced by a portion of the spread over the risk free rate, according to its systematic risk.
This amount is still a future amount, and must be discounted by the risk free rate to present value.
If an investment’s cash flows do not have constant risk across time, and can be resolved as time passes, this must be accounted for in the analysis, or the risk may be over-estimated for future cash flows (beyond the resolution point.)
The dividend decision is, in mirror image, a cash retention and cash reinvestment decision.
If the were no frictions in transaction costs (taxes, brokerage fees or flotation costs), the shareholder would be indifferent to the form of wealth: cash or share value. These frictions may give shareholder ‘clienteles’ a preference for one form over another.
There is enough competition amongst capital users that there is little to be gained by catering to a clientele by changing dividend policy, and it may indeed prejudice existing shareholders.
Earnings before interest and taxes (i.e., operating income) is a measure of the total amount of money available to service debt, taxes (the priority dividends paid to an unwelcome equity claimant) and equity.
The more borrowing a company does, the steeper will be the line depicting the EBIT -EPS relationship (hence the term ‘leveraged’).
The transaction might be regarded as the sale of a claim to assets, with an option to repurchase that claim by making interest payments.
The incremental return required on geared equity as the result of increasing debt is often called the implicit cost of borrowing.
As both the equity (re) rate and the debt rate (rd) increase with increases in D/V, the value weight [1 – D/V] on the higher equity rate steadily declines, exactly offsetting the higher proportion of lower-cost debt, so that their weighted average is unchanged.
The operating cash flows of a company are transformed by the taxation system before they can be claimed by capital suppliers. This transformation is different depending on the capital structure of the company.
We can think of a company’s value as the sum of its unleveraged value plus the value of its leveraging-based tax benefits.
Interest deductibility makes the company’s cost of capital lower, the more debt it uses.
The essence is a change in legal ownership of the company’s assets from the shareholders to the bondholders.
Bankruptcy costs are not the declines in value that precipitate the default – those are independent of capital structure. The true costs are those of the legal process and of the opportunity costs (when compared to equity financing).
One consideration for the lender is the value of the debt claim to the total value of the company. A market value of assets might be difficult to obtain, so practitioners often rely on book values . These are thought less vulnerable to upset when the company is in financial distress.
A financial planning exercise, using a simulation model, would compare the financing alternatives under a range of economic outcomes.
A higher level of receivables may boost credit sales, but at the costs of a longer collection period and of bad debt.
An attempt to discriminate between good and bad credit risks should continue until the incremental expenditure is equal to the expected gain.
To analyze the effects of a change, accumulate: (1) the NPV of the sales value when received, less the previous NPV, (2) less the change in costs, (3) plus the cost of increased working capital, (4) less the NPV of the recoupment of that capital.
When an investment proposal carries with it an option to alter, curtail or extend a project’s cash flows at some future time, classic NPV is an inadequate valuation technique.
Project cash flows after the exercise, discounted back to the time of the exercise, represent the option payout. This payout, discounted to the present, represents the S 0 value.The exercise price is the premium.