Finance
Cost of Capital
P = D1 /(r-g) Therefore, to calculate the cost of Capital (r) r = (D1/P) +g
Net Present Value (NPV)
Present value of difference between cash inflows and outflows discounted at opportunity cost
Internal Rate of Return IRR
Rate of return that makes the NPV equal to zero (NPV= 0)
Compound Interest
Recognition that the interest earned on an investment can itself earn interest. • Income stream from an investment at t0 is CF0 [1 + ( i /m)]^mt, where m is the number of times per period that compounding takes place.
Interest Tax Shield
Tax laws allow corporations to reduce their taxes by deducting interest expense: • The interest tax shield is found by multiplying the period's interest expense by the corporate income tax rate.
Government Cash Flows
Taxes paid due to the investment.
Debt Market Value
The Initial Investment + interest payments • debt suppliers' wealth is unaffected by the success or failure of the investment.
Present Value (PV)
The amount of money to be invested or lent now to end up with a particular amount in the future. • Called discounting
Customers Cash Flows
The amounts of cash taken in from sales When the money actual changes hands (ie not credit sales)
Capital Suppliers Cash Flows
The amounts of cash that could be taken out by capital suppliers from the company as a result of the investment while leaving all of the plans of the company unchanged (AKA Free Cash Flow)
Internal Rate of Return (IRR)
The average per-period rate of return on the money invested. • Can be viewed as the discount rate that equates an investment's cash inflows and outflows (NPV = 0).
Opportunity Cost
The cost of not going forward with a project or the cash outflows that will not be earned as a result of utilizing an asset for another alternative.
Constant dividend
The firm will pay a constant dividend forever The price is computed using the perpetuity formula P0 = D / R
Sunk Costs
The initial outlays required to analyse a project that cannot be recovered even if a project is accepted. As such, these costs will not affect the future cash flows of the project and should not be considered when making capital-budgeting decisions.
Free Cash Flow
The net amounts of cash that the company could pay to its capital suppliers from the proceeds of a project at each time point without upsetting the expectations associated with the project.
Bond Valuation
The present value of the annuity (or possibly multiple period cash flows) + the present value of the lump sum • If equal payments. PV = (C[(1-(1+r)^-t)/r]) + (FV/(1+r)^t) Where: FV = Face Value C = Face Value / coupon rate r = YTM t = time to maturity
Yield
The rate of return anticipated on a bond if held until the end of its lifetime.
The Price Earnings Rati0
The ratio between the present value of all the company's future dividends (its market price) and its expected earnings (for example: earnings x payout rate x growth) during the first period.
term structure of interest rates.
The set of all spot rates
Equity Market Value
The sum of the expected Free Cash Flow values excluding debt market value discounted at an appropriate rate
Weighted Average Cost of Capital - formula
WACC = (weight of debt x cost of debt) + (weight of equity x cost of equity) • Weight of debt is calculated by taking the (current value of debt)/( current value of debt + current value of equity) given the percentage of investment in debt • The weights are based on the target market values of the relevant components. But if no market values are available we base the weights on book values. • Costs are after taxes i.e. (rate *(1 - corporate tax rate)
Assets Cash Flows
While the cash flow is made at time listed, it is not deductible at that point and must therefore be capitalised and depreciated across time.
Dividends are not a liability of the firm until a dividend has been declared by the Board therefore ...
a firm cannot go bankrupt for not declaring dividends
overall project rate
a market-value weighted average of the rates required by the various capital claims upon the investment. • Rates debt and equity are based on their proportional claims upon the corporate cash flow. • ((Debt Market Value / Total Market Value) x Debt rate) + ((Equity Market Value / Total Market Value) x Equity rate) • Gives a discount rate that can be used to calculate the NPV of a project
Dividend payments...
are not considered a business expense and are not tax deductible In Canada,
Dividends received by individual shareholders ...
are partially sheltered by the dividend tax credit
The Cross-Over Rate is calculated by
by taking the difference between the Cash Flows from the two Projects and finding the IRR
The YTM of bonds with different maturity or risk
cannot be compared
Covenants / indenture provisions
contractual arrangement for periodic payment of money (e.g. interest)
Factors that affect volatility of bonds
coupon rate: lower coupons -- higher volatility duration: higher duration -- higher volatility maturity: higher maturity -- higher volatility YTM: lower YTM -- higher volatility
Non-cash items
depreciation and overheads
A bond priced above par (a premium bond)
has a coupon rate higher than the interest rate
a bond priced below par
has a coupon rate lower than the interest rate.
Imputation systems
mitigates double taxation of dividends
Limited Liability
possible losses that a shareholder can incur are limited to the value of the shares • nice but not free, the company would be able to borrow money more cheaply if its creditors also got a claim on the personal resources of the company's shareholders.
If the required return is higher than the cross over point ...
the NPV will favour one of the projects. If lower it will favour the other
The lower the coupon
the higher the volatility
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 t1 and t2 is noted as 1f2 .
The higher the coupon
the lower the volatility
The interest rate is equal to the coupon rate
when the bond is priced at par.
Bonds of similar RISK and maturity
will have similar YTM (even if the coupon rates are different).
Finance is the economics of allocating resources across time
• Borrowing shifts from future to present • Lending and investing shift from present to future
Calculating APV for an all equity investment
• Calculate issue costs • Equity amount - (Equity amount/(1 - issue cost rate)) • Calculate the ungeared NPV • The sum of (fcf*/(1+rate)^t) - initial investment • Substract the issue costs from the ungeared NPV
Calculating APV for an investment using debt financing
• Calculate issue costs using -- loan amount - (loan amount/(1 - issue cost rate)) • Add issue costs to loan amount for the remaining calculations • Calculate after tax interest costs for 1 year using -- Interest costs = loan amount × borrowing rate × (1 - corporate tax rate) • Calculate the PV of the interests costs until the end of the loan using -- (Corporate debt rate, length of loan annuity factor) × interest costs • Calculate the PV of of the loan repayment using -- loan amount/(1- corporate debt rate) ^t • Calculate the npv of loan using (loan amount - pv of int pmts - pv of loan repayment) • Calculate the ungeared NPV using --the sum of (fcf*/(1+rate)^t) - initial investment • Substract the npv of the loan from the ungeared npv
Effect of depreciation on Cash Flow
• Considered a non-cash expense • Depreciation does have an indirect effect on cash flow, When a company prepares its income tax return, • Depreciation only exists because it is associated with a fixed asset. When that fixed asset was originally purchased, there was a cash outflow to pay for the asset. Thus, the net positive affect on cash flow of depreciation is nullified by the underlying payment for a fixed asset.
Types of Cash Flow
• Customers • Operations • Assets • Government • Capital Suppliers
Factors to consider when choosing NPV/WACC as the NPV technique
• Does not require that actual amounts of debt to be issued be known • Requires that the proportions of debt and equity market values be known • It adjusts for the deductibility of corporate interest in the discount rate as opposed to the cash flows of the project • Finds the present value by discounting the combined claims' cash flows
What Makes a Good Decision Criteria?
• Does the decision rule adjust for the time value of money? • Does the decision rule adjust for risk? • Does the decision rule provide information on whether we are creating value for the firm?
Investments are of two kinds
• Financial: mere reallocation across time • Real assets: creates new future resources, such as buildings and equipment
NPV - Decision Rule
• If the NPV is positive, accept the project • A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners.
Influences on Interest rates
• Inflation • Changes in creditworthiness of bond issuers • Real-asset returns
Types of Project Cash Flows
• Initial Investment Outlay • Operating Cash Flow over a Project's Life • Terminal-Year Cash Flow
Spot Rates
• Interest rates that begin at the present and run to some future time point. • If interest rates are 5% between t0 and t1 , 6% between t0 and t2 and 7% between t0 and t3 , then the one-period spot rate is 5%, the two-period spot rate is 6% and the three-period spot rate is 7%.
Advantages of IRR
• Knowing a return is intuitively appealing • It is a simple way to communicate the value of a project to someone who doesn't know all the estimation details • If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task • Generally leads to the same answers as the NPV method
Disadvantages of IRR
• May result in multiple answers or no answer with non-conventional cash flows, if the cash flows change sign • IRR usually unsuccessful when cash flows have differing discount rates • May lead to incorrect decisions in comparisons of mutually exclusive investments
Factors to consider when choosing APV as the NPV technique
• Requires that actual amounts of debt to be issued be known • Does not require that the proportions of debt and equity be known • Requires that the interest tax shields of the project's debt be estimated. • Finds present values by splitting up the cash flows into the all-equity cash flows) and the interest tax shield cash flows. These are each then discounted separately at rates appropriate to their individual risks. Easier to adjust to changing capital structure -- no need to recalculate WACC • highlights the present value benefit of the borrowing they are doing. • useful in isolating the benefits of government subsidies and the costs of financial distress.
Examples of Terminal Year Cash Flows
• Return of net working capital +$300 • Salvage value of the machine +$800 • Tax reduction from loss (salvage < BV) +$80 • Net terminal cash flow $1,180
Shareholders' Rights
• Share proportionally in declared dividends • Share proportionally in remaining assets during liquidation • Pre-emptive right - first shot at new stock issue to maintain proportional ownership if desired
Initial Investment Outlay
• These are the costs that are needed to start the project, such as new equipment, installation, etc. • Include opportunity costs as a negative cash flow
Terminal-Year Cash Flow
• This is the final cash flow, both the inflows and outflows, at the end of the project's life; for example, potential salvage value at the end of a machine's life. • The key metrics for determining the terminal cash flow are salvage value of the asset, net working capital and tax benefit/loss from the asset.
The market interest rate is the rate of exchange between present and future resources
• This rate is always positive, since no lender is prepared to receive fewer future resources than they give up in the present. • There are actually many such rates at one time, covering different riskiness and different periods of time.
Reasons for conflicts between NPV and IRR
• Timing of cash flows • Scale of cash flows
Weighted Average Cost of Capital - Example
• Value of debt = 30 • Value equity = 70 • Cost of debt = 4% • Cost of equity = 3 % • = ((30 / (30 + 70) ) x 0.04) + ((70/(30 + 70)) x 0.03)
IRR and Non-Conventional Cash Flows
• When the cash flows change sign more than once, there is more than one IRR • When you solve for the IRR, you are solving for the root of an equation. When you cross the x-axis more than once, there will be more than one return that solves the equation
Corporate Equity
• a security known variously as 'ordinary shares', 'common stock', 'equity', 'common shares', 'ownership capital' etc. • Has no specific contract with the company that requires any particular amounts of money to be paid • Is a residual claim, shareholders have agreed to stand last in queue for the corporate largesse, in exchange for everything that is left over.
High P/E Ratios
• a signal of the market's high opinion of a company's shares, • a sign that the company's share prices may be too high. • might be a growth company or where profits have almost disappeared, but the stockmarket may see this as being a temporary episode. • could be that the company is a takeover target and the shares have been bid up.
Calculating Free Cash Flow
• changes in net working capital = changes in current assets - current liabilities • Operating revenues (sales - returns) • Operating profit = operating revenues - operating expenses • Operating cash flow = operating profit - changes in NWC • Fixed Asset Cash flow = Fixed Asset Sales - Fixed Asset Purchases • Free cash flow = Operating cash flow + Fixed-asset cash flow - Income tax • Adjust to FCF*, by taking out the interest tax shields
Using P/E to compare companies
• only be used to compare similar companies that also have similar capital structures. • should not be used to compare companies across sectors..
Factors to consider in finance decisions
• the cost of retained earnings in relation to the opportunity cost -- how funds can be used elsewhere. • Pecking order -- internal financing is generally thought to be less expensive for the firm than external financing, • no transaction costs • affects shareholder wealth without paying the taxes associated with dividends • New shareholders dilute ownership • an all-equity project will report higher net income, because in the accounting figures interest is regarded as an expense, so the debt-financed company will have higher expenses and lower profits as a result. • conversely debt will have lower taxes and more free cash flow
The Weighted Average Cost of Capital WACC is a discount rate that reflects ...
• the operating risks of the project; • the project's proportional debt and equity financing with attendant financial risks; and • the effect of interest deductibility for the debt-financed portion of the project.
A company's P/E ratio is a very complex number in terms of the information that can influence it. It is affected by
• the pattern of dividends that a company pays, • its payout ratio, • the riskiness of the company as evidenced by the discount rate of its equity, • and the stream of earnings that the company is expected to be able to generate across the future.
Holding period return
(selling price + dividends - buying price) / buying price
The first equation uses the spot rates, the second uses the forward interest rates, and the last uses the bond's YTM.
923 = 40/1.05 + 40/1.06^2 + 1040/1.07^3 923 = 40/1.05 + 40/(1.05 x 1.07) + 1040/(1.05 x 1.07 x 1.09) 923 = 40/1.069 + 40/1.069^2 + 1040/1.069^3
Perpetuity
A cash flow stream that is assumed to continue forever • PV= C/r
Futures Contract
A contract to sell/buy an asset at a later date, at a price agreed upon well in advance.
Weighted Average Cost of Capital WACC
A discount rate based on the relative costs of the different capital claims. It is calculated by multiplying the cost of each source of finance by the relevant weight and summing the products up.
Purpose of Futures Contracts
A form of insurance. The buyer of a future would rather take the bird in the hand with a price that's guaranteed today, rather than the possibility of two (or zero) in the bush later, protecting himself from low prices while forgoing the chance to profit off high ones • Contract which can be bought or sold as such are often used for speculation and arbitrage.
The difference between futures and option
A future is both right and obligation. When the time comes, you're legally bound to sell or buy the underlying asset.
Yield Curve
A line that plots the interest rates, at a set point in time, of bonds having equal credit quality, but differing maturity
Present Wealth
A market participant's entire time-specified resources discounted to a single number. • This can be used as a benchmark to measure the benefit of a proposed financial decision as it is a company's sole task for it to be maximised.
After tax cash flow
A measure of financial performance that looks at the company's ability to generate cash flow through its operations. It is calculated by adding back non-cash accounts such as amortization, depreciation, restructuring costs and impairments to net income.
Duration
A measurement of how long, in years, it takes for the price of a bond to be repaid by its internal cash flows. It is an important measure for investors to consider, as bonds with higher durations carry more risk and have higher price volatility than bonds with lower durations.
Forward Interest rates
A rate applicable to a financial transaction that will take place in the future
Annuity
A set of cash flows that are the same amounts across future time points • PV = C[ (1-(1+r)^-t)/r] • FV = C[((1+r)^t - 1)/r]
Adjusted Present Value
An investment appraisal technique similar to net present value method. However, instead of using weighted average cost of capital as the discount rate, ungeared cost of equity is used to discount the cash flows from a project and there is an adjustment for the tax shield provided by related debt capital and possibly for issuing costs. • Ungeared NPV + financing effects (tax shield benefit and issue costs (if necessary...may not be if the loan is directly from the government)
Stock Price Sensitivity to Dividend Growth (Required Return)
As the growth rate approaches the required return the price and sensitivity increases significantly
Cash Flows differ from Accounting Statement in terms of accounts payable/receivable
Cash flows simply state that companies receive cash from, and pay cash out to, various groups during each period. • companies rarely pay cash 'on the spot' for the assets or services that they buy, and customers often take some time to pay their bills. • something the company sells right now does not result in a cash payment from a customer until next period.
Operations Cash Flows
Cash flows that are paid in cash that year, be deductible for taxes that year, and not be a payment to a capital supplier.
Dividend Growth Model
Dividends are expected to grow at a constant percent per period. • P0 = D0(1+g)/(R-g) Which also equals • D1/(R-g) The price will grow at the same rate as the dividends
Total Market Value
Equity Market Value + Debt Market Value
project's NPV
Equity Market Value - Debt Market Value • it is not one of the more commonly used techniques in the modern company, there is a tendency to use techniques that do not separate the cash flows into those going to the various capital claims, but instead merely deal with the company's cash flows as a whole.
Two projects with different cash flows can produce a conflict between NPV and IRR.
Example: Two Projects, the required rate of return is 10 % Initial Investment A : 500 B : 400 Year 1 A : 325 B : 325 Year 2 A : 325 B : 200 NPV A : 64.05 B : 60.74 (A is better) IRR A : 19.43 B : 22.17 (B is better) The cross over rate is the discount rate at which the NPV of the two projects is equal
The implied forward rate can be calculated by ...
Generalized formula (1+it)t = (1+z1) (1+1f2) (1+2f3) (1+3f4) ... (1+it)t = (1+it-1)t-1 (1+t-1ft) examples (1+ 1f2 )=(1+ i2 )^2/(1+0f1 ) (1+ 2f3 )=(1+i3)^3/(1+0f1)(1+1f2) Multiple period examples (1 + i5)^5 = (1 + i3)^3 * (1 +3f5)^2
Payback Period
How long does it take to get the initial cost back in a nominal sense? • Decision Rule - Accept if the payback period is less than some preset limit
Growing cash flow in perpetuity
If cash flows continue forever, but grows or decline at a constant rate g , the formula becomes: PV = CF/ ( i - g ). • This might provide a reasonable approximation for a stream from a long-lived asset.
Coupon Effect
If maturity and a bond's initial price remain constant, the higher the coupon, the lower the volatility, and the lower the coupon, the higher the volatility.
Free Cash Flow and Profit
If we separately add up the free cash flows and after tax profits they will amount to the same figure. They will not be the same figures at the same time periods, reflecting the timing differences between accounting figures and cash flows
Interest payments and cash flows
Interest payments are a payment to a capital supplier so they should be excluded. They are part of the financing decision, not the investment decision. To include interest payments would result in an underestimation of the NPV of a project.
Duration calculated
Macaulay duration is defined as: (sum of (PV of (period number * cash flow))/price Steps: a. Multiply each cash flow by the period number it will be paid in b. Find the present value of each of the above c. Sum the above PV values d. Divide the above sum by the current price
Existing shareholders of the company get a wealth increase equal to ...
NPV regardless of who contributes the money necessary to undertake the investment (i.e. forgone dividend, new equity holders, the original holders i.e. new shares going to existing shareholders, or creditors).
