KNGX NOTES FINS1613 [FINS1613] Comprehensive Notes

Transcription

1 1 [] Comprehensive Notes 1

2 2 TABLE OF CONTENTS Table of Contents Introduction & Time Value of Money Net Present Value & Interest Rates Valuation of Securities I Valuation of Securities II Investment Decision Rules Capital Budgeting I Capital Budgeting II Capital Asset Pricing Model The Cost of Capital Capital Structure Payout Policy/Free Cash Flow Valuation Models

3 3 1. INTRODUCTION & TIME VALUE OF MONEY 1.1 INTRODUCTION PROJECTS Key characteristics: 1. Profits and Costs cash flows: determined by a. Expected amount and; b. Expected timing 2. Uncertainty risk: described by possible outcomes from the project TERMINOLOGY - Ownership: the right to a share in a firm s profits - Control: the right to directly manage or elect management of a firm - Personal liability: the responsibility to pay a firm s financial obligations using personal assets when the firm cannot - Limited Liability: a limit that the owner can only lose the value of their investment when the firm cannot pay its financial obligations 1.2 TYPES OF COMPANIES SOLE TRADER A sole trader is a business owned and run by one person. - Straightforward to set up - No separation between the firm and the owner - Owner has unlimited personal liability for the firm s debts - The life of a sole trader is limited to the life of the owner PARTNERSHIP A partnership is a business owned and run by more than one owner - Has two types of partners o General partners: ownership, control and personal liability o Limited partners: ownership, no control and limited liability - The partnership ends in the event of the death or withdrawal of a single general partner unless other provisions are made 3

4 4 - Profit taxed at personal level CORPORATIONS A corporation is a legally defined, artificial being, separate from its owners. It acts as its own entity, able to enter contracts, acquire assets in its own name, sue and be sued and incur obligations directly without recourse to its owners. Ownership of a corporation - Shares: the divided ownership or equity of a corporation - Equity: the collection of all outstanding shares of a corporation - Shareholder: an owner of a share of the equity in a corporation - Dividend Payment: payments made at the discretion of the corporation to its shareholders - Shares can be owned by anyone, and can be traded freely on the stock exchange Tax implications for corporate entities - The corporation pays tax on its own personal income as it is its own legal entity - When the remaining profits are distributed to the shareholders, the shareholders pay their own personal income tax on this income - This results in what is known as double taxation where you are taxed twice on the income received - Note: in Australia, the imputation system of taxation is used where a tax credit (franking credit) is transferred to shareholders for the amount of tax the company has paid Firm Structure: Person(s) Role Board of Directors - Each director is elected by the firm s owners - Hires the Chief Executive Officer - Monitors firm and sets high level strategy - Has the ultimate decision-making authority - Objectives is to maximize firm value Chief Executive Officer (CEO) - Everyday manager of the firm - Implements rules and policies set by board of director - Advised by high (C-) level executives - Objectives is to maximize firm value Chief Financial Officer (CFO) - Evaluates investment decisions for the firm - Evaluates financing decisions for the firm - Objectives is to maximize firm value 4

5 5 Advantages - Limited liability for the owners - Business continues operation when ownership changes Disadvantages - Agency Costs between owners and management - Taxation (in jurisdictions with classical tax systems) Agency Costs - We assume that employees have their own personal objectives - These personal objectives may not always agree with the value maximizing objective of the firm s owners - An agency cost arises when an employee takes an action that serves their own interests instead of maximizing firm value. Owners Liability Owner s Control Ownership change dissolves firm Taxation Sole Trader One Personal Yes Yes Personal General Partnership Limited Partnership Two to 20 (some may have more) General Partners (GP) At least one Limited Partners (LP) - Unlimited Personal Yes Yes Personal Personal Yes Yes Personal Limited No No Personal Corporations Unlimited Limited No No Company and personal 5

6 6 THE FINANCIAL MANAGER We will focus on two primary responsibilities of the financial manager: - Investment decisions o Which projects should the firm pursue? - Financing decisions o How should the firm raise capital to finance these projects? o How should the firm distribute profits to investors? 1.4 THE STOCK MARKET The stock market or stock exchange is an organized market on which the shares of many corporations are traded PRIMARY VS SECONDARY MARKETS: - Primary market: when a corporation issues new shares and sells them to investors - Secondary market: markets such as the ASX or NYSE, where shares of a corporation are traded between investors without the involvement of the corporation BID VS ASK PRICE - Bid price: the price at which a buyer is willing to buy a security - Ask price: the price at which a seller is wiling to sell a security - Bid-ask spread: the amount by which the ask price exceeds the bid price - Transaction cost: in most markets, an expense such as a broker s commission and the bid-ask spread investors must pay in order to trade securities 1.5 FINANCIAL INSTITUTIONS Financial institutions: are entities that provide financial services, such as taking deposits, managing investments, brokering financial transactions or making loans The financial cycle: 1. People invest and save their money 2. That money grows through loans and shares, flows to companies who use it to fund growth through new products, generating profits and wages 3. The money then flows back to the savers and investors All financial institutions play a role at some point in this cycle. 6

7 7 1.6 TIME VALUE OF MONEY AND INTEREST RATES Time value of money: the difference in value between money today and money in the future. Or, the observation that two cash flows at two different points in time have different points in time have different values. - Money received today is worth more than money received in the future - To compare or combine cash flows it is necessary to convert all values to the same units by moving them to a common point in time - The current interest rate can be used to determine the future value of money COMPOUNDING FINDING THE FUTURE VALUE Compounding assumption: we will always assume that interest is kept in the account. Therefore, the ending value in a given period becomes the starting principal used to compute the interest payment in the subsequent period. To calculate the equivalent future value of a cash flow multiply the cash flow s present value by the interest rate factors associated with the intervening time periods. FV = PV(1 + r) n FV = Future value: the value of a PV = Present value: the initial value of an investment r = Interest rate: expressed as decimal (R/100) n = Period This has the effect of earning interest on interest Note: we refer to (1 + r) as the interest rate factor DISCOUNTING FINDING THE PRESENT VALUE To calculate the present value of a cash flow in the future, multiply the future cash flow by a discount factor or, equivalently, divide the appropriate interest rate factor. PV = FV / (1 + r) n PV = Present value: the value today of the expected future cash flow FV = Future value: the expected value of a future cash flow r = Interest rate: expressed as decimal (R/100) n = Period It is called discounting because a $1 future cash flow is worth less than $1 today 7

8 8 2. NET PRESENT VALUE & INTEREST RATES 2.1 INTEREST RATES ANNUAL PERCENTAGE RATE (APR) - Financial mathematics equations are always stated in terms of periods and interest rates per period - Interest rates are often quoted in terms of an Annual Percentage Rate (APR) - APRs must be converted into number of periods and interest rates per period for calculations Annual Percentage Rate (APR): a simplified way to quote interest rates. It is equal to the total interest that would be earned in a year without compounding APR = Per Period Interest Rate(r) x Number of Compounding Periods per Year (m) APR = rm Common APR compounding periods: Compounding # of periods per year Monthly 12 Quarterly 4 Semi-Annually 2 Annually 1 EFFECTIVE ANNUAL RATE (EAR) Effective Annual Rate (EAR): the total amount of interest that will be earned at the end of one year with compounding EAR = (1 + r) m - 1 r = per period rate m = periods per annum Given an APR and m compounding periods per year, the EAR can be found as follows: 8

9 9 1. Compute the per-period discount rate, r 2. Compute the m-period interest rate factor 3. Compute the effective annual rate SUMARY: APR AND EPR Converting APR from EAR Converting EAR from APR 2.2 VALUING A STREAM OF CASH FLOWS - Projects have cash flows occurring at different points in time - Evaluation of cash flows requires: o Building a timeline of the stream of cash flows describing the timing and amount of expected cash flows o Computing the value of the stream as of a reference point in time, usually the initial period - Valuing a stream of cash flows can be done by two approached: o Sequential Approach: move cash flows one period at a time, computing the total value of cash flows already considered o Reference Time Approach: compute the value of each individual cash flow at the reference time. Add these to get the total value - Both approaches will give the same value - The term future value can be confusing and imprecise when applied to a stream of cash flows. - Instead we use the terms: o Time-t value: a value found by moving all cash flows to a time t and taking the sum o Present value: the value found at the implied reference point of a problem, time t=0 EXAMPLE FUTURE VALUE OF A STREAM OF CASH FLOWS 9

10 10 - You plan on investing $300 immediately in an accounting - You will invest $400 and $500 at times 1 and 2 respectively - Account pays an interest of 5% per annum Sequential Approach: Move forward one period at a time, computing the total value of cash flows already received T 0 à T 1 = 300*(1+0.05) = $ = 715 T 1 à T 2 = 715*(1+0.05) =$ = T 2 à T 3 = *(1+0.05) = $ Reference Time Approach: Compare the value of each individual cash flow at the reference time. Add these to get the total value 300*(1+0.05) 3 = $ *(1+0.05) 2 = $ *(1+0.05) 3 = $ $ EXAMPLE PRESENT VALUE OF A STREAM OF CASH FLOWS - A project requires an upfront cost of 1500 at t=0 - The project generates positive cash flows of 500, 1300, 2000 at times 1, 2 and respectively - The discount rate is 12% - What is the project value as of time t=0? Sequential Approach: move backwards one period at a time, computing the total value of cash flows already discounted 10

11 11 T 3 à T 2 = 2000/(1+0.12) = $ = T 2 à T 1 = /(1+0.12) =$ = T 1 à T 0 = /(1+0.12) = $ Deduct upfront cost = $ Reference Time Approach: compute the value of each individual cash flow at the reference time. Add these to get the total value T 3 à T 2 = 2000/(1+0.12) 3 = $ T 2 à T 1 = 1300/(1+0.12) 2 = $ T 1 à T 0 = 500/(1+0.12) 1 = $ Deduct upfront cost - ($1500) $ ANNUITIES Annuity: a stream cash flows arriving at a regular interval over a specified time period CONSTANT ANNUITY Constant Annuity: a stream of specified number of equal cash flows that occurs at regular intervals C = Periodic cash payment r = per period rate The annuity value formula gives the total time-t value of all n cash flows beginning at t+1 EXAMPLE CONSTANT ANNUITY 11

12 12 What is the present value of a 2-ear annuity making semi-annual payments of $50 at a discount rate of 4% APR? Annuity Value t=0 = 50 x (1/0.02) * [ 1 (1/ ) ] = $ ANNUITY FACTORS The annuity formula can be stated in terms of an annuity factor: GROWING ANNUITY Growing Annuity: a stream of specified number of growing cash flows that occurs at regular intervals. The initial cash flow is C and all subsequent cash flows grow at a rate g per period C = periodic cash payment r = per period rate g = payment growth rate The growing annuity value formula gives the total time-t value of all n growing cash flows beginning at t+1 12

13 PERPETUITIES Perpetuity: a stream of cash flows that occur at regular intervals and makes payments forever CONSTANT PERPETUITY A stream of equal cash flows that occurs at regular intervals and lasts forever C = Periodic Cash Payment r = per period interest rate The perpetuity value formula gives the total time-t value of the infinite cash flows beginning at t+1 EXAMPLE CONSTANT PERPETUITY Q. What is the present value of a perpetuity paying $100 per year at a discount rate of 12%? Perpetuity value = 100/12% = $ Q. What is the present value of a perpetuity paying $20 per month at a discount rate is 15% APR? R = 15%/12 = 1.25% Perpetuity value = $1600 GROWING PERPETUITY A stream of cash flows that occurs at regular intervals and lasts forever. The initial cash flow is C and all subsequent cash flows grow at a rate g per period. 13

14 14 C = Periodic Cash Payment r = per period interest rate g = payment growth rate The growing perpetuity value formula gives the total time-t value of the infinite growing cash flows beginning at t+1 SUMMARY: ANNUITIES AND PERPETUITIES When using the formulas be sure that: - The discount rate, r, is positive - For perpetuities, the growth rate, g, must be less than the discount rate g < r Check the timing of cash flows carefully - Formulas give value at time t when the first cash flow is received at t+1 (the next period) All annuity and perpetuity equations can be derived from the growing annuity equation 2.5 THE LAW OF ONE PRICE The Law of One Price: if equivalent investment opportunities trade simultaneously in different competitive markets, then they must trade for the same price in both markets. - Prices respond to supply and demand o The more people want to buy something, the higher the price o The more people want to sell something, the lower the price - Arbitrage represents an opportunity to make without taking any risks à riskless profit - The Law of One Price must hold because arbitrage opportunities cannot exist in financial markets for long periods of time 14

15 15 Key implications of the Law of One Price when valuing cash flows relate to: - Scaling cash flows - Adding and subtracting cash flows - Delaying and accelerating cash flows EXAMPLE SCALING OF CASH FLOW Given: What is the present value of the cash flows at a 10% discount rate? If the time t value of the cash flow is: The present value of the cash flows above at a 10% discount rate is M*X = 2*599.2 = $ Then the time t value of M times the cash flow is: EXAMPLE ADDING AND SUBTRACTING CASH FLOWS Given: What is the present value of the cash flows below at 10% discount rate? 15

16 16 The present value of the cash flows A and B above at a 10% discount rate is X + Y = = $ If the time t value of the cash flows A and B are: Then the time t value of the combined cash flows is Note: the values X and Y must be at the same reference time and use the same discount rate EXAMPLE DELAYED CASH FLOWS Given What is the time t=0 value of the cash flows below at a 10% discount rate? Just discount once more at a rate of 10% = $ EXAMPLE ACCELERATED CASH FLOWS Given: What is the time t=0 value of the cash flows below at a 10% discount rate? Just compound one period at a rate of 10% = $

17 17 SUMMARY: DELAYED/ACCELERATED CASH FLOWS If the time t value of cash flows is: Delayed by s periods Accelerated by u periods Delayed cash flows are received later, they are worth less, so divide (discount). Accelerated cash flows are received earlier. They are more valuable, so multiply (compound). SAMPLE PROBLEM 1 Q. An annuity due is an annuity where the first cash flow is received immediately. What is the formula for the present value of a 7-period annuity due? Solution 1: Present Value = Cash Flow Today + 6-period Standard Annuity Value = c + c * (1/r) * [ 1-1/(1+r) 6 ] Solution 2: Present value = A 7-period annuity accelerated by 1 period = c + c * (1/r) * [ 1-1/(1+r) 7 ] * (1+r) 17

18 18 SAMPLE PROBLEM 2 Q. What is the formula for the present value of a perpetuity where the first cash flow is received at t=5? Solution: Present value = Perpetuity Value delayed 4 years = (c/r) / (1+r) 4 SAMPLE PROBLEM 3 Q. A two-stage growth model combines an annuity and perpetuity. Assume a project is expected to pay $100 in 1 period. Cash flows will grow by 15% until period 5. After this, cash flows grow by 3% in perpetuity. What is the present value if the discount rate is 12% per period? Present value = Value of 5-period rowing annuity + Value of growing perpetuity delayed by 5 periods = = $