Week 1 Lecture 1: Introduction to Principles of Finance - AWS
Week 1 Lecture 1: Introduction to Principles of Finance
Finance is the study of how individuals, businesses and institutions acquire, spend and manage financial resources Accounting is more backward looking Finance is more forward looking Financial system – comprises financial institutions, instruments and markets facilitating transactions for goods and services and financial transactions Developed financial systems perform several functions Settle commercial transactions (domestic and internationally) Arrange the flow of funds between surplus and deficit units (that is, financing) Transfer and manage risk Generate information to assist decision making Deal with incentive problems in contracting Pooling of Funds Surplus units – suppliers of funds (e.g. lenders, investors, shareholders, depositors) Deficit units – users of funds, use someone else’s money (e.g. borrowers, credit card users, companies/issuers People and companies/corporation can be surplus and deficit units at the same time The financing system organises the flow of funds: From surplus units To deficit units Funds can flow via intermediaries (intermediation), or through financial markets (direct financing) Surplus and Deficit Units are connected through contracts A contract is a promise or set of promises for the breach of which the law gives remedy A promise is a commitment or an undertaking that some event will or will not occur in the future Finance is entirely built on promises Intermediation (also called ‘indirect financing’) Involves the transfer of funds between ultimate savers and ultimate borrowers via deposit-taking institutions (e.g. bank deposit loan) Advantages: o Asset transformation – Borrowers and savers are offered a range of products o Maturity transformation – Borrowers and savers are offered products with a range of terms to maturity o Credit risk diversification and transformation – Saver’s credit risk is limited to the intermediary, which has expertise and information o Economies of scale – Financial and operational benefits of organisational size and business volume Direct Financing
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The transfer of funds from ultimate savers to ultimate borrowers without an intermediary (e.g. issue of shares) Advantages: o Avoid costs of intermediation o Increases access to diverse range of markets o Greater flexibility in range of securities users can issue for different financing needs Disadvantages: o Matching of preferences – time, difficulty o Liquidity and marketability of security o Search and transaction costs Security – a financial contract that can be traded in a financial market that specifies: Asset involved: commodity (e.g. gold), hard asset (e.g. property), financial asset (e.g. shares) Quantity and unit (e.g. thousand shares, ounce of gold) Price, Date and Payment and settlement terms
Primary markets The issue of a new financial instrument to raise funds to purchase goods, services or assets by: o Businesses: company shares or debentures o Government: Treasury notes or bonds Funds are obtained by the issuer Direct financing raises funds in larger amounts because the issue of securities requires a substantial effort that is only economical for large amounts Secondary markets The buying and selling of existing financial securities No new funds raised and therefore no direct impact on original issuer of security Transfer of ownership from one saver to another saver
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Provides liquidity, which facilitates the restructuring of portfolios of security owners It does not raise funds for issuers but a liquid and efficient secondary market greatly assists the operations of the primary market Perform three main functions: o Provide investors with liquidity – this transforms the maturity of funds o Identify the price (or value) of the securities – known as price discovery o Identify investors who are interested in securities – who could be approached to supply funds in the primary market Different firms have different organisational structures with implications for: Ownership Liability Incentives Risk and return Taxation Agency/Informational issues Types of firms (main ones): Limited liability Companies – public and private Partnerships Sole Trader Limited Liability Companies Separate legal entity from its owners Limits owners liability to their investment Taxed in its own right and can be sued in its own right They can be public (traded on an exchange) or private (banned from being traded on an exchange) Most of the time especially for public limited liability companies, professional managers (agents) run the firm on behalf of the owners on a day-to-day basis o This can result in agency/information type of issues o The incentive of the managers may not always be aligned with the owners Sole proprietorships No separation between owner and the firm Unlimited liability and taxed as if the same Business is owned and run by one person with some employees It is easy to set up and agency issues are not a big problem Size of business is limited by wealth of the owner and how much this owner can borrow Partnerships Very similar to sole proprietorship except more than one owner All partners are liable for the debts of the business Combines the wealth and abilities of multiple individuals Easy to setup but a new partnership will need to be formed if an existing partner sells their stake or dies Finance focuses on cash flows and is more forward-looking Finance seeks to identify and value the benefits and costs of a decision To quantity assets, we need to evaluate them in the same terms – e.g. cash today Competitive market if asset can be bought and sold at the same price
3 FNCE10002 H1 Notes
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 (assuming minimal transaction costs) Arbitrage trade make a riskless profit Time value of money: a dollar received today is different in value to that received in one year’s time The observed (or realized) return of an asset or security is measured as the change in cash flows (interest/dividend/cash flow received during the period AND the change in capital value of the investment) divided by the initial investment The risk is the uncertainty of receiving the return in one year’s time The higher the risk, the higher the expected return (assuming risk aversion) The return of a risky asset would be risk free return plus risk premium The main goal of managers is to maximize the market value of the firm Value of the firm = Present value of future expected cash flows This maximizes the wealth of shareholders Shareholder wealth = Present value of shareholder’s future expected cash flows Firm value is the present value of future expected cash flows 𝐧 𝐄(𝐂𝐅𝐭 ) ∑ (𝟏 + 𝐫)𝐭 𝐭=𝟏
o E(CFt) = Expected cash flows received at the end of period t o n = Number of periods over which cash flows are received o r = Rate of return required by investors Main factors to consider when valuing a firm Magnitude of expected cash flows – E(CFt) Timing of cash flows – n Risk of expected cash flows – r Efficiency of capital markets Simple interest – the value of a cash flow is calculated without including any accrued interest to the principal 𝐹0 = 𝑃0 (1 + 𝑛 × 𝑟) 𝑃0 = 𝐹0 /(1 + 𝑛 × 𝑟) Compound interest – interest accrued is added to the principal and reinvested The future value of a cash flow is calculated based on the principal and interest accrued Effective interest rate (ie) – annualised rate that takes account of compounding within the year (or period) 𝒓 𝒊𝒆 = (𝟏 + 𝒎)𝒎 − 𝟏 As the compounding becomes more frequent, m approaches infinity, and in the limit 𝒓 (𝟏 + 𝒎)𝒎 approaches er Effective annual rate with continuous compounding: 𝒓 𝒆 = 𝒆𝒓 − 𝟏 Calculating the future value using the interest paid m times a year 𝒓 𝑺𝒏 = 𝑷𝟎 × (𝟏 + )𝒎×𝒏 𝒎 o r/m = Per period interest rate o m x n = Total periods over which interest is compounded
4 FNCE10002 H1 Notes
Future value of a single cash flow 𝑭𝒏 = 𝑷𝟎 (𝟏 + 𝒓)𝒏 Present value of a single cash flow 𝑷𝒏 = 𝑭𝟎 /(𝟏 + 𝒓)𝒏 The time period, n Future value increases as n increases Present value decreases as n increases The interest rate, r Future value increases as n increases Present value decreases as n increases The method of computing interest Future value increases as the compounding frequency increases Present value decreases as the compounding frequency increases In a competitive market, with minimal frictions, assets with equivalent investment opportunities should sell for the same price Money has time value because of compounded interest
5 FNCE10002 H1 Notes
Week 2 Lecture 2: Introduction to Financial Mathematics and Debt
A perpetuity is an equal, periodic cash flow that goes on forever 𝐶 𝐶 𝑃0 = + +⋯ 1 + 𝑟 (1 + 𝑟)2 𝑃0 = 𝐶/𝑟 First payment to be made at the end of Year 1
A deferred perpetuity is an equal, periodic cash flow that starts at some future date and goes on forever In general, the present value of a perpetuity is deferred to the end of time n+1 (n is the number of payments) 𝑃0 = [𝐶/𝑟]/(1 + 𝑟)𝑛
A growth perpetuity is a perpetuity of C dollars today growing at a constant rate of g percent per period and has the cash flow stream C(1+g), C(1+g)2,… C(1+g)n, and so on The first cash flow is assumed to be C(1+g) and not C 𝑃0 =
𝐶(1+𝑔) 1+𝑟
+
𝐶(1+𝑔)2 (1+𝑟)2
+⋯
As n approaches infinity: 𝑃0 = 𝐶(1 + 𝑔)/(𝑟 − 𝑔)
An ordinary annuity is a series of equal, periodic cash flows occurring at the end of each period and lasting for n periods with n cash flows 𝑃0 = [𝐶/𝑟]/[1 − 1/(1 + 𝑟)𝑛 ] The first cash flow occurs at the end of period 1 and the last cash flow occurs at the end of period n Ordinary annuities can be valued as the difference between an ordinary perpetuity (starting at the end of period 1) and a deferred perpetuity (starting at the end of period n + 1)
6 FNCE10002 H1 Notes
𝑃0 (𝑂𝐴) =
𝐶 𝑟
𝐶
1
− [ ] [(1+𝑟)𝑛] 𝑟
𝐹0 (𝑂𝐴) = [𝐶/𝑟]/[1 − 1/(1 + 𝑟)𝑛 ](1 + 𝑟)𝑛 𝐹0 (𝑂𝐴) = [𝐶/𝑟]/[(1 + 𝑟)𝑛 − 1] A deferred ordinary annuity is a series of equal, periodic cash flows occurring at the end of each period where the first cash flow occurs at a future date
7 FNCE10002 H1 Notes
An annuity due is a series of equal, periodic cash flows occurring at the beginning of each period. There are n cash flows but only n-1 periods
The present value of an annuity due at r% p.a. is equivalent to the present value of an ordinary annuity compounded one additional period o The future value of an annuity due at r% p.a. is equivalent to the future value of an ordinary annuity compounded one additional period o 𝑃0 (𝐴𝐷) = 𝐶 + [𝐶/𝑟]/[1 − 1/(1 + 𝑟)𝑛−1 ] o 𝐹𝑛 (𝐴𝐷) = {𝐶 + [𝐶/𝑟]/[1 − (1 + 𝑟)−(𝑛−1) ]}[1 + 𝑟]𝑛−1 A loan amortization schedule shows the interest paid, principal repaid and principal remaining over the loan’s duration Interest paid = (Previous period’s principal) x (Interest rate) Principal repaid = Loan Payment – Interest paid Principal remaining = Previous period’s principal – Principal repaid Effective interest rate: r = re only when the compounding interval is one year (m=1); otherwise re will always exceed r
8 FNCE10002 H1 Notes
Debt instruments require the company (issuers) to repay the creditors (debt holders) both interest and principal when they are due Short term debt instruments Mature within the year – typically in 90 and 180 days Issuer has contractual obligation to make promised payments Lower risk than equity because you must make promised payments Examples: Treasury Bills, Bank Bills, etc. Face (or par value) is the dollar amount paid at maturity o Typically $100,000 or its multiple o Denoted as Fn (or Pn) o No other payments made to debtholders (investors) o Return (or interest) earned by investors is based on the difference between the price paid (P0) and face value (Fn) Long term debt instruments o Typically mature after several years o May or may not promise a regular interest (coupon) payment o Issuer has contractual obligation to make all promised payments Face (or par value) is the dollar amount paid at maturity o Typically $1000 or its multiples o Denoted as Fn (or Pn) o Interest (coupon) payment is the periodic (annual or semi-annual) payment made to debtholders o Coupon payment = Coupon rate x Face value o Denoted as C (or I) The Valuation Principle – the price of a security today is the present value of all future expected cash flows discounted at the “appropriate” required rate of return (or discount rate) The valuation variables are:
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1. Market price 2. Future expected cash flows – Face value and/or coupons (numerator) 3. Yield to maturity or required rate of return (denominator) The valuation problem is to 1. Estimate the price; given the future cash flows and required rate or return, or 2. Estimate the required rate of return, given the future cash flows and price Discount Securities The face value (Fn) is promised at a pre-specified date and no other payment is promised o The interest earned is “implicit” in the difference between the face value and market price, P0 o Examples: Treasury Bills, Bank Accepted Bills, etc. o Face value is typically $100,000 or its multiple Bank Accepted Bills – very liquid o Short-term debt instruments where the acceptor (or endorser) of the bill is a bank – the bank promises to pay the holder the face value of the bill at maturity o Most common maturities are 90 to 180 days
The price of discount securities is computed as the present value of the face value at a market determined yield to maturity (YTM, r or kd) o The yield to maturity is the rate of return earned by an investor who holds the security until it matures assuming no default on the security Market yields are always quoted on an annual basis o For securities maturing in less than a year: Interest rate factor = (Time to maturity/365) x r = (n/365) x r P0 = Fn /[1 + (n/365) x r] Acceptance fee = Face value x Annual fee rate x (n/365) Net proceeds = P0 – Acceptance fee In general, the annualised cost of funds can be computed as 𝑭𝒂𝒄𝒆 𝑽𝒂𝒍𝒖𝒆 𝟑𝟔𝟓 ( − 𝟏) 𝑷𝟎 − 𝑪𝒐𝒔𝒕𝒔 𝒏 Coupon Paying Securities
10 FNCE10002 H1 Notes
Finance is the study of how individuals, businesses and institutions acquire, spend and manage financial resources Accounting is more backward looking Finance is more forward looking Financial system – comprises financial institutions, instruments and markets facilitating transactions for goods and services and financial transactions Developed financial systems perform several functions Settle commercial transactions (domestic and internationally) Arrange the flow of funds between surplus and deficit units (that is, financing) Transfer and manage risk Generate information to assist decision making Deal with incentive problems in contracting Pooling of Funds Surplus units – suppliers of funds (e.g. lenders, investors, shareholders, depositors) Deficit units – users of funds, use someone else’s money (e.g. borrowers, credit card users, companies/issuers People and companies/corporation can be surplus and deficit units at the same time The financing system organises the flow of funds: From surplus units To deficit units Funds can flow via intermediaries (intermediation), or through financial markets (direct financing) Surplus and Deficit Units are connected through contracts A contract is a promise or set of promises for the breach of which the law gives remedy A promise is a commitment or an undertaking that some event will or will not occur in the future Finance is entirely built on promises Intermediation (also called ‘indirect financing’) Involves the transfer of funds between ultimate savers and ultimate borrowers via deposit-taking institutions (e.g. bank deposit loan) Advantages: o Asset transformation – Borrowers and savers are offered a range of products o Maturity transformation – Borrowers and savers are offered products with a range of terms to maturity o Credit risk diversification and transformation – Saver’s credit risk is limited to the intermediary, which has expertise and information o Economies of scale – Financial and operational benefits of organisational size and business volume Direct Financing
1 FNCE10002 H1 Notes
The transfer of funds from ultimate savers to ultimate borrowers without an intermediary (e.g. issue of shares) Advantages: o Avoid costs of intermediation o Increases access to diverse range of markets o Greater flexibility in range of securities users can issue for different financing needs Disadvantages: o Matching of preferences – time, difficulty o Liquidity and marketability of security o Search and transaction costs Security – a financial contract that can be traded in a financial market that specifies: Asset involved: commodity (e.g. gold), hard asset (e.g. property), financial asset (e.g. shares) Quantity and unit (e.g. thousand shares, ounce of gold) Price, Date and Payment and settlement terms
Primary markets The issue of a new financial instrument to raise funds to purchase goods, services or assets by: o Businesses: company shares or debentures o Government: Treasury notes or bonds Funds are obtained by the issuer Direct financing raises funds in larger amounts because the issue of securities requires a substantial effort that is only economical for large amounts Secondary markets The buying and selling of existing financial securities No new funds raised and therefore no direct impact on original issuer of security Transfer of ownership from one saver to another saver
2 FNCE10002 H1 Notes
Provides liquidity, which facilitates the restructuring of portfolios of security owners It does not raise funds for issuers but a liquid and efficient secondary market greatly assists the operations of the primary market Perform three main functions: o Provide investors with liquidity – this transforms the maturity of funds o Identify the price (or value) of the securities – known as price discovery o Identify investors who are interested in securities – who could be approached to supply funds in the primary market Different firms have different organisational structures with implications for: Ownership Liability Incentives Risk and return Taxation Agency/Informational issues Types of firms (main ones): Limited liability Companies – public and private Partnerships Sole Trader Limited Liability Companies Separate legal entity from its owners Limits owners liability to their investment Taxed in its own right and can be sued in its own right They can be public (traded on an exchange) or private (banned from being traded on an exchange) Most of the time especially for public limited liability companies, professional managers (agents) run the firm on behalf of the owners on a day-to-day basis o This can result in agency/information type of issues o The incentive of the managers may not always be aligned with the owners Sole proprietorships No separation between owner and the firm Unlimited liability and taxed as if the same Business is owned and run by one person with some employees It is easy to set up and agency issues are not a big problem Size of business is limited by wealth of the owner and how much this owner can borrow Partnerships Very similar to sole proprietorship except more than one owner All partners are liable for the debts of the business Combines the wealth and abilities of multiple individuals Easy to setup but a new partnership will need to be formed if an existing partner sells their stake or dies Finance focuses on cash flows and is more forward-looking Finance seeks to identify and value the benefits and costs of a decision To quantity assets, we need to evaluate them in the same terms – e.g. cash today Competitive market if asset can be bought and sold at the same price
3 FNCE10002 H1 Notes
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 (assuming minimal transaction costs) Arbitrage trade make a riskless profit Time value of money: a dollar received today is different in value to that received in one year’s time The observed (or realized) return of an asset or security is measured as the change in cash flows (interest/dividend/cash flow received during the period AND the change in capital value of the investment) divided by the initial investment The risk is the uncertainty of receiving the return in one year’s time The higher the risk, the higher the expected return (assuming risk aversion) The return of a risky asset would be risk free return plus risk premium The main goal of managers is to maximize the market value of the firm Value of the firm = Present value of future expected cash flows This maximizes the wealth of shareholders Shareholder wealth = Present value of shareholder’s future expected cash flows Firm value is the present value of future expected cash flows 𝐧 𝐄(𝐂𝐅𝐭 ) ∑ (𝟏 + 𝐫)𝐭 𝐭=𝟏
o E(CFt) = Expected cash flows received at the end of period t o n = Number of periods over which cash flows are received o r = Rate of return required by investors Main factors to consider when valuing a firm Magnitude of expected cash flows – E(CFt) Timing of cash flows – n Risk of expected cash flows – r Efficiency of capital markets Simple interest – the value of a cash flow is calculated without including any accrued interest to the principal 𝐹0 = 𝑃0 (1 + 𝑛 × 𝑟) 𝑃0 = 𝐹0 /(1 + 𝑛 × 𝑟) Compound interest – interest accrued is added to the principal and reinvested The future value of a cash flow is calculated based on the principal and interest accrued Effective interest rate (ie) – annualised rate that takes account of compounding within the year (or period) 𝒓 𝒊𝒆 = (𝟏 + 𝒎)𝒎 − 𝟏 As the compounding becomes more frequent, m approaches infinity, and in the limit 𝒓 (𝟏 + 𝒎)𝒎 approaches er Effective annual rate with continuous compounding: 𝒓 𝒆 = 𝒆𝒓 − 𝟏 Calculating the future value using the interest paid m times a year 𝒓 𝑺𝒏 = 𝑷𝟎 × (𝟏 + )𝒎×𝒏 𝒎 o r/m = Per period interest rate o m x n = Total periods over which interest is compounded
4 FNCE10002 H1 Notes
Future value of a single cash flow 𝑭𝒏 = 𝑷𝟎 (𝟏 + 𝒓)𝒏 Present value of a single cash flow 𝑷𝒏 = 𝑭𝟎 /(𝟏 + 𝒓)𝒏 The time period, n Future value increases as n increases Present value decreases as n increases The interest rate, r Future value increases as n increases Present value decreases as n increases The method of computing interest Future value increases as the compounding frequency increases Present value decreases as the compounding frequency increases In a competitive market, with minimal frictions, assets with equivalent investment opportunities should sell for the same price Money has time value because of compounded interest
5 FNCE10002 H1 Notes
Week 2 Lecture 2: Introduction to Financial Mathematics and Debt
A perpetuity is an equal, periodic cash flow that goes on forever 𝐶 𝐶 𝑃0 = + +⋯ 1 + 𝑟 (1 + 𝑟)2 𝑃0 = 𝐶/𝑟 First payment to be made at the end of Year 1
A deferred perpetuity is an equal, periodic cash flow that starts at some future date and goes on forever In general, the present value of a perpetuity is deferred to the end of time n+1 (n is the number of payments) 𝑃0 = [𝐶/𝑟]/(1 + 𝑟)𝑛
A growth perpetuity is a perpetuity of C dollars today growing at a constant rate of g percent per period and has the cash flow stream C(1+g), C(1+g)2,… C(1+g)n, and so on The first cash flow is assumed to be C(1+g) and not C 𝑃0 =
𝐶(1+𝑔) 1+𝑟
+
𝐶(1+𝑔)2 (1+𝑟)2
+⋯
As n approaches infinity: 𝑃0 = 𝐶(1 + 𝑔)/(𝑟 − 𝑔)
An ordinary annuity is a series of equal, periodic cash flows occurring at the end of each period and lasting for n periods with n cash flows 𝑃0 = [𝐶/𝑟]/[1 − 1/(1 + 𝑟)𝑛 ] The first cash flow occurs at the end of period 1 and the last cash flow occurs at the end of period n Ordinary annuities can be valued as the difference between an ordinary perpetuity (starting at the end of period 1) and a deferred perpetuity (starting at the end of period n + 1)
6 FNCE10002 H1 Notes
𝑃0 (𝑂𝐴) =
𝐶 𝑟
𝐶
1
− [ ] [(1+𝑟)𝑛] 𝑟
𝐹0 (𝑂𝐴) = [𝐶/𝑟]/[1 − 1/(1 + 𝑟)𝑛 ](1 + 𝑟)𝑛 𝐹0 (𝑂𝐴) = [𝐶/𝑟]/[(1 + 𝑟)𝑛 − 1] A deferred ordinary annuity is a series of equal, periodic cash flows occurring at the end of each period where the first cash flow occurs at a future date
7 FNCE10002 H1 Notes
An annuity due is a series of equal, periodic cash flows occurring at the beginning of each period. There are n cash flows but only n-1 periods
The present value of an annuity due at r% p.a. is equivalent to the present value of an ordinary annuity compounded one additional period o The future value of an annuity due at r% p.a. is equivalent to the future value of an ordinary annuity compounded one additional period o 𝑃0 (𝐴𝐷) = 𝐶 + [𝐶/𝑟]/[1 − 1/(1 + 𝑟)𝑛−1 ] o 𝐹𝑛 (𝐴𝐷) = {𝐶 + [𝐶/𝑟]/[1 − (1 + 𝑟)−(𝑛−1) ]}[1 + 𝑟]𝑛−1 A loan amortization schedule shows the interest paid, principal repaid and principal remaining over the loan’s duration Interest paid = (Previous period’s principal) x (Interest rate) Principal repaid = Loan Payment – Interest paid Principal remaining = Previous period’s principal – Principal repaid Effective interest rate: r = re only when the compounding interval is one year (m=1); otherwise re will always exceed r
8 FNCE10002 H1 Notes
Debt instruments require the company (issuers) to repay the creditors (debt holders) both interest and principal when they are due Short term debt instruments Mature within the year – typically in 90 and 180 days Issuer has contractual obligation to make promised payments Lower risk than equity because you must make promised payments Examples: Treasury Bills, Bank Bills, etc. Face (or par value) is the dollar amount paid at maturity o Typically $100,000 or its multiple o Denoted as Fn (or Pn) o No other payments made to debtholders (investors) o Return (or interest) earned by investors is based on the difference between the price paid (P0) and face value (Fn) Long term debt instruments o Typically mature after several years o May or may not promise a regular interest (coupon) payment o Issuer has contractual obligation to make all promised payments Face (or par value) is the dollar amount paid at maturity o Typically $1000 or its multiples o Denoted as Fn (or Pn) o Interest (coupon) payment is the periodic (annual or semi-annual) payment made to debtholders o Coupon payment = Coupon rate x Face value o Denoted as C (or I) The Valuation Principle – the price of a security today is the present value of all future expected cash flows discounted at the “appropriate” required rate of return (or discount rate) The valuation variables are:
9 FNCE10002 H1 Notes
1. Market price 2. Future expected cash flows – Face value and/or coupons (numerator) 3. Yield to maturity or required rate of return (denominator) The valuation problem is to 1. Estimate the price; given the future cash flows and required rate or return, or 2. Estimate the required rate of return, given the future cash flows and price Discount Securities The face value (Fn) is promised at a pre-specified date and no other payment is promised o The interest earned is “implicit” in the difference between the face value and market price, P0 o Examples: Treasury Bills, Bank Accepted Bills, etc. o Face value is typically $100,000 or its multiple Bank Accepted Bills – very liquid o Short-term debt instruments where the acceptor (or endorser) of the bill is a bank – the bank promises to pay the holder the face value of the bill at maturity o Most common maturities are 90 to 180 days
The price of discount securities is computed as the present value of the face value at a market determined yield to maturity (YTM, r or kd) o The yield to maturity is the rate of return earned by an investor who holds the security until it matures assuming no default on the security Market yields are always quoted on an annual basis o For securities maturing in less than a year: Interest rate factor = (Time to maturity/365) x r = (n/365) x r P0 = Fn /[1 + (n/365) x r] Acceptance fee = Face value x Annual fee rate x (n/365) Net proceeds = P0 – Acceptance fee In general, the annualised cost of funds can be computed as 𝑭𝒂𝒄𝒆 𝑽𝒂𝒍𝒖𝒆 𝟑𝟔𝟓 ( − 𝟏) 𝑷𝟎 − 𝑪𝒐𝒔𝒕𝒔 𝒏 Coupon Paying Securities
10 FNCE10002 H1 Notes
