This document provides a summary of useful formulas from a finance textbook. It includes formulas for interest rates, annuities, bonds, options, and other financial instruments. The document lists key terms, concepts, and formulas for topics such as compound interest, present value calculations, yield curves, duration, immunization strategies, and derivative pricing. It is intended as a handy reference sheet for students and practitioners of finance and investment management.
Wayne lippman present s bonds and their valuationWayne Lippman
Bonds are simply long-term IOUs that represent claims against a firm’s assets.
Bonds are a form of debt
Bonds are often referred to as fixed-income investments.
Key Features of a Bond
Debt instrument issued by a corp. or government.
Par value = face amount of the bond, which is paid at maturity (assume $1,000).
Coupon rate – stated interest rate (generally fixed) paid by the issuer. Multiply by par to get dollar payment of interest.
Wayne lippman present s bonds and their valuationWayne Lippman
Bonds are simply long-term IOUs that represent claims against a firm’s assets.
Bonds are a form of debt
Bonds are often referred to as fixed-income investments.
Key Features of a Bond
Debt instrument issued by a corp. or government.
Par value = face amount of the bond, which is paid at maturity (assume $1,000).
Coupon rate – stated interest rate (generally fixed) paid by the issuer. Multiply by par to get dollar payment of interest.
this is a lecture on time value of money which explains the topic time value of money in a very easy and simple way... it also explains some examples on the topic... plus definition of rate of return, real rate of return, inflation premium, nominal interest rate,market risk, maturity risk,liquidity risk,and default risk,
The presentation highlights some shortcut formulas that can speed up PV computations if a project have a particular set of cash flow patterns and the opportunity cost of capital is constant
time value of money
,
concept of time value of money
,
significance of time value of money
,
present value vs future value
,
solve for the present value
,
simple vs compound interest rate
,
nominal vs effective annual interest rates
,
future value of a lump sum
,
solve for the future value
,
present value of a lump sum
,
types of annuity
,
future value of an annuity
Fixed Income Securities Yield Measures.pptxanurag202001
Sources of Return
Yield Measures for Fixed-Rate Bonds
Yield to Call
Yield to Put
Yield to Worst
Cash Flow Yield
Yield Measures for Floating Rate Notes
Yield Measures for Money Market Instruments
Theoretical Spot rates (Bootstrapping)
Derivation of Forward Rates
Yield Spreads
Riding the Yield Curve
this is a lecture on time value of money which explains the topic time value of money in a very easy and simple way... it also explains some examples on the topic... plus definition of rate of return, real rate of return, inflation premium, nominal interest rate,market risk, maturity risk,liquidity risk,and default risk,
The presentation highlights some shortcut formulas that can speed up PV computations if a project have a particular set of cash flow patterns and the opportunity cost of capital is constant
time value of money
,
concept of time value of money
,
significance of time value of money
,
present value vs future value
,
solve for the present value
,
simple vs compound interest rate
,
nominal vs effective annual interest rates
,
future value of a lump sum
,
solve for the future value
,
present value of a lump sum
,
types of annuity
,
future value of an annuity
Fixed Income Securities Yield Measures.pptxanurag202001
Sources of Return
Yield Measures for Fixed-Rate Bonds
Yield to Call
Yield to Put
Yield to Worst
Cash Flow Yield
Yield Measures for Floating Rate Notes
Yield Measures for Money Market Instruments
Theoretical Spot rates (Bootstrapping)
Derivation of Forward Rates
Yield Spreads
Riding the Yield Curve
Management of funds is a critical aspect of financial management. Management of funds acts as the foremost concern whether it is in a business undertaking or in an educational institution. Financial management, which is simply meant dealing with management of money matters.
Financial Management is efficient use of economic resources namely capital funds. Financial management is concerned with the managerial decisions that result in the acquisition and financing of short term and long term credits for the firm. Here it deals with the situations that require selection of specific assets, or a combination of assets and the selection of specific problem of size and growth of an enterprise. Herein the analysis deals with the expected inflows and outflows of funds and their effect on managerial objectives. In short, Financial Management deals with Procurement of funds and their effective utilization in the business.Management of funds is a critical aspect of financial management. Management of funds acts as the foremost concern whether it is in a business undertaking or in an educational institution. Financial management, which is simply meant dealing with management of money matters.
Financial Management is efficient use of economic resources namely capital funds. Financial management is concerned with the managerial decisions that result in the acquisition and financing of short term and long term credits for the firm. Here it deals with the situations that require selection of specific assets, or a combination of assets and the selection of specific problem of size and growth of an enterprise. Herein the analysis deals with the expected inflows and outflows of funds and their effect on managerial objectives. In short, Financial Management deals with Procurement of funds and their effective utilization in the business.
Management of funds is a critical aspect of financial management. Management of funds acts as the foremost concern whether it is in a business undertaking or in an educational institution. Financial management, which is simply meant dealing with management of money matters.
Financial Management is efficient use of economic resources namely capital funds. Financial management is concerned with the managerial decisions that result in the acquisition and financing of short term and long term credits for the firm. Here it deals with the situations that require selection of specific assets, or a combination of assets and the selection of specific problem of size and growth of an enterprise. Herein the analysis deals with the expected inflows and outflows of funds and their effect on managerial objectives. In short, Financial Management deals with Procurement of funds and their effective utilization in the business.
Management of funds is a critical aspect of financial management. Management of funds acts as the foremost concern whether it is in a business undertaking or in an educational institution. Financial management, Management of fund
Business Valuation Principles for EntrepreneursBen Wann
This insightful presentation is designed to equip entrepreneurs with the essential knowledge and tools needed to accurately value their businesses. Understanding business valuation is crucial for making informed decisions, whether you're seeking investment, planning to sell, or simply want to gauge your company's worth.
RMD24 | Retail media: hoe zet je dit in als je geen AH of Unilever bent? Heid...BBPMedia1
Grote partijen zijn al een tijdje onderweg met retail media. Ondertussen worden in dit domein ook de kansen zichtbaar voor andere spelers in de markt. Maar met die kansen ontstaan ook vragen: Zelf retail media worden of erop adverteren? In welke fase van de funnel past het en hoe integreer je het in een mediaplan? Wat is nu precies het verschil met marketplaces en Programmatic ads? In dit half uur beslechten we de dilemma's en krijg je antwoorden op wanneer het voor jou tijd is om de volgende stap te zetten.
[Note: This is a partial preview. To download this presentation, visit:
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Sustainability has become an increasingly critical topic as the world recognizes the need to protect our planet and its resources for future generations. Sustainability means meeting our current needs without compromising the ability of future generations to meet theirs. It involves long-term planning and consideration of the consequences of our actions. The goal is to create strategies that ensure the long-term viability of People, Planet, and Profit.
Leading companies such as Nike, Toyota, and Siemens are prioritizing sustainable innovation in their business models, setting an example for others to follow. In this Sustainability training presentation, you will learn key concepts, principles, and practices of sustainability applicable across industries. This training aims to create awareness and educate employees, senior executives, consultants, and other key stakeholders, including investors, policymakers, and supply chain partners, on the importance and implementation of sustainability.
LEARNING OBJECTIVES
1. Develop a comprehensive understanding of the fundamental principles and concepts that form the foundation of sustainability within corporate environments.
2. Explore the sustainability implementation model, focusing on effective measures and reporting strategies to track and communicate sustainability efforts.
3. Identify and define best practices and critical success factors essential for achieving sustainability goals within organizations.
CONTENTS
1. Introduction and Key Concepts of Sustainability
2. Principles and Practices of Sustainability
3. Measures and Reporting in Sustainability
4. Sustainability Implementation & Best Practices
To download the complete presentation, visit: https://www.oeconsulting.com.sg/training-presentations
RMD24 | Debunking the non-endemic revenue myth Marvin Vacquier Droop | First ...BBPMedia1
Marvin neemt je in deze presentatie mee in de voordelen van non-endemic advertising op retail media netwerken. Hij brengt ook de uitdagingen in beeld die de markt op dit moment heeft op het gebied van retail media voor niet-leveranciers.
Retail media wordt gezien als het nieuwe advertising-medium en ook mediabureaus richten massaal retail media-afdelingen op. Merken die niet in de betreffende winkel liggen staan ook nog niet in de rij om op de retail media netwerken te adverteren. Marvin belicht de uitdagingen die er zijn om echt aansluiting te vinden op die markt van non-endemic advertising.
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As a business owner in Delaware, staying on top of your tax obligations is paramount, especially with the annual deadline for Delaware Franchise Tax looming on March 1. One such obligation is the annual Delaware Franchise Tax, which serves as a crucial requirement for maintaining your company’s legal standing within the state. While the prospect of handling tax matters may seem daunting, rest assured that the process can be straightforward with the right guidance. In this comprehensive guide, we’ll walk you through the steps of filing your Delaware Franchise Tax and provide insights to help you navigate the process effectively.
Attending a job Interview for B1 and B2 Englsih learnersErika906060
It is a sample of an interview for a business english class for pre-intermediate and intermediate english students with emphasis on the speking ability.
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2. Interest
Interest Discount
Simple Compound Simple Compound
a(t)
Period
when
greater
Interest Formulas
Force of Interest
The Method of Equated Time
The Rule of 72
The time it takes an investment of 1 to double is given by
Date Conventions
Recall knuckle memory device. (February has 28/29 days)
Exact
o “actual/actual”
o Uses exact days
o 365 days in a nonleap year
o 366 days in a leap year (divisible by 4)
Ordinary
o “30/360”
o All months have 30 days
o Every year has 360 days
o
Banker’s Rule
o “actual/360”
o Uses exact days
o Every year has 360 days
Basic Formulas
3. AnnuitiesBasic Equations
Immediate Due
Perpetuity
Annuities Payable Less Frequently than Interest is Convertible
Let = number of interest conversion periods in one payment period
Let = total number of conversion periods
Hence the total number of annuity payments is
Immediate Due
Perpetuity
Annuities Payable More Frequently than Interest is Convertible
Let = the number of payments per interest conversion period
Let = total number of conversion periods
Hence the total number of annuity payments is
Coefficient of is the total amount paid during on interest
conversion period
Immediate Due
Perpetuity
4. Continuous Annuities
Varying Annuities
Arithmetic
Immediate Due
General
P, P+Q,…,
P+(n-1)Q
Increasing
P = Q = 1
Decreasing
P = n
Q = -1
Perpetuity
Geometric
a = 1
r = 1+k
k ≠ i
If k = i
a = 1
r = 1-k
k ≠ i
If k=i
Perpetuity
Continuously Varying Annuities
Consider an annuity for n interest conversion periods in which
payments are being made continuously at the rate and the interest
rate is variable with force of interest .
Under compound interest, i.e. , the above becomes
5. Rate of Return of an Investment
Rate of Return of an Investment
Yield rate, or IRR, is the interest rate at which
Hence yield rates are solutions to NPV(i)=0
Discounted Cash Flow Technique
Uniqueness of IRR
Theorem 1
Theorem 2
Let Bt be the outstanding balance at time t, i.e.
o
o
Then
o
o
Interest Reinvested at a Different Rate
Invest 1 for n periods at rate i, with interest reinvested at rate j
Invest 1 at the end of each period for n periods at rate i, with interest
reinvested at rate j
Invest 1 at the beginning of each period for n periods at rate i, with
interest reinvested at rate j
6. Dollar-Weighted Interest Rate
A = the amount in the fund at the beginning of the period, i.e. t=0
B = the amount in the fund at the end of the period, i.e. t=1
I = the amount of interest earned during the period
ct = the net amount of principal contributed at time t
C = ∑ct = total net amount of principal contributed during the period
i = the dollar-weighted rate of interest
Note: B = A+C+I
Time-Weighted Interest Rate
Does not depend on the size or timing of cash flows.
Suppose n-1 transactions are made during a year at times t1,t2,…,tn-1.
Let jk = the yield rate over the kth subinterval
Ct = the net contribution at exact time t
Bt = the value of the fund before the contribution at time t
Then
The overall yield rate i for the entire year is given by
Exact Equation Simple Interest Approximation Summation Approximation
The summation term is tedious.
Define
“Exposure associated with i"= A+∑ct(1-t) If we assume uniform cash
flow, then
7. Bonds
Notation
P = the price paid for a bond
F = the par value or face value
C = the redemption value
r = the coupon rate
Fr = the amount of a coupon payment
g = the modified coupon rate, defined by Fr/C
i = the yield rate
n = the number of coupons payment periods
K = the present value, compute at the yield rate, of the
redemption value at maturity, i.e. K=Cvn
G = the base amount of a bond, defined as G=Fr/i. Thus, G is
the amount which, if invested at the yield rate i, would produce
periodic interest payments equal to the coupons on the bond
Quoted yields associated with a bond
1) Nominal Yield
a. Ratio of annualized coupon rate to par value
2) Current Yield
a. Ratio of annualized coupon rate to original price of the
bond
3) Yield to maturity
a. Actual annualized yield rate, or IRR
Pricing Formulas
Basic Formula
o
Premium/Discount Formula
o
Base Amount Formula
o
Makeham Formula
o
Yield rate and Coupon rate of Different Frequencies
Let n be the total number of yield rate conversion periods.
Case 1: Each coupon period contains k yield rate periods
o
Case 2: Each yield period contains m coupon periods
o
Amortization of Premium or Discount
Let Bt be the book value after the tth coupon has just been paid, then
Let It denote the interest earned after the tth coupon has been made
Let Pt denote the corresponding principal adjustment portion
Date Coupon
Interest
earned
Amount for
Amortization
of Premium
Book Value
June 1, 1996
Dec 1, 1996
June 1, 1997
Approximation Methods of Bonds’ Yield Rates
Exact Approximation Bond Salesman’s Method
Where
Power series
expansion
Equivalently
8. Valuation of Bonds between Coupon Payment Dates
The purchase price for the bond is called the flat price and is
denoted by
The price for the bond is the book value, or market price, and is
denoted by
The part of the coupon the current holder would expect to
receive as interest for the period is called the accrued interest
or accrued coupon and is denoted by
From the above definitions, it is clear that
Theoretical Method
The flat price should be the book value Bt
after the preceding coupon accumulated by (1+i)k
Practical Method
Uses the linear approximation
Semi-theoretical Method
Standard method of calculation by the securities industry. The flat
price is determined as in the theoretical method, and the accrued
coupon is determined as in the practical method.
Premium or Discount between Coupon Payment Dates
Callable Bonds
The investor should assume that the issuer will redeem the bond to the
disadvantage of the investor.
If the redemption value is the same at any call date, including the
maturity date, then the following general principle will hold:
1) The call date will be at the earliest date possible if the bond
was sold at a premium, which occurs when the yield rate is
smaller than the coupon rate (issuer would like to stop repaying
the premium via the coupon payments as soon as possible)
2) The call date will be at the latest date possible if the bond was
sold at a discount, which occurs when the yield rate is larger
than the coupon rate (issuer is in no rush to pay out the
redemption value)
Serial Bonds
Serial bonds are bonds issued at the same time but with different
maturity dates.
Consider an issue of serial bonds with m different redemption dates.
By Makeham’s formula,
where
Book value
Flat price
1 2 3 4
$
9. Loan Repayment Methods
Amortization Method
Prospective Method
o The outstanding loan balance at any time is equal to the
present value at that time of the remaining payments
Retrospective Method
o The outstanding loan balance at any time is equal to the
original amount of the loan accumulated to that time
less the accumulated value at that time of all payments
previously made
Consider a loan of at interest rate i per period being repaid with
payments of 1 at the end of each period for n periods.
Period Payment
amount
Interest paid Principal
repaid
Outstanding loan
balance
… … … … …
… … … … …
Total
Sinking Fund Method
Whereas with the amortization method the payment at the end of each
period is , in the sinking fund method, the borrower both deposits
into the sinking fund and pays interest i per period to the lender.
Example
Create a sinking fund schedule for a loan of $1000 repaid over four
years with i = 8%.
If R is the sinking fund deposit, then
Period Interest
paid
Sinking
fund
deposit
Interest
earned
on
sinking
fund
Amount
in
sinking
fund
Net
amount
of loan
0 1000
1 80 221.92 0 221.92 778.08
2 80 221.92 17.75 461.59 538.41
3 80 221.92 36.93 720.44 279.56
4 80 221.92 57.64 1000 0
10. Measures of Interest Rate Sensitivity
Stock
Preferred Stock
o Provides a fixed rate of return
o Price is the present value of future dividends of a
perpetuity
o
Common Stock
o Does not earn a fixed dividend rate
o Dividend Discount Model
o Value of a share is the present value of all future
dividends
o
Short Sales
In order to find the yield rate on a short sale, we introduce the
following notation:
M = Margin deposit at t=0
S0 = Proceeds from short sale
St = Cost to repurchase stock at time t
dt = Dividend at time t
i = Periodic interest rate of margin account
j = Periodic yield rate of short sale
Inflation
Given i' = real rate, i = nominal rate, r = inflation rate,
Fischer Equation
A common approximation for the real interest rate:
Duration
Method of Equated Time (average term-to-maturity)
o where R1,R2,…,Rn are a series of payments
made at times 1,2,…,n
Macaulay Duration
o , where
o is a decreasing function of i
Volatility (modified duration)
o
o
o if P(i) is the current price of a bond, then
Convexity
o
Modified Duration and Convexity of a Portfolio
Consider a portfolio consisting of n bonds. Let bond K have a current
price , modified duration , and convexity . Then the
current value of the portfolio is
The modified duration of the portfolio is
Similarly, the convexity of the portfolio is
Thus, the modified duration and convexity of a portfolio is the
weighted average of the bonds’ modified durations and convexities
respectively, using the market values of the bonds as weights.
11. Redington Immunization
Effective for small changes in interest rate i
Consider cash inflows A1,A2,…,An and cash outflows L1,L2,…,Ln.
Then the net cash flow at time t is
Immunization conditions
We need a local minimum at i
o The present value of cash inflows (assets) should be
equal to the present value of cash outflows (liabilities)
o The modified duration of the assets is equal to the
modified duration of the liabilities
o The convexity of PV(Assets) should be greater than the
convexity of PV(Liabilities), i.e. asset growth > liability
growth
Full Immunization
Effective for all changes in interest rate i
A portfolio is fully immunized if
Full immunization conditions for a single liability cash flow
1)
2)
3)
Conditions (1) and (2) lead to the system
where δ=ln(1+i) and k=time of liability
Dedication
Also called “absolute matching”
In this approach, a company structures an asset portfolio so that the
cash inflow generated from assets will exactly match the cash outflow
from liabilities.
Interest Yield Curves
The k-year forward n years from now satisfied
where it is the t-year spot rate
12. Price at Maturity
Payoff
Profit
Option Styles
European option – Holder can exercise the option only on the
expiration date
American option – Holder can exercise the option anytime during the
life of the option
Bermuda option – Holder can exercise the option during certain pre-
specified dates before or at the expiration date
Buy Write
Call ↑ ↓
Put ↓ ↑
Floor – own + buy put
Cap – short + buy call
Covered Call – stock + write call = write put
Covered Put – short +write put = write call
Cash-and-Carry – buy asset + short forward contract
Synthetic Forward – a combination of a long call and a short put with
the same expiration date and strike price
Fo,T = no arbitrage forward price
Call(K,T) = premium of call
Put-Call Parity
Long Forward Short Forward
Long Call Short Call
Long Put Short Put
Derivative
Position
Maximum Loss Maximum Gain Position wrt
Underlying Asset
Strategy Payoff
Long
Forward
-Forward Price Unlimited Long(buy) Guaranteed price PT-K
Short
Forward
Unlimited Forward Price Short(sell) Guaranteed price K-PT
Long Call -FV(Premium) Unlimited Long(buy) Insures against high price max{0,PT-K}
Short Call Unlimited FV(Premium) Short(sell) Sells insurance against high price -max{0,PT-K}
Long Put -FV(Premium) Strike Price – FV(Premium) Short(sell) Insures against low price max{0,K-PT}
Short Put FV(Premium) – Strike Price FV(Premium) Long(buy) Sells insurance against low price -max{0,K-PT}
13. (Buy index) + (Buy put option with strike K) = (Buy call option with strike K) + (Buy zero-coupon bond with par value K)
(Short index) + (Buy call option with strike K) = (Buy put option with strike K) + (Take loan with maturity of K)
Spread Strategy
Creating a position consisting of only calls or only puts, in which some
options are purchased and some are sold
Bull Spread
o Investor speculates stock price will increase
o Bull Call
Buy call with strike price K1, sell call with strike
price K2>K1 and same expiration date
o Bull Put
Buy put with strike price K1, sell put with strike
price K2>K1 and same expiration date
o Two profits are equivalent (Buy K1 call) + (Sell K2
call) = (Buy K1 put) + (Sell K2 put)
o Profit function
Bear Spread
o Investor speculates stock price will decrease
o Exact opposite of a bull spread
o Bear Call
Sell K1 call, buy K2 call, where 0<K1<K2
o Bear Put
Sell K1 put, buy K2 put, where 1<K1<K2
Long Box Spread
Bull Call Spread Bear Put Spread
Synthetic Long Forward Buy call at K1 Sell put at K1
Synthetic Short Forward Sell call at K2 Buy put at K2
Regardless of spot price at expiration, the box spread guarantees a cash
flow of K2-K1 in the future.
Net premium of acquiring this position is PV(K2-K1)
If K1<K2, then lending money
Invest PV(K2-K1), get K2-K1
If K1>K2, then borrow money
Get PV(K1-K2), pay K1-K2
Butterfly Spread
An insured written straddle
Let K1<K2<K3
o Written straddle
Sell K2 call, sell K2 put
o Long strangle
Buy K1 call, buy K3 put
Profit
o Let F
o
Asymmetric Butterfly Spread
K2-K1
Payoff
PT
K2K1
Profit
K2-K1-FV[…
-FV[…
PT
14. Collar
Used to speculate on the decrease of the price of an asset
Buy K1-strike at-the-money put
Sell K2-strike out-of-the-money call
K2>K1
K2-K1 = collar width
Collared Stock
Collars can be used to insure assets we own
Buy index
Buy at-the-money K1 put
Buy out-of-the-money K2 call
K1<K2
Zero-cost Collar
A collar with zero cost at time 0, i.e. zero net premium
Straddle
A bet on market volatility
Buy K-strike call
Buy K-strike put
Strangle
A straddle with lower premium cost
Buy K1-strike call
Buy K2 strike put
K1<K2
Profit Function
Profit Function
Profit Function
Profit Function
15. Equity-linked CD (ELCD)
Can financially engineer an equivalent by
Buy zero-coupon bond at discount
Use the difference to pay for an at-the-money call option
Prepaid Forward Contracts on Stock
Let FP
0,T denote the prepaid forward price for an asset bought
at time 0 and delivered at time T
If no dividends, then FP
0,T = S0, otherwise arbitrage
opportunities exist
If discrete dividends, then
o
If continuous dividends, then
o Let δ=yield rate, then the
and 1 share at time 0 grows to eδT
shares at
time T
Forward Contracts
Discrete dividends
o
Continuous dividends
o
Forward premium = F0,T / S0
The annualized forward premium α satisfies
o
If no dividends, then α=r
If continuous dividends, then α=r-δ
Financial Engineering of Synthetics
(Forward) = (Stock) – (Zero-coupon bond)
o Buy e-δT
shares of stock
o Borrow S0e-δT
to pay for stock
o Payoff = PT – F0,T
(Stock) = (Forward) + (Zero-coupon bond)
o Buy forward with price F0,T = S0e(r-δ)T
o Lend S0e-δT
o Payoff = PT
(Zero-coupon bond) = (Stock) – (Forward)
o Buy e-δT
shares
o Short one forward contract with price F0,T
o Payoff = F0,T
o If the rate of return on the synthetic bond is i, then
S0e(i-δ)T
= F0,T or
Implied repo rate