115.114 Finance Fundamentals. Chpt4&6 Cheat Sheet

A Business › Accounting cheat sheet in English by MJ McGiver

Glossary of theories and concepts.

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Chpt4. TVM-Single Payments

Time Value of money	Individuals prefer to receive a dollar today to receiving that same dollar promised in a year's time.

Interest	The cost of funds to a borrower or part of the return for a lender or investor
Mortgage	recover money by selling property
Term Loan	bank loan with maturity^{due date}

4.1 Simple Interest & Future Value

Future Value	amount received later; cash value of investment at future date: `FV=P(1+rn)`
Simple Interest	Interest calculated on the original amount: `I=(P)(r)(n)`
Money Markets	short-term debt markets: companies can borrow/ invest in the short-term.
Formula	`FV = P(1 + rn)`

4.2 Simple Interest & Present Value

Present Value	amount today: needed cash today, to yield a particular value at future.
Discounts	to find the present value of future amount: inverse for compounding interest.
Formula	`PV = FV/(1+rn)`

Working out/ Calculating how much the money we expect to receive in the future is worth today.

4.3 Compound Interest & FV

Compounded Interest	Interest is stacking: It is then added to the principal
Compounding	Process of finding future amounts where interest is paid on interest already earned.
Opportunity Cost	best market yield achieve through alternative course of action: Market Yield is often benchmarked for opportunity costs
Formula	`FV = PV(1+r)ⁿ`

Working out/ calculating future value through interest for each period (plus any interest), then added to the principal.

4.4 PV of a single payment

Discounting	The process of finding current amounts by the process of present value.
Formula	`PV = FV / (1+r)ⁿ`
Formula2	`PV = FV x (1+r)^-n`

4.5 Compounding frequency

Coupon	Interest paid, based on a percentage of a bond's face value.
Zero- coupon Bond	single-payment: no interest payment during its lifetime since interest is included with the repayment of principal at maturity.
Maturity	Deadline:The date when security will be payed.
Formula	`FV = PV x (1 + r/m)^{m x n}`
Formula2	`PV = FV / (1 + r/m)^{m x n}`

When compounding period per year is increased by semi-annually, quarterly, monthly or daily.

PV formula can be used to calculate the current value of a zero-coupon bond.

4.6 Continuous compounding/ discounting

Formula	`FV = PV (PV x e^{r x n})`
or	`FV = PVe^rn`

When compounding frequency is increased to a very large number of (infinity).

Where e is constant, e = 2.718

4.7 Nominal & Effective Interest Rates

Nominal Rate	contractual rate, ignores compounding. includes inflation: quoted rate
Effective Rate	actual rate, accounts compounding. includes adjustments: adjustments to nominal rate for the frequency of compounding.
Annual Percentage Rate (APR)	contractual rate, ignores compounding. when short-term rates are annualized
Rate of Return	rate of profit/ loss from investment
Formula	`r_e = (1 + r/m)^m - 1`

4.8 Unknown Interest Rate

Formula

r = (FV/PV)^1/n - 1

FV and PV is given, but find interest rate.

Chpt. 6 Risk and Return

Risk-free assets

assets that do not have risk: e.g. Treasury Bills and Government Bonds.

6.1 Two components of a return.

Nominal Interest Rates	Borrower's POV: costs they incur in order to use the funds of investors.
Nominal Returns	Investors (Lender)'s POV: Compensates the investor for deferring consumption.
These terms are made up of two components,
Real Interest Rate	Rate with no inflation or uncertainty
Inflation	Increase level of prices from supply and demand.

The real interest rate

The interest rate adjusted for inflation, showing the true cost of borrowing or the real yield of an investment.

Real Interest Rate = Nominal IR + Expected Inflation

Expected Inflation

Inflation may be due to government policies, oil price rises, world events, etc.

Investors require compensation for expected future inflation over the period of the loan or investment, and that historical rates of inflation are irrelevant.

Consumer Price Index (CPI) measures changes in the general level of prices each quarter.

6.2 Nominal Interest Rate

Fisher Equation by Irving Fisher
Formula: Nominal Interest Rate	`NiR = [(1 + Real interest rate) x (1 + % Expected inflation)] - 1`
Formula: Real interest rate	`RiR = (1 + NiR / 1 + % Expected Inflation) - 1`
Risk Premium	Additional return investors require for investing in risky assets

6.3 Shaped of Yield Curves

Yield Curves	Depicted in graphical form which presents the relationship between time to maturity and percentage yield, know as Term structure of interest rates.
Normal yield curve	upward-sloping curve: short-term yields are low, will rise with longer maturities.
Inverse yield curve	downward-sloping: short-term yields are high, yields on long-term maturities fall over time.
Flat yield curve	straight line: little change in interest rates across time periods.
Humped yield curve	Short-term securities are higher, longer-term bonds are lower.

6.4 Risky Assets

Risk	The possibility of loss: the uncertainty of receiving the expected returns because a borrower may not be able to repay the principal on fixed-interest securities when required.
Formula: Nominal Return	Nominal Return = Risk-free return + Risk Premium
5 Risk components
Business Risk	Fluctuations in cash inflows, notably sales.
Financial Risk	Amount of debt used to fund a firm's operations: high debt levels may threaten the firm's ability to pay dividends.
Liquidity Risk	The risk an investor holding equity in a company may be unable to sell them to another investor: chances of selling investments without losing a lot of money.
Exchange rate risk	The chances of losing money from changes in offshore currencies relative to the local currency: Adverse movements in exchange rates can erode the level of return the investor expects to receive.
Country Risk	Uncertainty of return from investments in another country: level of risk differs from country to country.

The greater the risk, the higher the premium to compensate.

6.5 Measuring historical risk and return

Ex Ante	before the event
Ex Post	after the event
Holding Period	the length of time an investment is owned
Holding Period Yield (HPY)	investment's percentage return over the period it was owned.

6.6 Standard deviation as a measure of risk

Variance	measures how far each return is from the mean (average) of all returns.
Standard Deviation	measures the variability of a set of values

6.7 Standard deviation as a measure of risk

Variance	measures how far each return is from the mean (average) of all returns.

Standard Deviation	measures the variability of a set of values

6.8 Risk averse investors' investment rules

Investment rule 1: If two investment choices have the same expected returns, select the one with the lower expected risk.
Investment rule 2: If two investment choices have similar risk profiles, select the one with the higher expected return.

An investor's tolerance for and attitude towards risk matters.

In a world fraught with uncertainty and risk, diversification is the key.

6.9 The benefit of diversification

Diversification	The practice of spreading wealth over a variety of different assets.
	Diversification works to reduce risk (variability), because it is unlikely that all investment assets will perform in exactly the same way.
Diversify	Place funds in a range of assets in order to spread risk: objective of investments.
Unsystematic Risk	Risk that can be minimized by diversification
Systematic Risk	Non-diversifiable risk: pertaining to uncertainty surrounding future economic conditions that affects all companies. e.g. war, international incidents, and inflation.
	The higher the systematic risk, the higher the return investors will be compensated.

Some investments will perform well when others are performing poorly, so that the returns on assets will not move in the same direction at the same time.

6.10 CAPM

Capital Asset Pricing Model (CAPM)	calculates the required rate of return of risk assets.
Market Risk Premium (MRP)	extra return investors require to compensate them for investing in the market portfolio.

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