Finance Chapter on Annuities and Investment Returns

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the rate of return you could earn on an alternative investment of similar risk called?

Opportunity Cost

Finding Present Value is called what, the reverse of compounding?

Discounting

If payments are equal and are made at fixed intervals, then the series is an what?

Annuity

If payments occur at the end of each period, then what is it called?

Ordinary Annuity Signup and view all the answers

Mortgages, car loans, and student loans are what type of annuities?

Ordinary Annuity Signup and view all the answers

If payments are made at the beginning of each period, then what is it called?

Annuity Due Signup and view all the answers

Rental payments and life insurance are what type of annuities?

Annuity Due Signup and view all the answers

How do you find the Future Value of an Ordinary Annuity?

FV = PMT[((1+r)^n - 1)/r] Signup and view all the answers

How do you find the Future Value of an Annuity Due?

P = (PMT [((1 + r)n - 1) / r])(1 + r) Signup and view all the answers

The FV of an annuity due will be greater than that of a similar ordinary annuity.

True Signup and view all the answers

How do you find the Present Value of an Ordinary Annuity?

P = PMT [(1 - (1 / (1 + r)n)) / r] Signup and view all the answers

How do you find the Present Value of an Annuity Due?

P = (PMT [(1 - (1 / (1 + r)n)) / r]) x (1+r) Signup and view all the answers

The PV of an annuity due will be less than that of a similar ordinary annuity.

False Signup and view all the answers

In 1749 the British government issued some bonds whose proceeds were used to pay off other British bonds and since this action consolidated the government's debt, what were the new bonds called?

Consols Signup and view all the answers

What is a promise to pay interest perpetually called?

Perpetuity Signup and view all the answers

What is the interest rate that is actually earned or paid on an investment, loan, or other financial product due to the result of compounding over a given time period called?

Effective Annual Rate (EAR) Signup and view all the answers

What is another name for Effective Annual Rate (EAR)?

EFF% Signup and view all the answers

What is the calculation for Effective Annual Rate (EAR)?

(1 + Inom/M)^M - 1.0 Signup and view all the answers

Study Notes

Rate of Return and Opportunity Cost

Opportunity cost is the rate of return that could be earned on an alternative investment with similar risk.

Discounting and Present Value

Finding present value is called discounting, the opposite of compounding.

Annuities

An annuity is a series of equal payments made at fixed intervals.
An ordinary annuity has payments at the end of each period.
Examples of ordinary annuities include mortgages, car loans, and student loans.
An annuity due has payments at the beginning of each period.
Examples of annuity due include rental payments and life insurance premiums.

Future Value of Annuities

Ordinary Annuity (END): FV = PMT[((1+r)^n - 1)/r] (PV=0 for calculator)
Annuity Due (BEGIN): P = (PMT [((1 + r)n - 1) / r])(1 + r)

Present Value of Annuities

Ordinary Annuity: P = PMT [(1 - (1 / (1 + r)n)) / r]
Annuity Due: P = (PMT [(1 - (1 / (1 + r)n)) / r]) x (1+r)

Consols and Perpetuities

Consols are perpetual government bonds.
A perpetuity is a promise to pay interest perpetually.

Effective Annual Rate (EAR)

EAR (or EFF%) is the actual interest rate earned or paid on an investment, considering compounding.
Calculation: (1 + Inom/M)^M - 1.0 (Inom/M = Periodic rate, M = number of periods)

Amortized Loans and Schedules

Amortized loans have equal payments, consisting of interest and principal repayment.
An amortization schedule details the breakdown of each payment.

Time Value of Money and Interest Rates

The later the payment, the lower its present value.
Higher interest rates increase future cash flow value.

Bonds

Bonds are long-term contracts where borrowers make interest and principal payments to bondholders.
Treasury bonds are issued by the US government, with no default risk.
Corporate bonds are issued by corporations, with default (credit) risk.
Municipal bonds are issued by state and local governments, carrying lower interest rates than comparable corporate bonds.
Foreign bonds are issued by foreign entities, with default and currency risk.

Yield to Maturity (YTM)

YTM (or Market Rate of Interest) is the total return anticipated on a bond if held until maturity.

Time to Maturity and Bond Prices

Longer maturities mean larger price changes for a given yield change.

Preferred Stock

Preferred stock is a hybrid, similar to bonds and common stock. Preferred dividends must be paid before common dividends.

Preferred Stock Valuation

Value of Preferred Stock (Vps) = Dps / rps (Dps = preferred dividend, rps = required rate of return)

Dividend Discount Model (DDM)

The DDM values stock based on the present value of future dividends.
Applies to dividend-paying stocks.
Helps determine future dividend growth's worth.

Constant Growth DDM

Assumes constant dividend growth: P0 = D1 / (rs - g).

Earnings and Free Cash Flow Models

Earnings per share (EPS): NI - Div. on Pref. Stock/ Stock Outstanding
Value of a firm equals its future expected free cash flows, discounted at the weighted average cost of capital.
Free Cash Flow is the cash flow available to all investors.
Free Cash Flow Model: V = FCF (1 + G) / WACC - g

Expected Return of Common Stock

Expected return of stock = (Return x Percentage of possibility)

Current Yield of Stock

Current Yield = Annual Interest Payments / Bond's Current Price

Risk Relative in Claims

Bonds carry the least risk; they have priority claims on assets and income.
Preferred stock carries more risk.
Common stock holds the most risk and claims on income/assets.

Discount Rates and Asset Prices

Higher discount rates lead to lower asset prices.

Merger Financing

Temporarily high debt financing is used for mergers expected to gain value over time.

Government Taxes and Levered Firms

Government taxes are lower from levered firms.

Adjusted Present Value (APV)

APV calculates merger value: Vops = Vunlevered + Vtaxshield.

Forward and Futures Contracts

Forward contracts are agreements to buy/sell a commodity at a specific price on a future date.
Futures contracts are similar but marked-to-market daily on exchanges.

Swaps

Swaps are agreements exchanging specified payment streams.

Efficient Market Hypothesis (EMH)

EMH suggests that stock prices reflect all available information.
Types of market efficiency: weak-form (past prices), semi-strong-form (all public), and strong-form (all information).

Beta

Beta measures a security's volatility relative to the market.
Beta = Covariance (stock vs. market returns) / Variance (market returns).
Beta of 1: security moves with the market.
Beta < 1: security is less volatile than the market.
Beta > 1: security is more volatile than the market.

Alpha

Alpha measures a portfolio's abnormal return, exceeding what an equilibrium model (like CAPM) predicts.
Alpha = Return on portfolio - (risk-free rate +beta * (Market return - risk free))

Diversification

Diversification reduces risk by spreading investment across different assets.
Diversification can help take advantage of profits, although it may reduce potential returns as well.

Systematic and Unsystematic Risk

Systematic risk (market risk) is inherent in the market.
Unsystematic risk (specific risk) is company-specific and can be reduced through diversification.

Sharpe Ratio

Sharpe ratio measures risk-adjusted return.
Sharpe Ratio = (Asset Return - Risk-free rate) / Standard Deviation of asset return.

Capital Budgeting

Capital budgeting involves long-term, large-expenditure projects.

Independent and Mutually Exclusive Projects

Independent projects have no impact on each other's cash flows.
Mutually exclusive projects affect each other's cash flows.

Cost of Capital with Flotation Costs

Adjust models for flotation costs: rps = Dps/[Pps(1-F)]; r(e )=D1/(P0 (1-F) )+ g (F = flotation cost)

Weighted Average Cost of Capital (WACC)

WACC is the average rate of return required by all investors.
Factors affecting WACC include firm capital structure, interest rates, risk, and investor attitude.

Marginal Cost of Capital

Marginal cost of capital is the rate to raise the next dollar of capital. NPV calculations using this should be considered.

Payback Period and Discounted Payback Period

Payback period is the time to recover a project cost. It's simple but ignores TVM.
Discounted payback period accounts for time value of money.

Internal Rate of Return (IRR)

IRR is the discount rate that makes the present value of inflows equal to cost.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

This quiz covers key concepts related to annuities, rate of return, discounting, and present value. Explore the differences between ordinary annuities and annuity due, as well as the implications of opportunity cost in financial decisions. Test your understanding of how future and present values are calculated for various financial products.