Unit 3 Study Guide

Three Main Sources of Inflation

1. Increased demand for goods and services 2. Rising costs 3. Built-in Inflation linked to adaptive expectations

Present Value and Future Value

A present value of cash flows is a value that measures the worth of cash flows in terms of the dollar amount in the relative past. On the other hand, future value is a value that measures the worth of relative cash flows in terms of the dollar amount in the relative future.

Annuities

An annuity is a stream of cash flows of an equal amount paid every consecutive period. Term for patterned, recurring cash flows. Three Types of Annuities 1. Ordinary Annuities 2. Annuities Due 3. Perpetuities An ordinary annuity is a series of equal payments made at the end of consecutive periods over a fixed length of time. (An example of ordinary annuity may be taking out an auto loan. You take out a loan when you purchase a car and pay a monthly, equal payment for the term of the loan starting a month from today.) An annuity due is paid at the beginning of consecutive periods. (your rent payment—a monthly, equal payment for the term of the contract starting when you sign the contract—is an example of annuity due.) A perpetuity is a constant stream of identical cash flows that continues forever. it is an ordinary annuity that has no end.

Components of RRR

An interest rate is determined by the market's supply and demand and is thus composed of the following: 1. Opportunity cost 2. Risk 3. Inflation Businesses must also consider the effects of opportunity costs, risk, and inflation when making decisions. Publicly traded companies also consider the impact of opportunity costs, risk, and inflation when determining required rates of return. The required rate of return for these organizations is driven partly by the financing they use to do projects, namely, debt and equity. Debt and equity holders have their own required rates of return that they expect based on their opportunity costs (other returns they could earn in the market), the risk inherent in specific public companies as well as in the market, and the anticipated effects of inflation. These required returns demanded by debt and equity holders become the cost of financing (or cost of capital) for a firm.

Opportunity Cost

An opportunity cost is the loss of potential gain from other alternatives when one alternative is chosen. Opportunity costs can be easily overlooked because you cannot always see them. However, understanding the potential opportunities forgone by choosing one alternative over another allows you to make better decisions with your money. Opportunity cost is included as a part of the required rate of return because investors who put their money into an investment give up potential earning opportunities from alternative investments.

What is Inflation?

As you might have guessed from the introduction, inflation is the rise in prices over time. The official definition of inflation is the rate at which the average price level of a basket of chosen goods and services in an economy increases over a period of time. Inflation is often expressed as a percentage and indicates a decline in the purchasing power of goods and services given the same amount of money.

Compounding VS. Discounting

Compounding means finding a future value given a present value. Discounting means finding a present value given a future value. For example, if you are currently earning $50,000 a year and you receive a 3% raise each year, finding your earnings in 10 years is compounding. If you make a goal to have $10,000 in 30 years and you can earn a 5% return on an investment, finding how much you have to put aside today is discounting.

Rising costs

Costs may increase due to regulations, accidents, high demand, and any number of other factors. Many different events can cause the cost of producing goods and providing services to increase. If the costs of production increase, then suppliers must increase the prices of their goods and services to maintain the financial health of their company. These rising costs thus cause the prices of goods and services to rise as well.

Adaptive Expectations

Finally, built-in inflation is linked to adaptive expectations. When the prices of goods and services go up, employees expect and even demand higher wages to maintain their standard of living. An increase in wages therefore reflects the increased prices of goods and services.

Different Terms for Interest Rates

In finance, there are a few different names for interest rates. First, you use the names interest rate and discount rate interchangeably. You can find the future value or past value of today's dollars given the discount rate. Another name for interest rate is required rate of return, or required rate. This is the rate that the lender requires the borrower to pay. Finally, the interest rate can also be called the cost of capital. the required rate becomes the cost of borrowing to you. Since it is the cost to the borrower to raise capital or borrow capital, we call the interest rate from the borrower's perspective the cost of capital. Different Terms for Interest Rate 1. Discount Rate 2. Required Rate of Return, or Required Rate 3. Cost of Capital

Inflation

Inflation is the rate at which the average price level of goods and services in an economy increases over a period of time. Inflation causes the value or purchasing power of a dollar to decrease. When prices of goods and services rise, a single unit of currency (for example, a dollar) loses value as it buys fewer goods and services than it did before the change in prices occurred. This loss of purchasing power impacts the general cost of living if wages do not increase at the same rate as the prices do. Because of inflation, receiving $1,000 today is not equivalent to receiving $1,000 a year from today. If the inflation rate is 2%, you would need to receive $1,020 in a year from today to have the same purchasing power as you would if you received $1,000 today. Inflation therefore must be included in the required rate as well.

Decomposing Interest Rate

Interest rates include three components: opportunity cost, risk, and inflation. The interest rate, or required rate of return, is determined by Rate=Risk-Free Rate+Risk Premium where risk-free rate is an indicator of inflation and opportunity cost and describes the rate of return on an investment with no risk, and risk premium is the compensation for the amount of risk taken on by investors. This implies that the higher risk you take, the higher return you require. Likewise, higher inflation and higher opportunity cost both require a higher return.

Annuity Due

Now that you are familiar with ordinary annuities, learn how to find the future value and present value of an annuity due. Until now, you have set type equal to 0 in the Excel examples. The 0 signals to both the FV and PV functions that you are working with an ordinary annuity paid at the end of the period ("end"). For an annuity due, you will switch type from 0 to 1, which signals that the annuity is paid at the beginning of each period, starting today ("begin").

Calculating Real Rate

Real Rate = Nominal Rate - Inflation

Increased demand for goods and services

Resources, goods, and services are scarce, meaning that the supply is not sufficient to meet the demand. Therefore, the demand for goods and services pushes prices up to the level where the supply and demand are in balance.

Risk

Risk is the possibility that the realized or actual return will differ from the expected return. By receiving $1,000 today, you ensure its receipt. If you must wait six months before receiving $1,000, there is a risk that you will not receive the money. Getting your money now removes the risk of not getting it in the future.

Calculating Interest Formulas

Simple Interest Formula Annual Interest=Principal×Interest Rate - Total interest amount using simple interest for t years Total Interest=Annual Interest×t Compounding Interest Total Interest=Principal×(1+Interest Rate)Number of Periods−Principal

Ordinary Annuity

So far, you have learned how to find a present value or a future value of a single sum of cash. However, there are different types of cash flows. One of the most common types of cash flows is an annuity. Annuity = Cash Flow Annuities are particularly common in lending relationships such as car loans, mortgages, and bonds, as well as financial contracts such as insurance contracts and rental agreements. All of these arrangements are based upon equally spaced (e.g., monthly or yearly) payments of the same dollar amount.

Technology and Inflation

Technological developments are one factor that can actually decrease the effects of inflation. Technological advancements can bring down the price of goods, elevate productivity, and substitute labor with automation, which may subdue inflation. While many innovations have helped to drive down the prices of cars over the last 100 years, the inclusion of new and more expensive technology, the increase in the cost of raw materials and other resources, and many other factors have influenced the overall rise in the price of a new car. The adaptive expectations of employees themselves to continue to make more money each year have also contributed to inflation. As overall inflation has occurred and is anticipated in the market, employees have expected higher wages as well to be able to afford the goods and services they want and need.

Time Value of Money

The discussion of the time value of money (TVM) often starts by posing a question like this: Would you rather receive $1,000 today or $1,000 in 10 years from today? Inflation causes money available today to be worth more than the same amount of money in the future. Most long-term projects or investments have cash flows that occur at various points in time. Given that the passage of time impacts the value of cash flows, the value of a project depends on how we assess these differences in cash flow timing. The time value of money is a relatively simple concept. Essentially, you bring together three variables: 1. The amount of cash flows 2. The timing of cash flows 3. The rate at which the value of cash flows changes due to the passage of time However, while simple in concept, the impact of TVM is sometimes referred to as the "language of finance." Time Value of Money Functions 1. Present Value 2. Future Value 3. Compounding 4. Discounting

Business Decisions and Time Value of Money

The financial manager of the firm has the important task of making investment decisions and financing decisions. Through combined analysis of both of these aspects, the financial manager determines whether a project is worth undertaking or not. For investment decisions, the financial manager analyzes cash flows: how much revenue the project would bring and how much cost would be incurred. When making a financing decision to raise capital, the financial manager must think about the incentives needed to compensate investors for the risk they are taking on. These incentives constitute the cost of capital (also called the interest rate or the discount rate), which was briefly discussed in the previous module.

Single Sum

The first type of cash flow calculation we are going to learn is a single sum. A single sum simply means that you are looking at only one cash flow, either today or in a future period. You will first explain how to calculate the value of a cash flow in the future (the future value) and then show how to calculate the value today (the present value).

Interest Rate

The interest rate is the percentage of the principal that a lender charges a borrower for the use of assets. Interest is often paid in cash, but it can also be paid in vehicles, buildings, or consumer goods. It is generally expressed on an annual basis, known as the annual percentage rate (APR). Interest is like a lease or rental charge to a borrower for the use of an asset. Interest rates apply not only to auto loans but also to most other borrowing and lending transactions.

Nomial Rate Vs. Real Rate

The interest rate most often used in our daily lives is the nominal rate. The nominal rate is the rate at which invested money grows for a certain period of time. The nominal rate includes inflation, so it does not measure the actual purchasing power you will earn in the future. Using the nominal rate results in the amount of money you will have in the future, but not how much you will be able to buy with it. Thereal rateis the same as the growth rate in purchasing power, even though the formula seems different. This is called theFisher Effect, an economic theory created by the economist Irving Fisher. The real rate is

Required Rate of Return

The required rate of return is the rate of return or compensation that an investor or a lender will accept for investments such as stocks, bonds, or loans. - The word compensation is used because this is the rate that investors or lenders will be compensated for a given level of risk associated with investments or loans. - The required rate of return is also known as the hurdle rate in the context of corporate finance. - When a financial manager decides whether to invest in a certain project or not, the project return needs to meet the minimum rate of return or else the firm must "hurdle" the rate in order to accept the project. Different Names for Rate of Return 1. Compensation 2. Hurdle Rate

Types of Interest

There are two types of interest: simple interest and compound interest. Calculating simple interest is an easy method of determining the interest charges on a principal. The other type of interest is compounding interest, which is more common. The concept of compounding interest can be described as interest on interest. Two Types of Interest 1. Simple Interest 2. Compound Interest

Non-Annual Annuity

While you have learned about finding a present value or a future value of an annual annuity, an annuity can be spread out in different intervals: semi-annually, quarterly, monthly, and so forth. What do you do when the annuity is not annual? What you need to do is change all the frequency-sensitive variables to the same frequency as the annuity frequency. For example, if an annuity is paid monthly, then you will divide the interest rate by 12 and multiply the number of years by 12.