Tag Archives | rate of return

Capital Asset Pricing Model (CAPM)

See Also:
Cost of Capital
Cost of Capital Funding
Arbitrage Pricing Theory
APV Valuation
Capital Budgeting Methods
Discount Rates NPV
Required Rate of Return

Capital Asset Pricing Model (CAPM)

The most popular method to calculate cost of equity is Capital Asset Pricing Model (CAPM). Why? Because it displays the relationship between risk and expected return for a company’s assets. This model is used throughout financing for calculating expected returns for assets while including risk and cost of capital.

Cost of Equity

Also known as the required rate of return on common stock, define the cost of equity as the cost of raising funds from equity investors. It is by far the most challenging element in discount rate determination.


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Calculating Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) states that the expected return on an asset is related to its risk as measured by beta:

E(Ri) = Rf + ßi * (E(Rm) – Rf)

Or = Rf + ßi * (risk premium)

Where

E(Ri) = the expected return on asset given its beta

Rf = the risk-free rate of return

E(Rm) = the expected return on the market portfolio

ßi = the asset’s sensitivity to returns on the market portfolio

E(Rm) – Rf = market risk premium, the expected return on the market minus the risk free rate.

Expected Return of an Asset

Therefore, the expected return on an asset given its beta is the risk-free rate plus a risk premium equal to beta times the market risk premium. Beta is always estimated based on an equity market index. Additionally, determine the beta of a company by the three following variables:

  1. The type business the company is in
  2. The degree of operating leverage of the company
  3. The company’s financial leverage

Risk-Free Rate of Return

Short-term government debt rate (such as a 30-day T-bill rate, or a long-term government bond yield to maturity) determines the risk-free rate of return. When cash flows come due, it is also determined. Define risk-free rate as the expected returns with certainty.

Risk Premium

Additionally, risk premium indicates the “extra return” demanded by investors for shifting their money from riskless investment to an average risk investment. It is also a function of how risk-averse investors are and how risky they perceive investment opportunities compared with a riskless investment.

Cost of Equity Calculation

For example, a company has a beta of 0.5, a historical risk premium of 6%, and a risk-free rate of 5.25%. Therefore, the required rate of return of this company according to the CAPM is: 5.25% + (0.5 * 6%) = 8.25%

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capital asset pricing model

Originally published by Jim Wilkinson on July 23, 2013. 

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Yield to Maturity of a Bond

See Also:
What is a Bond
Non-Investment Grade Bonds
Covenant Definition of a Bond Contract
Zero Coupon Bonds
Financial Instruments

Yield to Maturity Concept

The yield to maturity (YTM) of a bond represents the annual rate of return for the full life of the bond. The YTM assumes the investor will hold the bond to maturity, and that all interest payments will (hypothetically) be reinvested at the YTM rate.

For example, a bond with a maturity of 10 years and a YTM of 5% implies that buying this bond and holding it for the full ten years would give the investor an annual return of 5% on the invested capital.

Given the bond’s price, par value, maturity date, coupon rate and coupon payment schedule, the YTM represents the time value of money – incorporating the aforementioned variables – that sets the bond price equal to the present value of the future payments of the bond, including coupon payments and principal redemption. The YTM is equal to the bond’s discount rate and internal rate of return.

Define Yield to Maturity

Yield to maturity is the implied annual rate of return on a long-term interest-bearing investment, such as a bond, if the investment is held to maturity and all interest payments are reinvested at the YTM rate.

Current Yield Calculation

The current yield of a bond differs from the yield to maturity. The current yield of a bond represents the implied return on the bond for one year, given the coupon payments and the current market price. For example, if an investor buys a bond for $95 with an annual coupon payment of $5, the current yield for that bond would be 5.26% (.0526 = 5/95). The current yield formula is:

Current Yield = Annual Payment/Current Market Price

Yield to Maturity – Bond Price

If a bond’s yield to maturity is greater than its current yield, the bond is selling at a discount, or a price less than par value. If YTM is less than current yield, the bond is selling at a premium, or a price above the par value. If YTM equals current yield, the bond is selling at par value.

Discount Price – Yield to Maturity > Current Yield

Premium Price – Yield to Maturity < Current Yield

Par Value Price – Yield to Maturity = Current Yield

Bond Yield To Maturity Formula

The formula for a bond’s yield to maturity is complicated and solving it mathematically often requires a process of trial and error. It is possible to get an approximate YTM for a bond using a bond yield table. The best way to compute the YTM for a bond is to use a financial calculator. Using a financial calculator, punching in four out of five of the relevant variables (price, par value, maturity, coupon payment, YTM) will give you the fifth variable.

To calculate the bond’s YTM, solve this formula for YTM:

Price = Coupon Payment x 1/YTM (1 – (1/((1+YTM)^Time Periods)) + Future Value/((1 + YTM)^Time Periods)

 

yield to maturity

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Treasury Inflation Protected Securities

Treasury Inflation Protected Securities

Treasury Inflation Protected Securities or TIPS for short are debt instruments that are issued by the U.S. government. TIPS are indexed with the Consumer Price Index (CPI), and adjust accordingly to the inflation rate presented in the CPI.

Treasury Inflation-Protected Securities (TIPS) Explained

Treasury TIPS means that the security will adjust for inflation or deflation on whether the CPI increases or decreases. Because of this extra protection from inflation rates, TIPS owners are forced to pay more in taxes, a major disadvantage, when the security matures or it is sold. Treasury tips are normally sold with 5, 10, or 30 year maturities in denominations of $1,000 or more.

Treasury Inflation Protected Securities (TIPS) Example

Timmy has just invested in a TIPS note which has a 4% rate of return and a 10 year maturity. The following results are how an inflation protected security react to inflation and the market.

If interest rates rise by 1% in the first year then the principal would change to $1,010 (1,000 * 1.01). Thus the coupon rate would be calculated by taking 4% * $1,010 which equals a coupon payment of $40.40.

If the interest rates were to rise again by 2% then the new principal would change to $1,020 ($1,000 * 1.02), and the coupon payment would be 4% * $1,020 which equals $40.8.

Note: The new coupon payment and interest will change in the same manner no matter if deflation or inflation occurs.

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treasury inflation protected securities
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treasury inflation protected securities

See Also:
Treasury Securities
Treasury Notes (t notes)

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Risk Premium

See Also:
Finance Beta Definition
Hedging Risk
Common Stock
Preferred Stock
Stock Options

Risk Premium Definition

Risk premium is any return above the risk-free rate. The risk-free rate refers to the rate of return on a theoretically riskless asset or investment, such as a government bond. All other financial investments entail some degree of risk, and the return on the investment above the risk-free rate is called the risk premium.

When an investor purchases a financial instrument, such as stock or bonds, that investor is putting his capital at risk. The company that issued the stock could perform poorly and its stock could plummet in value; or the company issuing the bonds could default and its bonds could become worthless. Both of these potential scenarios represent risk for the investor or speculator. The return on an investment, which corresponds to the riskiness of the investment, is supposed to compensate the investor for that risk.

Different financial instruments have different degrees of riskiness and the returns on these instruments typically correspond with the level of risk. More risky assets have higher returns; less risky assets have lower returns. An asset with no risk, such as a U.S. government bond, has a comparatively low rate of return because there is little or no risk of the U.S. government defaulting. Therefore, the rate of return on that type of riskless asset is referred to as the risk-free rate. Any return above that rate is a risk premium which compensates the investor for the riskiness of the asset.

Risk Premium Example

Assume the risk-free rate is 5%. This means a riskless U.S. government treasury bond offers an annual return of 5%. Let’s say an investor invests in the stock of a company and that stock has an annual return of 7%. The risk premium for that company’s stock is the difference between the risk-free rate of 5% and the expected return of the stock of 7%. So the risk premium is 2%.

Risk Premium = Asset Return – Risk-Free Rate

2% = 7% – 5%

Risk Premium and the CAPM

The risk premium is also used in calculating the expected return on asset when using the capital asset pricing model (CAPM). In that case, the risk premium combines the market risk premium, or the overall stock market’s return above the risk-free rate, with the beta of the individual stock. This gives the risk premium for the particular stock over the risk-free rate.

risk premium

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Required Rate of Return

See Also:
Valuation Methods
Arbitrage Pricing Theory
Capital Budgeting Methods
Discount Rates NPV
Internal Rate of Return Method

Required Rate of Return

The required rate of return, defined as the minimum return the investor will accept for a particular investment, is a pivotal concept to evaluating any investment. It is supposed to compensate the investor for the riskiness of the investment. If the expected return of an investment does not meet or exceed the required rate of return, the investor will not invest. The required rate of return is also called the hurdle rate of return.

Required Rate of Return Explanation

Required rate of return, explained simply, is the key to understanding any investment. This essentially requires determining the investor’s cost of capital. The investment will be attractive as long as the expected returns on the project or investment exceed the cost of capital. The cost of capital can be the cost of debt, the cost of equity, or a combination of both.

If the investor is a company considering the required rate of return on a corporate project, then calculating the cost of debt is simple. It is the interest rates on the company’s debt obligations. If the company has numerous differing debt obligations, then use the weighted average of those interest rates to find the cost of debt.

Calculating the cost of equity can be done using the capital asset pricing model (CAPM). Estimate this by finding the cost of equity of projects or investments with similar risk. Like with the cost of debt, if the company has more than one source of equity – such as common stock and preferred stock – then the cost of equity will be a weighted average of the different return rates.

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Required Rate of Return Formula

The core required rate of return formula is:

Required rate of return = Risk-Free rate + Risk Coefficient(Expected Return – Risk-Free rate)

Required Rate of Return Calculation

The calculations appear more complicated than they actually are. Using the formula above. See how we calculated it below:

Required rate of Return = .07 + 1.2($100,000 – .07) = $119,999.99

If:

Risk-Free rate = 7%
Risk Coefficient = 1.2
Expected Return = $100,000

Weighted Average Cost of Capital (WACC)

Combining the cost of equity and the cost of debt in a weighted average will give you the company’s weighted average cost of capital, or WACC. Consider this rate to be the required rate of return, or the hurdle rate of return, that the proposed project’s return must exceed in order for the company to consider it a viable investment.

Required Rate of Return for Investments

In terms of investments, like stocks, bonds, and other financial instruments, the required rate of return refers to the necessary expected return on the investment needed by the investor in order for him to consider investing. This rate can be based on investments with similar risk, or it can be the rate of the investor’s next best alternative investment opportunity.

For example, if an investor has his money in a savings account earning 5% annual interest, and he is considering investing in a risk-free treasury bond, then he might say the return on assets for such an investment is 5%. The treasury bond must yield more than 5% per year for the investor to consider taking his money out of the savings account and investing it in the bond. In this case, the investor’s required rate of return would be 5%.

Required Rate of Return Example

For example, Joey works for himself as a professional stock investor. Because he is highly analytical, this work perfectly fits him. Joey prides himself on his ability to evaluate where the market is and where it will be.

Joey knows his next investment option is high-stakes and risky. He wants to know his required rate of return on equity for a stock he is thinking about investing in. Joey performs the calculation below to find his answer:

Required Rate of Return = .07 + 1.2($100,000 – .07) = $119,999.99

If:
Risk-Free rate = 7%
Risk Coefficient = 1.2
Expected Return = $100,000

Joey decides that his investment is not a good decision because his required rate of return is quite high. He resolves to find less risky decisions in order to protect the success he has already created. Without calculating his required rate of return on stock Joey could have ruined everything that he has created so far. Joey uses this experience to humble himself as he moves forward.

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Market Rate

Market Rate Definition

The market rate, defined as the rate of interest, on a loan or investment, which is commonly available on the market for that product, defined the cost of benefit of the tool. For a loan, the market rate is the average rate of interest that will be charged to the receiver from a variety of providers. To the investor, the market rate is the average rate of interest gained from all or a certain set of investment vehicles which are available on the open market. These create the market rate of interest definition as a whole.

Market Rate Explanation

Market rate, explained as the rate to expect when seeking out an interest bearing tool, is the estimated average of all of the vehicles available. This, as listed above, can be applied to both loan and investment instruments. The market rate of return definition should be understood before the search begins.

Better than or worse than market rates are available. These, however, are the statistical anomaly. Market rate is what should be expected. When a party finds a more favorable rate it should first check other factors. If these do not decrease the benefit of use, the tool with the more favorable rate should be used. This requires market rate analysis to check the validity of each deal.

Market Rate Example

For example, Dwight will soon be receiving 2 market rates: the market rate on a loan for his business and the market rate for his investments. Dwight pays close attention to the market rate of return because he can create an expectation of both cost and benefit from it. He thinks his actions through.

First, Dwight looks for the market rate of loans. Soon after this research, Dwight finds a lender who is asking for less than the market rate. His research has paid off and he takes the loan.

Next, Dwight looks at the market rate vs coupon rate for a bond he may purchase. In this comparison, he evaluates the market rate of return on stock he may purchase. Deciding that more stock is too risky, Dwight relies on his research and opts to buy the bond. He appreciates diversification over the highest interest rate.

Dwight also looks at the market rate of return cash balance he has gained from employee benefits he used to receive. He is happy to receive that he is running average. This tool will be useful for his retirement planning.

Dwight relies on his research. Rather than assuming, he lets the market and his sense of judgement decide for him. Dwight has been a success so far and it seems he will continue to be one.

Market Rate definition

See Also:
Delivery Order
Financing Lease
Lower of Cost or Market (LCM)
Excess Insurance Wiki

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Internal Rate of Return Method

See also:
Internal Rate Of Return Example
NPV versus IRR
Owner’s Equity
Net Present Value (NPV) vs Payback Method
Cost of Capital
Valuation Methods

Internal Rate of Return Method Definition

The Internal Rate of Return method is the process of applying a discount rate that results in the present value of future net cash flows equal to zero. This is the base internal rate of return calculation formula and will be described later in this wiki. Internal rate of return assumes that cash inflows are reinvested at the internal rate. Investment projects with a return greater than the cost of capital or hurdle rate should be accepted. The greater the internal rate of return the more attractive the investment. Below is the IRR hurdle rate comparison.

IRR > hurdle rate, accept the investment
IRR < hurdle rate, reject the investment
IRR = hurdle rate, the investment is marginal

The internal rate of return meaning is described in more detail below.

Internal Rate of Return Method Explanation

Internal Rate of Return is a method to compare and evaluate different investments based on their cash flows. A proper internal rate of return calculation provides an interest rate equal to the total gains expected from a given investment. After discovering the internal rate of return for one project other IRRs can be compared in order to find the most valuable investment choice. Additionally, one compares an internal rate of return to the weighted average cost of capital of a project to decide whether the investment will create profit. IRR also accounts for the time value of monetary gains. It is generally used to evaluate a series of cash flows but can also be applied for other needs. Many equity investors, including angels and venture capitalists, have a required rate of return which must be met or exceeded by the IRR of a company seeking investment. This ensures the investment warrants the associated risk and will provide the cash flows necessary for profit.

Internal Rate of Return Formula

The internal rate of return formula can be found algebraically by using the Net Present Value formula below. In this:

NPV = (CF 1 / (1 + r) ^1) + (CF 2 / (1 + r)^2) + (CF 3 / (1 + r) ^ 3) + …

Where:
NPV = Net Present Value
CF 1, 2, or 3 = Cash flow in period 1, Cash flow in period 2, Cash flow in period 3, etc.
r = The Rate of Return

The rate of return (r) for which NPV = 0 is the internal rate of return calculator. So, if:

0 = (Cash flow in period 1 / (1 + IRR) ^1) + (Cash flow in period 2 / (1 + IRR)^2) + (Cash flow in period 3 / (1 + IRR) ^ 3) + …

Where:
NPV = Net Present Value
CF 1, 2, or 3 = Cash flow in period 1, Cash flow in period 2, Cash flow in period 3, etc.
IRR = Internal Rate of Return

Internal rate of return can be found algebraically using this method as the IRR calculator. Below is a common internal rate of return calculation example.

Internal Rate of Return Method

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Internal Rate of Return Method

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