Tag Archives | discount rate

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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Originally published by Jim Wilkinson on July 23, 2013. 

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Time Value of Money

See Also:
Valuation Methods
Adjusted Present Value (AVP)
Net Present Value Method
Internal Rate of Return Method
Required Rate of Return

Time Value of Money (TVM)

Time value of money is the difference between an amount of money in the present and that same amount of money in the future. Having money now is more valuable than having money later.

The present amount is called the present value, the future amount is called the future value, and the appropriate rate that relates the two amounts is called the discount rate.

Present Value = Future Value / (1 + Discount Rate)

Future Value = Present Value x (1 + Discount Rate)

Time Value of Money Examples

Now, let’s look at time value of money examples. If you invest $100 (the present value) for 1 year at a 5% interest rate (the discount rate), then at the end of the year, you would have $105 (the future value). So, according to this example, $100 today is worth $105 a year from today.

$105 = $100 x 1.05

$100 = $105 / 1.05

Likewise, $100 a year from today, discounted back at 5%, is worth only $95.24 today.

$95.24 = $100 / 1.05

To calculate the time value of money for a period longer than one year, you simply raise the discount factor by the appropriate number of time periods. For example, to calculate the future value of $100 at 5% for 5 years:

$127.63 = $100 x (1.05)5

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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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Discount Rate

See Also:
EBITDA Definition
Cost of Capital Funding
Arbitrage Pricing Theory
Capital Budgeting Methods
Required Rate of Return

Discount Rate Definition

The discount rate definition, also known as hurdle rate, is a general term for any rate used in finding the present value of a future cash flow. In a discounted cash flow (DCF) model, estimate company value by discounting projected future cash flows at an interest rate. This interest rate is the discount rate which reflects the perceived riskiness of the cash flows.


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Discount Rate Explanation

Using discount rate, explained as the risk factor for a given investment, has many benefits. The purpose is to account for the loss of economic efficiency of an investor due to risk. Investors use this rate because it provides a way to account and compensate for their risk when choosing an investment. Furthermore, this provides, with each choice, a buffer to provide for the chance of failure in an investment over time as well as many investments over a portfolio. Though risk is somewhat of a sunk cost, still include it to add a real-world element to financial calculations. It is a measure used to prevent one from becoming “calculator rich” without actually increasing personal wealth.

In DCF model, there are two methods to get discount rate: weighted average cost of capital (WACC) and adjusted present value (APV). For WACC, calculate discount rate for leveraged equity using the capital asset pricing model (CAPM). Whereas for APV, all equity firms calculate the discount rate, present value, and all else.

The Discount Rate should be consistent with the cash flow being discounted. For cash flow to equity, use the cost of equity. For cash flow to firm, use the cost of capital.

Discount Rate Formula

A succinct Discount Rate formula does not exist; however, it is included in the discounted cash flow analysis and is the result of studying the riskiness of the given type of investment. The two following formulas provide a discount rate:

First, there is the following Weighted Average Cost of Capital formula.

Weighted Average Cost of Capital (WACC) = E/V * Ce + D/V * Cd * (1-T)

Where:
E = Value of equity
D = Value of debt
Ce = Cost of equity
Cd = Cost of debt
V = D + E
T = Tax rate

Then, there is the following Adjusted Present Value formula.

Adjusted Present Value = NPV + PV of the impact of financing

Where:
NPV = Net Present Value
PV = Present Value

Calculation

See the following calculation of WACC and APV.

For WACC:

WACC = $10,000/$20,000 * $2,000 + $10,000/$20,000 * $1,000 * (1-.3) = $1,050,000

If:
E = $10,000
D = $10,000
Ce = $2,000
Cd = $1,000
V = $20,000
T = 30%

For APV:

APV = $1,000,000 + $50,000 = $1,050,000

If:
NPV = $1,000,000
PV of the impact of financing = $50,000

Discount Rate Example

For example, Donna is an analyst for an entrepreneur. Where her boss is the visionary, Donna performs the calculations necessary to find whether a new venture is a good decision or not. She does not need a discount rate calculator because she has the skills to provide value above and beyond this. Donna is the right hand woman to the entrepreneur which she aspires to be. But she first needs to prove herself in the professional world.

Donna’s boss wants to know how much risk he has taken on his last venture. He would like, eventually, to find the discount rate business valuation to judge levels for performance and new ventures alike.

Donna’s boss gives Donna the financial information she needs for one venture. She finds the discount rate (risk) using the following equation:

WACC = $10,000/$20,000 * $2,000 + $10,000/$20,000 * $1,000 * (1-.3) = $1,050,000

If:
E = $10,000
D = $10,000
Ce = $2,000
Cd = $1,000
V = $20,000
T = 30%

Next, Donna’s boss has her find the discount rate for another venture that he is involved in. The results are below:

Adjusted Present Value = NPV + PV of the impact of financing

Where:
NPV = Net Present Value
PV = Present Value

Donna appreciates her experience with her employer. As a result, she is sure that with this experience she can find the path to mentor another just like her.

Discount Rate

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Capitalization Rate Example

See Also:
Capitalization Rate

Capitalization Rate Example

John started a real estate company in Indiana. His company has recently begun operations and is beginning to make money. John now wants to strengthen his business; to do this requires the best understanding of the company and it’s working environment. John wants to know the capitalization rate of his company as a whole. This includes net operating income and costs for the financials of the entity.

John speaks with his accountant and finds the data to calculate his capitalization rate. With this, he can find his answer.

Net income = $1,000,000 Cost = $250,000

Capitalization Rate = $100,000 / $250,000 = 4

John knows that his capitalization rate is 4. Next, he speaks with his accountant. He finds that, for this industry, John is doing fairly well for himself. He can use the net income, beyond cost of the bank loan he took, to pay down his loan and begin expanding the company on cash flow. This has immense benefits for both John’s growth and profit potential. John begins to compare the capitalization rate with the discount rate that banks take to create expectations for his next capital project.

He is very happy to hear this. John can now find out how he will use the money rather than worrying about what he will do to please his banker. With the future in sight, he can become a forward thinking business owner.

Conclusion of Capitalization Rate Example

By developing a better understanding about his company, John is more likely to be running a successful and profitable company. The capitalization rate is a good indicator of the overall capabilities of the company. By utilizing the capitalization rate, John now has the overall profits of the company compared with the overall costs of the company. The ratio created is useful for John because it shows that the overall profits of the company is four times that of the overall costs. As said above, John now knows that he can now concentrate on expenditures of money because his capitalization rate is so positive.

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