# 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. Strategic CFO Lab Member Extra

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# 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.

## 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. 1

# Carried Interests Definition

What are carried interests? The carried interests definition is a portion of an investment fund’s annual profit that is given to the fund manager at the end of the year. Carried interests are designed to incentivize to the fund manager to achieve outstanding performance for the fund. They are often set at around 20% of the fund’s profits.

You can also call carried interest carry, or profit interests. Use the amount to compensate fund managers and general partners at private equity firms and hedge funds. The carried interest may be the primary source of compensation for the fund managers; however, it does not include any of the fund manager’s own money that he may have invested in the fund.

There may be a hurdle rate of return stipulated, as well. For instance, the policy at a private equity fund may be that all of the investors must earn at least 7% return on their initial investment. In addition, the policy may consider everything above and beyond that pure profit and may use it to compute the fund manager’s carry.

## Carried Interest Example

For example, a hedge fund has \$100 million of invested capital from 10 investors. The hedge fund has told the investors to expect at lease a 5% return on their investment. In addition, the fund manager will earn a 20% carry on the profits above the 5% hurdle rate. Now, motivate the fund manager to maximize the fund’s performance. Furthermore, he will earn 20% of anything above \$105 million.

At the end of the year, the fund is worth \$125 million. The fund made a profit of \$25 million, or 25%. Let’s see how much of this profit will go to the fund manager for his efforts.

#### Profit the Fund Manager Gets

Ten investors contributed \$10 million each to make the full amount in the fund, \$100 million. Each of the investors was told to expect at least a five percent return on their investments, or \$500,000 each. For all ten investors, this adds up to \$5 million. This means, according to the hurdle rate, the fund manager earns 20% on anything above \$105 million.

The fund made \$25 million. So subtract the \$5 million for the hurdle rate. That leaves you with \$20 million. Now, the fund manager earns 20% of the \$20 million. This turns out to be \$4 million. Then distribute the remaining \$16 million among the investors or use it to cover other expenses or simply reinvest it in the fund.

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