Module+19000+Explanation+and+Examples

=__Payback Period Method__=

- Definition: Payback period is the length of time required to recover the [|cost]  of an investment. The basic premise of the payback method is that the more quickly the cost of an investment can be recovered, the more desirable is the investment. The payback period is expressed in years.

- Formula: When the **net annual cash inflow is the same** every year, the following formula can be used to calculate the payback period:

Payback Period = Original Investment / Annual Cash Flow
If an investment **involves uneven cash flows**, the computation requires scheduling cash inflows and outflows. The payback period is the point at which the cumulative net cash inflows begin to exceed the cumulative net cash outflows.

- Example of payback period: Cornerstone 19.1

Company ABC needs a new sewing machine. The company is considering two machines: Machine A and machine B, both have 4 year life. Machine A costs $15,000 and will create the cash flow of $5,000 per year. Machine B costs only $10,000 but will create the cash flow of $3,000, $5,000, $5,000, $2000.

//Required: //
 * Calculate payback period for machine A and B
 * Which machine should be purchased according to payback method?
 * What if a third machine, machine C became available with the same investment as machine B and annual cash flows of $3,000? Which machine would be chosen?

//Calculation: //

Machine A payback period = original investment/annual cash flow = $15,000 / $5,000 = **__3.0 years__**

(beginning of year) || Annual Cash Flow || Time Needed for Payback ||
 * Year || Unrecovered Investment
 * 1 || $10,000 || $3,000 || 1.0 year ||
 * 2 || $7,000 || $5,000 || 1.0 year ||
 * || $2,000 || $5,000 || 0.4 year ||

Machine B payback period = **__2.4 years__**

Machine B has shorter payback period and thus seems less risky than machine A, so the company should choose machine B based on payback period method.

<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Machine C payback period = $10,000 / $3,000 = **__3.3 years__**

<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">According to payback calculations, the company should purchase machine B, since it has a shorter payback period than machine A and C.

- <span style="color: #000000; font-family: 'Arial','sans-serif'; font-size: 20px;">Advantages of payback period method:
 * <span style="color: #000000; font-family: 'Arial','sans-serif'; font-size: 20px;">It is a popular and easy method
 * <span style="color: #000000; font-family: 'Arial','sans-serif'; font-size: 20px;">It is valuable when the key investment goal is to find projects where the initial investment is quickly recovered.

- <span style="color: #000000; font-family: 'Arial','sans-serif'; font-size: 20px;">Disadvantages of payback period method:
 * <span style="color: #000000; font-family: 'Arial','sans-serif'; font-size: 20px;">It ignores any benefits that occur after the payback period and, therefore, does not measure profitability.
 * <span style="color: #000000; font-family: 'Arial','sans-serif'; font-size: 20px;">It ignores the time value of <span style="color: #000000; font-family: 'Arial','sans-serif'; font-size: 20px; text-decoration: none;">[|money] <span style="color: #000000; font-family: 'Arial','sans-serif'; font-size: 20px;">.

<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px; text-align: justify;">Because of these reasons, other methods of capital budgeting like net present value, internal rate of return or discounted cash flow are generally preferred.

=__Accounting Rate of Return__=


 * <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Definition **<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">: The accounting rate of return (ARR) measures the return on a project in terms of income, as opposed to using a project’s cash flow. It is the second commonly used nondiscounting model.


 * <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Formula **<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">:

//<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Accounting Rate of Return = Average Income/Original Investment //

<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">The average income of a project is obtained by adding the income for each year of the project and then dividing this total by the number of years.


 * Example: **



**<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Advantages: **


 * <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Considers a project’s profitability

**<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Disadvantages: **


 * <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Ignores the time value of money which can cause a manager to choose investments that do not maximize profits.

=__Net Present Value Methods__=

**<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Definition **<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">: Net Present Value (NPV) is the difference in the present value of the cash inflows and outflows associated with a project. **<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Formula ** //<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">NPV = [E CFt / (1 + i^t)] -1 // = P - I

//<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Where P = the present value of the project’s future cash inflows and I = the present value of the project’s cost (usually the initial outlay) //

//<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">CFt: the cash inflow to be received in period t, with t=1,…n //

//<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">i: required rate of return //

//<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">t: time period //

**<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Example: **

**<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px; line-height: 0px; overflow: hidden;">﻿ **

**<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Advantages **<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">: **<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Disadvantages: **
 * <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Measures the profitability of an investment
 * <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">The size of a positive NPV measures the increase in value of the firm resulting from an investment.
 * <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Must assume that the cost of capital is the required rate of return

=__Internal Rate of Return Methods__=

**<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Definition **<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">: Internal Rate of Return (IRR) is the interest rate that sets the present value of a project’s cash inflows equal to the present value of the project’s costs. It sets the project’s NPV at zero. **<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Formula: ** //<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">I = ∑ CF ////<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 10px;">t ////<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">/ (1 + i)^t // //<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Where t = 1, …, n //

**<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Example **



**<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Advantages: ** **<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Disadvantages: **
 * <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">Solving for “I” to determine the IRR can be a straightforward process if the annual cash flows are uniform or even. A single discount factor from a “present value of an annuity” table can be used to compute the present value of the annuity.
 * <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 20px;">If the cash flows are not uniform, the discount factor must solved for by trial and error or by using a business calculator or a software package like Excel®.