Mastery Problem: Net Present Value and Internal Rate of Return

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Part One

Companies use capital investment analysis to evaluate long-term investments. Capital investment evaluation methods that use present values are (1) Net present value method (NPV) and (2) Internal rate of return (IRR) method.

Methods That Use Present Values

Of the two capital investment evaluation methods, a defining characteristic NPV and IRR is that they

considerignoreconsider

the time value of money. This means that money tomorrow is worth

less thanmore thanthe same asless than

money today. And, that cash invested today has the potential to earn income and

decrease increaseincrease

in value over time.

True or False: When making an investment decision between two mutually exclusive projects, the project with the greatest return on investment should be chosen.

FalseTrueTrue

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Review the definition of Methods that use present value by rolling your mouse over the underlined item.

Review the definition of Mutually Exclusive Projects by rolling your mouse over the underlined item.

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Part Two

Net Present Value Method

Net present value (NPV) is one method that can be used to evaluate the financial viability of potential projects. It determines the present value of all future cash flows associated with potential projects and measures this against the cost of the project. To use net present value, a required rate of return must be defined. The required rate of return is the

maximumminimumonlyminimum

acceptable rate of return that an investment must yield for it to make sense economically. Managers often choose a required rate of return above their cost of capital to ensure that the inherent uncertainties surrounding future cash flows is addressed. This can be risky, however, as it biases the process toward short-term projects. If the NPV is positive, then the project should be

acceptedrejectedaccepted

; if it is negative, then the project should be

acceptedrejectedrejected

.

Let's look at a net present value example using the present value of an ordinary annuity table.

The company has a project with a 5-year life that requires an initial investment of $200,000, and is expected to yield annual cash flows of $58,000. What is the net present value of the project if the required rate of return is set at 8%?

Calculation Steps

Present Value of an Annuity of $1 at Compound Interest.

Net Present Value =

(

58,000

x

fill in the blank ff33dd027fd801a_5

)

-

$fill in the blank ff33dd027fd801a_6

Note: Round your answer to the nearest whole dollar.

What NPV does the previous calculation yield?$fill in the blank ff33dd027fd801a_7

Based on the NPV computed above, what is indicated?

1.	The project is profitablenot profitableprofitable
2.	YesNoYes , the initial investment will be recovered.
3.	YesNoYes , the required rate of return will be recovered.
4.	A positivenegativepositive NPV in excess of the initial investment and required rate of return has been achieved.

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Click on the Present Value of an Annuity of $1 at Compound Interest link and look for the intersection of the number of years row and the required rate of return column.

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Part Three

Present Value Index

When funds for capital investments are limited, projects can be ranked using a present value index. A project with a negative net present value will have a present value index below 1.0. Also, it is important to note that a project with the largest net present value may, in fact, return a lower present value per dollar invested.

Let's look at an example of how to determine the present value index.

The company has a project with a 5-year life, an initial investment of $170,000, and is expected to yield annual cash flows of $55,500. Whathat is the present value index of the project if the required rate of return is set at 8%?

Present value index	=	Total present value of net cash flows
Initial investment

Calculation Steps

Note: Round total present value of net cash flows and initial investment to nearest dollar. Round present value index to two decimal places.

Present value index =	$fill in the blank 6874c9058fb5fcc_1	= fill in the blank 6874c9058fb5fcc_2
$fill in the blank 6874c9058fb5fcc_3

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To calculate the total present value of net cash flows, find the correct present value discount factor. Then multiply it by the annual cash flow for the project.

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Part Four

Internal Rate of Return Method

The internal rate of return (IRR) method uses present value concepts to compute the rate of return from a capital investment proposal based on its expected net cash flows. This method, sometimes called the time-adjusted rate of return method, starts with the proposal's net cash flows and works backward to estimate the proposal's expected rate of return.

Let's look at an example of internal rate of return calculation with even cash flows.

A company has a project with a 5-year life, requiring an initial investment of $225,600, and is expected to yield annual cash flows of $56,500. What is the internal rate of return?

IRR Factora	=	Investmentb
		Annual cash flowsc

aIRR Factor: This is the factor which you'll use on the table for the present value of an annuity of $1 dollar in order to find the percentage which corresponds to the internal rate of return.
bInvestment: This is the present value of cash outflows associated with a project. If all of the investment is up front at the beginning of the project, the present value factor is 1.000.
cAnnual Cash Flows: This is the amount of cash flows to be received annually as a result of the project.

Calculation Steps

Present Value of an Annuity of $1 at Compound Interest.

IRR Factor =	225.6000	= fill in the blank 4dc2befcffaef92_2, rounded to 6 decimals
56,500

The calculated factor corresponds to which percentage in the present value of ordinary annuity table?

fill in the blank 4dc2befcffaef92_4%

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The internal rate of return calculation is a two-step process. First, you must divide the present value of the initial investment by the annual cash flows of the project to arrive at the IRR factor. Next, use the table for the present value of an annuity of $1 at compound interest, looking down the row of the number of years the project will exist. At the column where you hit the value closest to your computed value, you have determined a percentage that is the internal rate of return for the project.

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Part Five

APPLY THE CONCEPTS: Net present value and Present value index

Rydell Corp. is looking to invest in Project A or Project B. The data surrounding each project is provided below. Rydell's cost of capital is 8%.
Project A	Project B
This project requires an initial investment of $167,500. The project will have a life of 8 years. Annual revenues associated with the project will be $130,000 and expenses associated with the project will be $35,000.	This project requires an initial investment of $130,000. The project will have a life of 7 years. Annual revenues associated with the project will be $105,000 and expenses associated with the project will be $60,000.

Calculate the net present value and the present value index for each project using the present value tables provided below.

Present Value of $1 (a single sum) at Compound Interest.

Present Value of an Annuity of $1 at Compound Interest.

Note:
	Use a minus sign to indicate a negative NPV.
	If an amount is zero, enter "0".
	Enter the present value index to 2 decimals.

	Project A	Project B
Total present value of net cash flow	$fill in the blank 2c41b3fc1fb3017_1		$fill in the blank 2c41b3fc1fb3017_2
Amount to be invested	167,500		130,000
Net present value	$fill in the blank 2c41b3fc1fb3017_5		$fill in the blank 2c41b3fc1fb3017_6
Present value index:
Project A	fill in the blank 2c41b3fc1fb3017_7
Project B			fill in the blank 2c41b3fc1fb3017_8

Based upon net present value, which project has the more favorable profit prospects?

Both are favorableProject AProject BCan't determineProject A

Based upon the present value index, which project is ranked higher?

Both are favorableProject AProject BCan't determineProject A

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Subtract the expenses from the revenues to determine net cash flow for each year. Since this is an annuity cash flow, use the appropriate table to look up the present value factor for the project life and required rate of return.

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Part Six

APPLY THE CONCEPTS: Internal rate of return

The Rydell purchasing department has made revisions to their costs and annual cash flows for Project A and Project B, as outlined below.
Project A	Project B
Project A's revised investment is $184,800. The project's life and cash flow have changed to 5 years and $47,500, respectively, while expenses have been eliminated.	Project B's revised investment is $127,100. The project's life and cash flow have changed to 6 years and $82,500 while expenses reduced slightly to $55,000.

Compute the internal rate of return factor for Project A and Project B and then identify each project's corresponding percentage from the PV ordinary annuity table.

Note: Enter the IRR factor, to 5 decimal places.

Project A: The calculated IRR factor is fill in the blank c224bffd102cfa3_1 and this value corresponds to which percentage in the present value of ordinary annuity table? fill in the blank c224bffd102cfa3_2%

Project B: The calculated IRR factor is fill in the blank c224bffd102cfa3_3 and this value corresponds to which percentage in the present value of ordinary annuity table? fill in the blank c224bffd102cfa3_4%