Question

Mastery Problem: Net Present Value and Internal Rate of Return

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 consider  the time value of money. This means that money tomorrow is worth less than  money today. And, that cash invested today has the potential to earn income and increase  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.
True

Feedback

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.

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 flowsassociated 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 minimum  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 accepted ; if it is negative, then the project should be rejected .

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 $210,000, and is expected to yield annual cash flows of $64,000. What is the net present value of the project if the required rate of return is set at 12%?

Calculation Steps

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

Net Present Value =

(

$

x

)

–

$

Note: Round your answer to the nearest whole dollar.

What NPV does the previous calculation yield?  $

Based on the NPV computed above, what is indicated?

1.	The project is profitable
2.	Yes , the initial investment will be recovered.
3.	Yes , the required rate of return will be recovered.
4.	A positive  NPV in excess of the initial investment and required rate of return has been achieved.

Feedback

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.

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 $220,000, and is expected to yield annual cash flows of $57,500. 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 =	$	=
	$

Feedback

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.

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 6-year life, requiring an initial investment of $237,800, and is expected to yield annual cash flows of $53,000. 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 =	$	= , rounded to 6 decimals
	$

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

%

Feedback

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.

Part Five

APPLY THE CONCEPTS: Net present value and Present value index

Darling Enterprises is looking to invest in Project A or Project B. The data surrounding each project is provided below. Darling'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 $132,500. The project will have a life of 7 years. Annual revenues associated with the project will be $109,000 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	$		$
Amount to be invested
Net present value	$		$
Present value index:
Project A
Project B

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

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

Feedback

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.

Part Six

APPLY THE CONCEPTS: Internal rate of return

The Darling 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 $202,300. The project's life and cash flow have changed to 5 years and $52,000, respectively, while expenses have been eliminated.	Project B's revised investment is $150,200. The project's life and cash flow have changed to 6 years and $87,500 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  and this value corresponds to which percentage in the present value of ordinary annuity table?  %

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

Answer 1

RC D Part two 0 1 2 3 4 5 (210,000) 64,000 64,000 64,000 64,000 64,000 Given in Question 12% 12% 12% 12% 12% Given in Question - NPY $20,705.68 NPV(12%.C3:G3)+B3 5 Therefore. The project is profitable, initial investment will be recovered, required rate of return will also be recovered 3 Part Three Year 1 57,500 2 57.500 3 57,500 4 57,500 2 NPV 3 Initial invesment # Present value index (220,000) $229,580.83 220.000 1.04 5 57,500 Given in Question NPV[87.C12:G12) Given in Question B13/B14 5 Part four 7 Year 53,000 53.000 53.000 53.000 53.000 (237,800) 8.993% 6 Given in Question 53,000 Given in Question IRR(B19:H11 IRR 3 130,000 i 35,000 95,000 i 4 130,000 35,000 95,000 5 130,000 35,000 95,000 6 130,000 35,000 95.000 7 130,000 35,000 95.000 130,000 Given in Question 35,000 Given in Question 95,000 C25-C26 1 Part Five 2 Project A 3 Revenues 4 Expenses 5 Net Cash Flow 6 Initial Investment 7 Total Present Value of Net Cash 8 Amount to be investment 9 Net Present Value o Present Value Index 1 2 130,000 130,000 35,000 35,000 95,000 95,000 (167,500) Given in Question $545,931 NPV[87.C27:J27) 167,500 167,500 $378,431 B30-B31 3.25928776 B30/B31 109,000 60,000 49,000 109,000 60,000 49,000 109,000 60,000 49,000 109,000 Given in Question 60,000 Given in Question 49,000 C37-C38 2 Project B 12 3 Revenues 109,000 109,000 109,000 i 4 Expenses 60,000 60,000 60,000 5 Net Cash Flow 49,000 49,000 49,000 i 6 Initial Investment (132,500) Given in question 7 Total Present value of Net Cash! $255,112 NPV(87.C39:39) 8 Amount to be investment 132,500 Given in question 9 Net Present Value $122,612 B42-B43 o Present Value Index $1.93 B42/B43 1 Project A has favorable prospects based on Net Present Value & Present value index