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 10%?

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 5-year life, requiring an initial investment of $211,600, 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 youll 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

Underwood Inc. is looking to invest in Project A or Project B. The data surrounding each project is provided below. Underwood's cost of capital is 11%.
Project A	Project B
This project requires an initial investment of $172,500. The project will have a life of 6 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 4 years. Annual revenues associated with the project will be $113,000 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 Underwood 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 $250,700. The project's life and cash flow have changed to 7 years and $51,500, respectively, while expenses have been eliminated.	Project B's revised investment is $119,800. 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 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? %