Question

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 $195,000, 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 =	$	=
	$

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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 $231,600, and is expected to yield annual cash flows of $58,000. 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?

%

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Part Five

APPLY THE CONCEPTS: Net present value and Present value index

Sutherland Inc. is looking to invest in Project A or Project B. The data surrounding each project is provided below. Sutherland's cost of capital is 8%.
Project A	Project B
This project requires an initial investment of $165,000. 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 $137,500. The project will have a life of 7 years. Annual revenues associated with the project will be $115,000 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

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Part Six

APPLY THE CONCEPTS: Internal rate of return

The Sutherland 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 $272,600. The project's life and cash flow have changed to 7 years and $56,000, respectively, while expenses have been eliminated.	Project B's revised investment is $108,900. The project's life and cash flow have changed to 6 years and $80,000 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

Solution

Part 3

Computation of present value index –

Present value index = total present value of net cash flows/ initial investment

Total present value of net cash flows = annual cash flows discounted at 10% rate of return, for 5 years

Annual cash inflows = $57,500

Present value = 57,500 x (P/A, 10%, 5)

Present value of cash inflows = 57,500 x 3.791 = $217,983 (rounded to nearest dollar)

Initial investment = $195,000

Present value index = 217,983/195,000 = 1.11

Part 4

Computation of internal rate of return:

IRR Factor = Investment/Annual cash flow

Initial investment = $231,600

Annual cash flow = $58,000

Period = 5 years

IRR factor = $231,600/$58,000 = 3.993103

The percentage that corresponds to the factor for 5-year period on the table for present value of an annuity of $1 is 8%.

Hence, the IRR for the project is 8%.

Part 5

Net Present Value and Present Value Index

	Project A	Project B
Total present value of net cash flow	$545,965	$286,330
amount to be invested	$165,000	$137,500
Net Present Value	$380,965	$148,830

Computations:

Project A –

Initial investment = $165,000

Useful life = 8 years

Annual revenues = $130,000

Annual expenses = $35,000

Annual income = $130,000 - $35,000 = $95,000

Annual cash inflow = $95,000

Present value of cash inflows = 95,000 x (P/A, 8%, 8)

= 95,000 x 5.747 = $545,965

Project B –

Initial investment = $137,500

Useful life = 7 years

Annual revenues = $115,000

Annual expenses = $60,000

Annual income = $115,000 - $60,000 = $55,000

Annual cash inflow = $55,000

Present value of cash inflows = 55,000 x (P/A, 8%, 7)

= 55,000 x 5.206 = $286,330

Computation of present value index –

Present value index = total present value of net cash flows/ initial investment

Project A -
= 545,965/165,000 = 3.309

Project B -

= 286,330/137,500 = 2.0824

Based upon net present value, Project A is more favorable.

Based upon present value index, Project A is more favorable.

Part 6

Calculation of IRR for Project A –

IRR factor –

IRR Factor = Investment/Annual cash flow

Initial investment = $272,600

Annual cash flow = $56,000

Period = 7 years

IRR factor = $272,600/$56,000 = 4.867857

By trial and error method, first check in the table for 8%, the corresponding P/A factor for 7 years is 5.206. Hence, we need to check for higher percentages.

For instance, 10% -

The P/A factor at 7 years in 10% annuity for $1 is 4.868. The same corresponds to the calculated factor above. Hence, the IRR for Project A is 10%.

The percentage that corresponds to the factor for 7-year period on the table for present value of an annuity of $1 is 10%.

Project B –

IRR Factor = Investment/Annual cash flow

Initial investment = $108,900

Period = 6 years

Annual cash flow -

Revenues = $80,000

Expenses = $55,000

Income = 80,000 – 55,000 = $25,000

Period = 6 years

IRR factor = $108,900/$25,000 = 4.356

By trial and error method, first check in the table for 8%, the corresponding P/A factor for 6 years is 4.623. Hence, we need to check for higher percentages.

For instance, 10% -

The P/A factor at 6 years in 10% annuity for $1 is 4.355. The same corresponds to the calculated factor above. Hence, c

The percentage that corresponds to the factor for 6-year period on the table for present value of an annuity of $1 is 10%.

Hence, the IRR for the project B is 10%.