Question

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

Answer 1

PV of cash inflow = annual cash inflow x PV annuity factor

where PV annuity factor = (1 - (1+r)^-n)/r

Present value index = NPV/ initial investment

Project A

cash inflow per year = revenue - expenses = 130000 - 35000 = 95000

years = 6

PV annuity factor = at 11% for 6 years = (1 - (1+11%)^-6)/11% = 4.23

PV of cash inflows of project A = 95000 x 4.23 = 401850

Amount to be invested = 172500

NPV = 401850 - 172500 = 229350

PV index = 229350/172500 = 1.33

Project B

cash inflow per year = revenue - expenses = 113000 - 60000 = 53000

years = 4

PV annuity factor = at 11% for 4 years = (1 - (1+11%)^-4)/11% = 3.1

PV of cash inflows of project A = 53000 x 3.1 = 164300

amount to be invested = 130000

NPV = 164300 - 130000 = 34300

PV index = 34300/130000 = 0.26

A is better based on both methods