Question

Net Present Value Method, Internal Rate of Return Method, and Analysis

The management of Advanced Alternative Power Inc. is considering two capital investment projects. The estimated net cash flows from each project are as follows:

Year Wind Turbines Biofuel Equipment
1 $250,000   $530,000  
2 250,000   530,000  
3 250,000   530,000  
4 250,000   530,000  

Present Value of an Annuity of $1 at Compound Interest
Year 6% 10% 12% 15% 20%
1 0.943 0.909 0.893 0.870 0.833
2 1.833 1.736 1.690 1.626 1.528
3 2.673 2.487 2.402 2.283 2.106
4 3.465 3.170 3.037 2.855 2.589
5 4.212 3.791 3.605 3.352 2.991
6 4.917 4.355 4.111 3.784 3.326
7 5.582 4.868 4.564 4.160 3.605
8 6.210 5.335 4.968 4.487 3.837
9 6.802 5.759 5.328 4.772 4.031
10 7.360 6.145 5.650 5.019 4.192

The wind turbines require an investment of $713,750, while the biofuel equipment requires an investment of $1,609,610. No residual value is expected from either project.

Required:

1a. Compute the net present value for each project. Use a rate of 10% and the present value of an annuity of $1 in the table above. If required, use the minus sign to indicate a negative net present value. If required, round to the nearest whole dollar.

Wind Turbines Biofuel Equipment
Present value of annual net cash flows $ $
Less amount to be invested $ $
Net present value $ $

1b. Compute a present value index for each project. If required, round your answers to two decimal places.

Present Value Index
Wind Turbines
Biofuel Equipment

2. Determine the internal rate of return for each project by (a) computing a present value factor for an annuity of $1 and (b) using the present value of an annuity of $1 in the table above. If required, round your present value factor answers to three decimal places and internal rate of return to the nearest whole percent.

Wind Turbines   Biofuel Equipment
Present value factor for an annuity of $1      
Internal rate of return % %

3. The net present value, present value index, and internal rate of return all indicate that the wind turbines

is a better financial opportunity compared to the biofuel equipment

, although both investments meet the minimum return criterion of 10%.

Answer 1

Solution:

Calculation of Net Present Value, Present Value Index and Internal Rate of Return of Wind Turbines

Year	Net Cash Flows	Present value factor @ 10%	Present value of Net Cash Flows $
1	250000	0.909091	227,272.73
2	250000	0.826446	206,611.57
3	250000	0.751315	187,828.70
4	250000	0.683013	170,753.36
		Total Present value of Net Cash Flows $	792,466.36
		Initial Investment	713,750.00
		Net Present Value $	78,716.36

Net Present Value = Total Present value of Net Cash Flows - Initial Investment

                                  = 792,466.36 - 713,750.00 = $78,716.36

Present Value Index = Total Present value of Net Cash Flows / Initial Investment

                                     = 792,466.36 / 713,750.00 = 1.11

Year	Net Cash Flows
0	-713750
1	250000
2	250000
3	250000
4	250000

Internal Rate of Return can be calculated on Microsoft Excel

Following are the steps to be followed on Microsoft Excel to calculate the IRR:

Step 1: Click on "FORMULAS" tab at the top of Microsoft Excel
Step 2: Select the option "Financial"
Step 3: Under "Financial" select the option "IRR"
Step 4: Under value type (-713750;250000;250000;250000;250000)

IRR = 15%

Calculation of Net Present Value, Present Value Index and Internal Rate of Return of Biofuel Equipment

Year	Net Cash Flows	Present value factor @ 10%	Present value of Net Cash Flows $
1	530000	0.909091	481,818.18
2	530000	0.826446	438,016.53
3	530000	0.751315	398,196.84
4	530000	0.683013	361,997.13
		Total Present value of Net Cash Flows $	1,680,028.69
		Initial Investment	1,609,610.00
		Net Present Value $	70,418.69

Net Present Value = Total Present value of Net Cash Flows - Initial Investment

                                  = 1,680,028.69 - 1,609,610.00 = $70,418.69

Present Value Index = Total Present value of Net Cash Flows / Initial Investment

                                     = 1,680,028.69 / 1,609,610.00 = 1.04

Year	Net Cash Flows
0	-1609610
1	530000
2	530000
3	530000
4	530000

Internal Rate of Return can be calculated on Microsoft Excel

Following are the steps to be followed on Microsoft Excel to calculate the IRR:

Step 1: Click on "FORMULAS" tab at the top of Microsoft Excel
Step 2: Select the option "Financial"
Step 3: Under "Financial" select the option "IRR"
Step 4: Under value type (-1609610; 530000; 530000; 530000; 530000)

IRR = 12.01%

Analysis of the performance Wind Turbines and Biofuel Equipment

	Wind Turbines	Biofuel Equipment
Net Present Value	$78,716.36	$70,418.69
Present Value Index	1.11	1.04
Internal Rate of Return	15%	12.01%

We see that the performance of Wind Turbines is better than Biofuel Equipment in all the above three aspects and hence, Wind Turbines is a better financial opportunity.