Net Present Value-Unequal Lives Al a Mode, Inc., is considering one of two inves
ID: 2766393 • Letter: N
Question
Net Present Value-Unequal Lives Al a Mode, Inc., is considering one of two investment options. Option 1 is a $58,000 investment in new blending equipment that is expected to produce equal annual cash flows of $21,000 for each of seven years. Option 2 is a $65,000 investment in a new computer system that is expected to produce equal annual cash flows of $27,000 for each of five years. The residual value of the blending equipment at the end of the fifth year is estimated to be $14,000. The computer system has no expected residual value at the end of the fifth year. Present Value of $1 at Compound Interest Year 6% 10% 12% 15% 20% 1 0.943 0.909 0.893 0.870 0.833 2 0.890 0.826 0.797 0.756 0.694 3 0.840 0.751 0.712 0.658 0.579 4 0.792 0.683 0.636 0.572 0.482 5 0.747 0.621 0.567 0.497 0.402 6 0.705 0.564 0.507 0.432 0.335 7 0.665 0.513 0.452 0.376 0.279 8 0.627 0.467 0.404 0.327 0.233 9 0.592 0.424 0.361 0.284 0.194 10 0.558 0.386 0.322 0.247 0.162 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 Assume there is sufficient capital to fund only one of the projects. Determine which project should be selected, comparing the (a) net present values and (b) present value indices of the two projects, assuming a minimum rate of return of 15%. Use the present value tables appearing above. a. Determine the net present values of the two projects. Blending Equipment Computer System Total present value of cash flows $ $ Less amount to be invested $ $ Net present value $ $ b. Determine the present value indices of the two projects. If required, round the present value index to two decimal places. Present Value Index Blending Equipment Computer System Which project should be selected? (If both present value indices are the same, either project will grade as correct.) SelectBlending EquipmentComputer System Check My Work (2 remaining) Icon Key Icon Key Previous Question 9 of 10 Next Exercise 26-22 (Algorithmic) Cengage Learning Cengage Technical Support
Explanation / Answer
Solution:
a)
Calculation of Net Present Value
Year
Cash Flow
PV factor @ 15%
Present Value of Option 1 (Cash Flow x PV factor)
Present Value of Option 2 (Cash Flow x PV factor)
Option 1
Option 2
0
-$58,000
-$65,000
1.000
-$58,000
-$65,000
1
$21,000
$27,000
0.870
$18,270
$23,490
2
$21,000
$27,000
0.757
$15,897
$20,439
3
$21,000
$27,000
0.658
$13,818
$17,766
4
$21,000
$27,000
0.572
$12,012
$15,444
5
$21,000
$27,000
0.497
$10,437
$13,419
6
$21,000
0.432
$9,072
$0
7
$21,000
0.376
$7,896
$0
7
$14,000
0.376
$5,264
$0
Net Present Value
$34,666
$25,558
Net Present Value of Option 1 = $34,666
Net Present Value of Option 2 = $25,558
b)
Calculation of Present Value indices of the two projects
Present Value Indices = Present Value of Cash Flows / Present Value of Cash Outflow
Year
Cash Flow
PV factor @ 15%
Present Value of Option 1 (Cash Flow x PV factor)
Present Value of Option 2 (Cash Flow x PV factor)
Option 1
Option 2
1
$21,000
$27,000
0.870
$18,261
$23,478
2
$21,000
$27,000
0.756
$15,876
$20,412
3
$21,000
$27,000
0.657
$13,797
$17,739
4
$21,000
$27,000
0.571
$11,991
$15,417
5
$21,000
$27,000
0.497
$10,437
$13,419
6
$21,000
0.432
$9,072
$0
7
$21,000
0.376
$7,896
$0
7
$14,000
0.376
$5,264
$0
Present Value of Cash Flow
$92,594
$90,465
Present Value Indices (Option 1) = $92,594 / $58,000 = 1.60 (Rank 1)
Present Value indices (Option 2) = $90,465 / $65,000 = 1.40 (Rank 2)
Year
Cash Flow
PV factor @ 15%
Present Value of Option 1 (Cash Flow x PV factor)
Present Value of Option 2 (Cash Flow x PV factor)
Option 1
Option 2
0
-$58,000
-$65,000
1.000
-$58,000
-$65,000
1
$21,000
$27,000
0.870
$18,270
$23,490
2
$21,000
$27,000
0.757
$15,897
$20,439
3
$21,000
$27,000
0.658
$13,818
$17,766
4
$21,000
$27,000
0.572
$12,012
$15,444
5
$21,000
$27,000
0.497
$10,437
$13,419
6
$21,000
0.432
$9,072
$0
7
$21,000
0.376
$7,896
$0
7
$14,000
0.376
$5,264
$0
Net Present Value
$34,666
$25,558