In: Accounting
A new machine that costs $80,800 is expected to save annual cash operating costs of $20,000 over each of the next seven years. The machine's internal rate of return is (see choices below the present value tables):
Present Value of $1 |
||||||||
Periods |
4% |
6% |
8% |
10% |
12% |
14% |
16% |
|
1 |
.962 |
.943 |
.926 |
.909 |
.893 |
.877 |
.862 |
|
2 |
.925 |
.890 |
.857 |
.826 |
.797 |
.769 |
.743 |
|
3 |
.889 |
.840 |
.794 |
.751 |
.712 |
.675 |
.641 |
|
4 |
.855 |
.792 |
.735 |
.683 |
.636 |
.592 |
.552 |
|
5 |
.822 |
.747 |
.681 |
.621 |
.567 |
.519 |
.476 |
|
6 |
.790 |
.705 |
.630 |
.564 |
.507 |
.456 |
.410 |
|
7 |
.760 |
.665 |
.583 |
.513 |
.452 |
.400 |
.354 |
|
8 |
.731 |
.627 |
.540 |
.467 |
.404 |
.351 |
.305 |
|
9 |
.703 |
.592 |
.500 |
.424 |
.361 |
.308 |
.263 |
|
10 |
.676 |
.558 |
.463 |
.386 |
.322 |
.270 |
.227 |
|
Present Value of a Series of $1 Cash Flows |
||||||||
Periods |
4% |
6% |
8% |
10% |
12% |
14% |
16% |
|
1 |
0.962 |
0.943 |
0.926 |
0.909 |
0.893 |
0.877 |
0.862 |
|
2 |
1.886 |
1.833 |
1.783 |
1.736 |
1.690 |
1.647 |
1.605 |
|
3 |
2.775 |
2.673 |
2.577 |
2.487 |
2.402 |
2.322 |
2.246 |
|
4 |
3.630 |
3.465 |
3.312 |
3.170 |
3.037 |
2.914 |
2.798 |
|
5 |
4.452 |
4.212 |
3.993 |
3.791 |
3.605 |
3.433 |
3.274 |
|
6 |
5.242 |
4.917 |
4.623 |
4.355 |
4.111 |
3.889 |
3.685 |
|
7 |
6.002 |
5.582 |
5.206 |
4.868 |
4.564 |
4.288 |
4.039 |
|
8 |
6.733 |
6.210 |
5.747 |
5.335 |
4.968 |
4.639 |
4.344 |
|
9 |
7.435 |
6.802 |
6.247 |
5.759 |
5.328 |
4.946 |
4.607 |
|
10 |
8.111 |
7.360 |
6.710 |
6.145 |
5.650 |
5.216 |
4.833 |
|
Group of answer choices:
A. approximately 14%
B. some other value than the choices shown
C. approximately 16%
D. approximate 12%
IRR means rate at which NPV is zero. | ||||
Let us calculate NPV at 10% rate and 16% rate | ||||
10% | 16% | |||
a | Annual Cash Inflow | $ 20,000 | $ 20,000 | |
b | PV annuity factor for 7 years | 4.868 | 4.039 | |
c | PV of cash inflow (a*b) | $ 97,360 | $ 80,780 | |
d | Initial investment | $ 80,800 | $ 80,800 | |
e | NPV (c-d) | $ 16,560 | $ -20 | |
We can directly conclude that IRR is 16% (approx) because NPV at | ||||
16% rate is very close to 0. | ||||
therefore corrct option : C |