Problem 1
The cost of a project is $50,000 and it generates cash inflows of $20,000, $15,000, $25,000, and $10,000 over four years.
Required: Using the present value index method, appraise the profitability of the proposed investment, assuming a 10% rate of discount.
Solution
The first step is to calculate the present value and profitability index.
| Year |
Cash Inflows |
Present Value Factor |
Present Value |
|
$ |
@10% |
$ |
| 1 |
20,000 |
0.909 |
18,180 |
| 2 |
15,000 |
0.826 |
12,390 |
| 3 |
25,000 |
0.751 |
18,775 |
| 4 |
10,000 |
0.683 |
6,830 |
|
|
|
56,175 |
Total present value = $56,175
Less: initial outlay = $50,000
Net present value = $6,175
Profitability Index (gross) = Present value of cash inflows / Initial cash outflow
= 56,175 / 50,000
= 1.1235
Given that the profitability index (PI) is greater than 1.0, we can accept the proposal.
Net Profitability = NPV / Initial cash outlay
= 6,175 / 50,000 = 0.1235
N.P.I. = 1.1235 - 1 = 0.1235
Given that the net profitability index (NPI) is positive, we can accept the proposal.
Problem 2
A company is considering whether to purchase a new machine. Machines A and B are available for $80,000 each. Earnings after taxation are as follows:
| Year |
Machine A |
Machine B |
|
$ |
$ |
| 1 |
24,000 |
8,000 |
| 2 |
32,000 |
24,000 |
| 3 |
40,000 |
32,000 |
| 4 |
24,000 |
48,000 |
| 5 |
16,000 |
32,000 |
Required: Evaluate the two alternatives using the following: (a) payback method, (b) rate of return on investment method, and (c) net present value method. You should use a discount rate of 10%.
Solution
(a) Payback method
24,000 of 40,000 = 2 years and 7.2 months
Payback period:
Machine A: (24,000 + 32,000 + 1 3/5 of 40,000) = 2 3/5 years.
Machine B: (8,000 + 24,000 + 32,000 + 1/3 of 48,000) = 3 1/3 years.
According to the payback method, Machine A is preferred.
(b) Rate of return on investment method
| Particular |
Machine A |
Machine B |
| Total Cash Flows |
1,36,000 |
1,44,000 |
| Average Annual Cash Flows |
1,36,000 / 5 = $27,000 |
1,44,000 / 5 = $28,800 |
| Annual Depreciation |
80,000 / 5 = $16,000 |
80,000 / 5 = $16,000 |
| Annual Net Savings |
27,200 - 16,000 = $11,200 |
28,800 - 16,000 = $12,800 |
| Average Investment |
80,000 / 2 = $40,000 |
80,000 / 2 = $40,000 |
| ROI = (Annual Net Savings / Average Investments) x 100 |
(11,200 / 40,000) x 100 |
(12,800 / 40,000) x 100 |
|
= 28% |
= 32% |
According to the rate of return on investment (ROI) method, Machine B is preferred due to the higher ROI rate.
(c) Net present value method
The idea of this method is to calculate the present value of cash flows.
| Year |
Discount Factor |
Machine A |
Machine B |
|
(at 10%) |
Cash Flows ($) |
P.V ($) |
Cash Flows ($) |
P.V ($) |
| 1 |
.909 |
24,000 |
21,816 |
8,000 |
7,272 |
| 2 |
.826 |
32,000 |
26,432 |
24,000 |
19,824 |
| 3 |
.751 |
40,000 |
30,040 |
32,000 |
24,032 |
| 4 |
.683 |
24,000 |
16,392 |
48,000 |
32,784 |
| 5 |
.621 |
16,000 |
9,936 |
32,000 |
19,872 |
|
|
1,36,000 |
1,04,616 |
1,44,000 |
1,03,784 |
Net Present Value = Present Value - Investment
Net Present Value of Machine A: $1,04,616 - $80,000 = $24,616
Net Present Value of Machine B: $1,03,784 - 80,000 = $23,784
According to the net present value (NPV) method, Machine A is preferred because its NPV is greater than that of Machine B.
Problem 3
At the beginning of 2024, a business enterprise is trying to decide between two potential investments.
Required: Assuming a required rate of return of 10% p.a., evaluate the investment proposals under: (a) return on investment, (b) payback period, (c) discounted payback period, and (d) profitability index.
The forecast details are given below.
|
Proposal A |
Proposal B |
| Cost of Investment |
$20,000 |
28,000 |
| Life |
4 years |
5 years |
| Scrap Value |
Nil |
Nil |
| Net Income (After depreciation and tax) |
|
|
| End of 2024 |
$500 |
Nil |
| End of 2025 |
$2,000 |
$3,400 |
| End of 2026 |
$3,500 |
$3,400 |
| End of 2027 |
$2,500 |
$3,400 |
| End of 2028 |
Nil |
$3,400 |
It is estimated that each of the alternative projects will require an additional working capital of $2,000, which will be received back in full after the end of each project.
Depreciation is provided using the straight line method. The present value of $1.00 to be received at the end of each year (at 10% p.a.) is shown below:
| Year |
1 |
2 |
3 |
4 |
5 |
| P.V. |
0.91 |
0.83 |
0.75 |
0.68 |
0.62 |
Solution
Calculation of profit after tax
| Year |
Proposal A $20,000 |
Proposal B $28,000 |
|
Net Income |
Dep. |
Cash Inflow |
Net Income |
Dep. |
Cash Inflow |
|
$ |
$ |
$ |
$ |
$ |
$ |
| 2024 |
500 |
5,000 |
5,500 |
- |
5,600 |
5,600 |
| 2025 |
2,000 |
5,000 |
7,000 |
3,400 |
5,600 |
9,000 |
| 2026 |
3,500 |
5,000 |
8,500 |
3,400 |
5,600 |
9,000 |
| 2027 |
2,500 |
5,000 |
7,500 |
3,400 |
5,600 |
9,000 |
| 2028 |
- |
- |
- |
3,400 |
5,600 |
9,000 |
| Total |
8,500 |
20,000 |
28,500 |
13,600 |
28,000 |
41,600 |
(a) Return on investment
|
Proposal A |
Proposal B |
| Investment |
20,000 + 2,000 = 22,000 |
28,000 + 2,000 = 30,000 |
| Life |
4 years |
5 years |
| Total Net Income |
$8,500 |
$13,600 |
| Average Return ($) |
8,500 / 4 = 2,125 |
13,600 / 5 = 2,720 |
| Average Investment ($) |
(22,000 + 2,000) / 2 = 12,000 |
(30,000 + 2,000) / 2 = 16,000 |
| Average Return on Average Investment ($) |
(2,125 / 12,000) x 100
= 17.7% |
(2,720 / 16,000) x 100
= 17% |
(b) Payback period
| Proposal A |
Cash Inflow ($) |
| 2024 |
5,500 |
| 2025 |
7,000 |
| 2026 |
7,500 (7,500 / 8,500 = 0.9) |
|
20,000 |
Payback period = 2.9 years
| Proposal B |
Cash Inflow |
|
$ |
| 2024 |
5,600 |
| 2025 |
9,000 |
| 2026 |
9,000 |
| 2027 |
4,400 (4,400 / 9,000 = 0.5) |
Payback period = 3.5 years
(c) Discounted payback period
| Proposal A |
Proposal B |
| P.V. of Cash Inflow |
P.V. of Cash Inflow |
| Year |
$ |
Year |
$ |
| 2024 |
5,005 |
2024 |
5,096 |
| 2025 |
5,810 |
2025 |
7,470 |
| 2027 |
6,375 |
2026 |
6,750 |
| 2028 |
2,810 (2,810 / 5,100 = 0.5) |
2027 |
6,120 |
|
|
2028 |
2,564 (2,564 / 5,580 = 0.4) |
|
20,000 |
|
28,000 |
| Discounted Payback Period = 3.5 years |
Discounted Payback Period = 4.4 years |
(d) Profitability index method
|
Proposal A |
Proposal B |
| Gross Profitability Index |
(22,290 / 20,000) x 100
= 111.45% |
(31,016 / 28,000) x 100
= 111.08% |
| Net Profitability Index |
(2,290 / 20,000) x 100
= 11.45% |
(3,016 / 28,000) x 100
= 10.8% |
