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: intial outlay = $50,000
Net present value = $6,175
Profitability Index (gross) = Present value of cash inflows / Intial 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 2015, 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 2015 | $500 | Nil |
End of 2016 | $2,000 | $3,400 |
End of 2017 | $3,500 | $3,400 |
End of 2018 | $2,500 | $3,400 |
End of 2019 | 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 | |
$ | $ | $ | $ | $ | $ | |
2015 | 500 | 5,000 | 5,500 | – | 5,600 | 5,600 |
2016 | 2,000 | 5,000 | 7,000 | 3,400 | 5,600 | 9,000 |
2017 | 3,500 | 5,000 | 8,500 | 3,400 | 5,600 | 9,000 |
2018 | 2,500 | 5,000 | 7,500 | 3,400 | 5,600 | 9,000 |
2019 | – | – | – | 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 ($) |
2015 | 5,500 |
2016 | 7,000 |
2017 | 7,500 (7,500 / 8,500 = 0.9) |
20,000 |
Payback period = 2.9 years
Proposal B | Cash Inflow |
$ | |
2015 | 5,600 |
2016 | 9,000 |
2017 | 9,000 |
2018 | 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 | $ |
2015 | 5,005 | 2015 | 5,096 |
2016 | 5,810 | 2016 | 7,470 |
2017 | 6,375 | 2017 | 6,750 |
2018 | 2,810 (2,810 / 5,100 = 0.5) | 2018 | 6,120 |
2019 | 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% |