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 in four years. Using present value index method, appraise profitability of the proposed investment assuming a 10% rate of discount.
Solution
Calculation of present value and profitability index
| Year | Cash Inflows | Present Value Factor | Present Value |
| $ | @10% | $ | |
| 1 | 20,000 | .909 | 18,180 |
| 2 | 15,000 | .826 | 12,390 |
| 3 | 25,000 | .751 | 18,775 |
| 4 | 10,000 | .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
As the P.I. is higher than 1, the proposal can be accepted.
Net Profitability = NPV / Initial cash outlay
= 6,175 / 50,000 = .1235
N.P.I. = 1.1235 – 1 = 0.1235
As the net profitability index is positive, the proposal can be accepted.
Problem 2
A company is considered the purchase of a machine. the machines A and B are available for $80,000 each. Earnings after taxation are as:
| 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 |
Evaluate the two alternatives according to (a). Payback Method, (b). Rate of Return Method and (c). Net Present Value Method (A discount rate of 10% is to be used).
Solution
(a). Payback Method
24,000 of 40,000 = 2 years and 7.2 month
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 will be 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 = $40,000 |
| ROI = (Annual Net Savings / Average Investments) x 100 | (11,200 / 40,000) x 100 | (12,800 / 40,000) x 100 |
| = 28% | = 32% |
According to rate of return on investment method machine B will be preferred due to higher rate of return on investment.
(c). Net Present Value Method
Calculation of Present Value of Cash Flows
| Year | Discount Factor | Machine A | Machine B | ||
| (at 10%) | Cash Flows ($) | 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 Valu = 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
Accroding to Net Present Value Method, Machine A will be preferred as its Net Present Value is higher than that of Machine B.
Problem 3
A business enterprise can make either of two investments at the beginning of 2015. assuming required rate of return in 10% p.a. evaluate the investment proposals under:
(a). Return on investment
(b). Payback Period
(c). Discounted payback period
(d). profitability index
The forecast particular 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 expiry of each project life. Depreciation is provided under the straight-line method. The present value of $1 to be received at the end of each year, at 10% p.a. is given below:
| Year | 1 | 2 | 3 | 4 | 5 |
| P.V. | .91 | .83 | .75 | .68 | .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% |