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. The first step is to calculate the present value and profitability index. 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 = 0.1235Problem 1
Solution
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
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% |
Capital Budgeting: Important Problems and Solutions FAQs
Examples of capital budgeting include purchasing and installing a new machine tool in an engineering firm, and a proposed investment by the company in a new plant or equipment or increasing its inventories.
It involves assessing the potential projects at hand and budgeting their projected cash flows. Once in place, the present value of these cash flows is ascertained and compared between each project. Typically, the project that offers the highest total net present value is selected, or prioritized, for investment.
The primary capital budgeting techniques are the payback period method and the net present value method.
The capital budgeting sums are the amounts of money involved in capital budgeting.
The capital budgeting numericals are the various types of numbers used in applying different capital budgeting techniques.
True Tamplin is a published author, public speaker, CEO of UpDigital, and founder of Finance Strategists.
True is a Certified Educator in Personal Finance (CEPF®), author of The Handy Financial Ratios Guide, a member of the Society for Advancing Business Editing and Writing, contributes to his financial education site, Finance Strategists, and has spoken to various financial communities such as the CFA Institute, as well as university students like his Alma mater, Biola University, where he received a bachelor of science in business and data analytics.
To learn more about True, visit his personal website or view his author profiles on Amazon, Nasdaq and Forbes.
