## 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%

### What are some examples of capital budgeting?

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.

### What is the process of capital budgeting?

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.

### What are the primary capital budgeting techniques?

The primary capital budgeting techniques are the payback period method and the net present value method.

### What are the capital budgeting sums?

The capital budgeting sums are the amounts of money involved in capital budgeting.

### What are the capital budgeting numericals?

The capital budgeting numericals are the various types of numbers used in applying different capital budgeting techniques.

True is a Certified Educator in Personal Finance (CEPF®), 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.

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