# Capital Budgeting: Important Problems and Solutions Written by True Tamplin, BSc, CEPF®
Updated on August 16, 2021

## 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%

### 4 thoughts on “Capital Budgeting: Important Problems and Solutions”

1. the above examples covers all the aspect at a preliminary stage and very easy to understand all the method of capital budgeting techniques .
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