Capital Budgeting: Important Problems and Solutions

Written by True Tamplin, BSc, CEPF®

Reviewed by Subject Matter Experts

Updated on January 30, 2024

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: 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 = 0.1235

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 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

About the Author

True Tamplin, BSc, CEPF®

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.