Capital Budgeting: Important Problems and Solutions

True Tamplin

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 .
    Thanks

    Reply

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