Capital budgeting important problems and solutions

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 in four years. Using present value index method, appraise profitability of the proposed investment assuming a 10% rate of discount.

Solution

Calculation of present value and profitability index

Year Cash Inflows Present Value Factor Present Value
$ @10% $
1 20,000 .909 18,180
2 15,000 .826 12,390
3 25,000 .751 18,775
4 10,000 .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

As the P.I. is higher than 1, the proposal can be accepted.

Net Profitability = NPV / Initial cash outlay

= 6,175 / 50,000 = .1235

N.P.I. = 1.1235 – 1 = 0.1235

As the net profitability index is positive, the proposal can be accepted.

Problem 2

A company is considered the purchase of a machine. the machines A and B are available for $80,000 each. Earnings after taxation are as:

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

Evaluate the two alternatives according to (a). Payback Method, (b). Rate of Return Method and (c). Net Present Value Method (A discount rate of 10% is to be used).

Solution

(a). Payback Method

24,000 of 40,000 = 2 years and 7.2 month

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 will be 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 rate of return on investment method machine B will be preferred due to higher rate of return on investment.

(c). Net Present Value Method

Calculation of 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 Valu = 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

Accroding to Net Present Value Method, Machine A will be preferred as its Net Present Value is higher than that of Machine B.

Problem 3

A business enterprise can make either of two investments at the beginning of 2015. assuming required rate of return in 10% p.a. evaluate the investment proposals under:

(a). Return on investment

(b). Payback Period

(c). Discounted payback period

(d). profitability index

The forecast particular 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 expiry of each project life. Depreciation is provided under the straight-line method. The present value of $1 to be received at the end of each year, at 10% p.a. is given below:

Year 1 2 3 4 5
P.V. .91 .83 .75 .68 .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%
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