Capital budgeting important problems and solutions

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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

YearCash InflowsPresent Value FactorPresent Value
$@10%$
120,000.90918,180
215,000.82612,390
325,000.75118,775
410,000.6836,830
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:

YearMachine AMachine B
$$
124,0008,000
232,00024,000
340,00032,000
424,00048,000
516,00032,000

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

ParticularMachine AMachine B
Total Cash Flows1,36,0001,44,000
Average Annual Cash Flows1,36,000 / 5 = $27,0001,44,000 / 5 = $28,800
Annual Depreciation80,000 / 5 = $16,00080,000 / 5 = $16,000
Annual Net Savings27,200 – 16,000 = $11,20028,800 – 16,000 = $12,800
Average Investment80,000 / 2 = $40,00080,000 / 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

YearDiscount FactorMachine AMachine B
(at 10%)Cash Flows ($)P.V ($)Cash Flows ($)P.V ($)
1.90924,00021,8168,0007,272
2.82632,00026,43224,00019,824
3.75140,00030,04032,00024,032
4.68324,00016,39248,00032,784
5.62116,0009,93632,00019,872
1,36,0001,04,6161,44,0001,03,784

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 AProposal B
Cost of Investment$20,00028,000
Life4 years5 years
Scrap ValueNilNil
Net Income (After depreciation and tax):
End of 2015$500Nil
End of 2016$2,000$3,400
End of 2017$3,500$3,400
End of 2018$2,500$3,400
End of 2019Nil$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:

Year12345
P.V..91.83.75.68.62

Solution

Calculation of Profit after Tax

YearProposal A $20,000Proposal B $28,000
Net IncomeDep.Cash InflowNet IncomeDep.Cash Inflow
$$$$$$
20155005,0005,5005,6005,600
20162,0005,0007,0003,4005,6009,000
20173,5005,0008,5003,4005,6009,000
20182,5005,0007,5003,4005,6009,000
20193,4005,6009,000
Total8,50020,00028,50013,60028,00041,600

(a). Return on Investment

Proposal AProposal B
Investment20,000 + 2,000 = 22,00028,000 + 2,000 = 30,000
Life4 years5 years
Total Net income$8,500$13,600
Average Return ($)8,500 / 4 = 2,12513,600 / 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 ACash Inflow ($)
20155,500
20167,000
20177,500 (7,500 / 8,500 = 0.9)
20,000

Payback Period = 2.9 years

Proposal BCash inflow
$
20155,600
20169,000
20179,000
20184,400 (4,400 / 9,000 = 0.5)

Payback period = 3.5 years

(c). Discounted Payback Period

Proposal AProposal B
P.V. of cash inflowP.V. of cash inflow
Year$Year$
20155,00520155,096
20165,81020167,470
20176,37520176,750
20182,810 (2,810 / 5,100 = 0.5)20186,120
20192,564 (2,564 / 5,580 = 0.4)
20,00028,000
Discounted Payback Period = 3.5 yearsDiscounted Payback Period = 4.4 years

(d). Profitability Index method

Proposal AProposal 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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