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%