Question

Fairwell company has recorded the following data related to two alternatives A and B.

Both require an investment of $56,125

Year ACFs after depre.Tax                                     ACFs after depre. Tax

1 $3,375 11,375 2 5,373 9,375

3 7,375 7,375

4 9,375 5,375

5   11,375 3,37   36,875 36,875

Cost of capital 10%                             

Estimated life 5 years 5 years

Estimated salvage value $3,000 $3,000

Tax rate 55% 55%

Depreciation has been charged on straight line basis calculate:

• ARR
• Payback period
• Net present value
• Profitability Index
• Internal Rate of Return

Answer 1

	A	B
COST	56125	56125
Cash flow after deprciation and tax
Yr1	3375	11375
Yr2	5375	9375
Yr3	7375	7375
Yr5	9375	5375
Yr5	11375	3375
Total	36875	36875
life	5year	5year
salvage value	3000	3000

Annual cash flow after tax (alternative A)-

Yr	cashflow after depreciation and tax	depreciation(Non cash )	cash flow after tax(CFAT)	Cumulative CFAT
1	3375	=(56125-3000)/5 =10625	14000	14000
2	5375	10625	16000	30000
3	7375	10625	18000	48000
4	9375	10625	20000	68000
5	11375	10625	22000+3000	93000

Note-CFAT AT 5TH YEAR INCLUDES 3000 SALVAGE VALUE

Annual cash flow after tax (alternative-B)-

Yr	cashflow after depreciation and tax	depreciation(Non cash )	cash flow after tax(CFAT)	Cumulative CFAT
1	11375	=(56125-3000)/5 =10625	22000	22000
2	9375	10625	20000	42000
3	7375	10625	18000	60000
4	5375	10625	16000	76000
5	3375	10625	14000+3000	93000

Note-CFAT AT 5TH YEAR INCLUDES 3000 SALVAGE VALUE

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(1) ARR( Average rate of return)

ARR = (Average income/Average investment) × 100.

Average income of Machines A and B =(Rs 36,875/5) = Rs 7,375.

Average investment = Salvage value + 1/2 (Cost of machine – Salvage
value) = Rs 3,000 + 1/2 (Rs 56,125 – Rs 3,000) = Rs 29,562.50.

ARR (for machines A and B) = (Rs 7,375/Rs 29,562.50) × 100 = 24.9%

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(2) Pay back period

Pay back period = A + (B/C)

A is the last period number with a negative cumulative cash flow;
B is the absolute value (i.e. value without negative sign) of cumulative net cash flow at the end of the period A; and
C is the total cash inflow during the period following period A

pay back period of Alternate A-

Period	Cash Flow	Cumulative
0	-56125	-56125
1	14000	-42125
2	16000	-26125
3(A)	18000	-8125(B)
4	20000(C)	11875
5	25000	36875

pay back period of A = 3 +(8125/20000) = 3.046 YEARS

pay back period of Alternate A-

Period	Cash Flow	Cumulative
0	-56125	-56125
1	22000	-34125
2(A)	20000	-14125(B)
3	18000(C)	3875
4	16000	19875
5	17000	36875

pay back period of A = 2 +(14125/18000) = 2.785 YEARS

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(3) NPV CALCULATION

		Alternate-A	-56125		Alternate-B	-56125
Yr	CFAT	PVF@10%	PV	CFAT	PVF@10%	PV
1	14000	0.909	12726	22000	0.909	19998
2	16000	0.826	13216	20000	0.826	16250
3	18000	0.751	13518	18000	0.751	13518
4	20000	0.683	14660	16000	0.683	10928
5	25000	0.621	15525	17000	0.621	10557
		NPV	13520		NPV	15396

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(4)IRR Calculation-

AT IRR PV OF CASH INFLOW = PV OF CASH OUTFLOW, MEANS NPV=0

Average Cash flow per year = 93000/5 = 18600

average IRR = 18600/9300*100 = 20%

Let take IRR for A = 18% & for B =21%

		Alternate-A	-56125		Alternate-B	-56125
Yr	CFAT	PVF@18%	PV	CFAT	PVF@21%	PV
1	14000	0.847	11858	22000	0.826	18172
2	16000	0.718	11488	20000	0.683	13660
3	18000	0.609	10962	18000	0.564	10152
4	20000	0.516	10320	16000	0.467	7472
5	25000	0.437	10925	17000	0.386	6562
		Total PV of cash inflow	55553		PV of cash inflow	56108
	Less-	Initial Investment	56125		initial investment	56125
	NPV		-572			-107

Since NPV is negative discountb rate should be lowered

let takeIRR for A = 17% AND for B = 20%

		Alternate-A	-56125		Alternate-B	-56125
Yr	CFAT	PVF@17%	PV	CFAT	PVF@20%	PV
1	14000	0.855	11970	22000	0.833	18326
2	16000	0.731	11696	20000	0.694	13880
3	18000	0.624	10232	18000	0.579	10442
4	20000	0.534	10680	16000	0.484	7712
5	25000	0.456	11400	17000	0.442	6834
		Total PV of cash inflow	56978		PV of cash inflow	57174
	Less-	Initial Investment	56125		initial investment	56125
	NPV		835			1049

APPLYING INTERPOLATION-

IRR of A = 17% + [(56978-56125)/(56978-55553)]*1 = 17.6%

IRR of B = 20% + [(57175-561250/(57174-56108)]*1 = 20.9%

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(5) Profitability index

Profitability index = PV of cash inflow / PV of cash outflow

		Alternate-A CASH Out flow	56125		Alternate-B cash outflow	-56125
Yr	CFAT	PVF@10%	PV	CFAT	PVF@10%	PV
1	14000	0.909	12726	22000	0.909	19998
2	16000	0.826	13216	20000	0.826	16250
3	18000	0.751	13518	18000	0.751	13518
4	20000	0.683	14660	16000	0.683	10928
5	25000	0.621	15525	17000	0.621	10557
		PV of cash inflow	69645		NPV	71521
		Profitability Index	=69645/56125 =1.24		Profitability Index	=71521/56125 =1.27