Define Payback Period. How Payback Period is used in capital budgeting decision? What are the major constraints of this method?

 Payback Period: The length of time required to recover the cost of an investment. The payback period of a given investment or project is an important determinant of whether to undertake the position or project, as longer payback periods are typically not desirable for investment positions.

 All other things being equal, the better investment is the one with the shorter payback period. For example, if a project costs $100,000 and is expected to return $20,000 annually, the payback period will be $100,000/$20,000, or five years.

 Calculated as:

 Payback Period = Cost of Project / Annual Cash Inflows 

Payback Period:

 Payback period in capital budgeting refers to the period of time required for the return on an investment to "repay" the sum of the original investment. For example, a $1000 investment which returned $500 per year would have a t^,.\o year payback period. The time value of money is not taken into account. Payback period intuitively measures how long something takes to "pay for itself." All else being equal, shorter payback periods are preferable to longer payback periods. The term is also widely used in other types of investment areas, often with respect to energy efficiency technologies, maintenance, upgrades, or other changes. The return to the investment consists of reduced operating costs. Although primarily a financial term, the concept of a payback period is occasio«ally extended to other uses, such as energy payback period . Payback period as a tool of analysis is often used because it is easy to apply and easy to understand for most individuals, regardless of academic training or field of endeavour.

 Payback period is usually expressed in years. Start by calculating Net Cash Flow for each year:

There are some main problems with the payback period method:

1. It ignores any benefits that occur after the payback period and, therefore, does not measure profitability.

2. It ignores the time value of money.

3. Additional complexity arises when the cash 9ow changes sign several times; i.e., it contains outflows in the midst or at the end of the project lifetime.

Because of these reasons, other methods of capital budgeting, like net present value, internal rate of return or discounted cash flow, are generally preferred.

Problem-1: The Azad Int. Ltd. is contemplating to invest in a new project that would require procurement of a machine costing Tk. 25,50,000; and a working capital of Tk. 1,00,000. The project is expected provide benefits for five years. The expected profit before depreciation and tax from the project is as below:

Year	Profit before Tax & Depreciation
ls` year	8,50,000
2"a year	7,00,000
3`d year	6,50,000
4"' year	6,00,000
5`h year	4,50,000

 (The policy of the company is to depreciate fixed assets on straight line basis over the period of the asset. Salvage value of the machine is expected to be Tk. 50,000. Assume a 40% tax rate and cost of capital of 10%.)

Required: Determine the acceptability of the project on the basis of

(i) Payback period; (ii) ARR; (iii) NPV; (iv) IRR; (v) Profitability Index.

(The present values of Tk.1 for five years at 10% are 0.9091; 0.8264; 0.7513; 0.6830; 0.6209)

Solution:

Depreciation= Cost-Salvage value/No. of year in lifetime = 25,50,000-50,000/5 = 5,00,000

Total investment= 25,50,000 (Machine price)+1,00,000(Working capital) = 26,50,000

Statement of cash inflow:

Particular	Ist year	2"d year	3`d year	4`h year	5`h year
Profit before Tax & Depreciation Less Depreciation	8,50,000 5,00,000	7,00,000 5,00,000	6,50,000 5,00,000	6,00,000 5,00,000	4,50,000 5,00,000
Profit before Tax Less Tax(~,40%	3,50,000 1,40,000	2,00,000 80,000	1,50,000 60,000	1,00,000 40,000	(50,000) -
Profit after tax Add depreciation	2,10,000 5,00,000	1,20,000 5,00,000	90,000 5,00,000	60,000 5,00,000	(50,000) 5,00,000
Cash before Terminal cash inflow Add Salvage value at 5'h year Add Working capital	7,10,000 - -	6,20,000 - -	5,90,000 - -	5,60,000 - -	4,50,000 50,000 1,00,000
	7,10,000	6,20,000	5,90,000	5,60,000	6,00,000

 Required 1:

Pay Back Period (PBP):

Year	Cash inflow	Cumulative cash inflow
1	7,10,000	7,10,000
2	6,20,000	13,30,000
3	5,90,000	19,20,000
4	5,60,000	24,80,000
5	6,00,000	30,80,000

 

PBP= 4+ (Total investment-4`<sup>h</sup> year cumulative cash inflow)/5`^h year cash inflow = 4+ (26,50,000-24,80,000)/6,00,000 = 4.28 years

 

Required-2:

Averaj!e rate of return:

 ARR= (Average annual profit/Average investment)x 100

_({(2, I 0,000+ I,20,000+90,000+60,000-50,000)/5}/(26,50,000+50,000)/2J x 100  (86,000/13,50,000)x]00

= 6.37%

 Required-3:

Net Present Value (NPV) calculation:

Year	Cash flow	Discount factor a,10%	Present value
1	7,10,000	0.9091	6,45,467
2	6,20,000	0.8264	5,12,368
_	5,90,000	0.7513	4,43,267
	5,60,000	0.6830	3,82,480
5	6,00,000	0.6209	3,72,540
Present value of cash                                     = 23,56,1 16 Less, investment                                            =(26,50,000)
Net Present Value (NPV)                                 (2,93,884)

 Required-4:

Internal Rate of Return (IRR):

Since the NPV at 10%, discounting rate is negative Let us take lower discounting rate 5%.

Therefore,

Present value={7,10,000/(1+0.05)+6,20,000/(1+0.05)²+5,90,000/(1+0.05)³ +5,60,000/(1+0.05)⁴+6,00,000/(1+0.05)⁵}-26,50,000(total investment)

=(6,76,190.48+5,62,358.28+5,09,664.18+4,60,713.39+4,70,115.70) - 26,50,000 (total investment)

= 26,77,488-26,50,000(total investment) =27488.

IRR= A+C/C-D(B-A)

= 5%+27488/27488-(-2,93,884)X(10%-5%)

= 5%+27488/321372x5% = 5%+ 0.0855 X 5%

= 0.05+0.0042 =0.0542 -5.42%

 Required-5:

Calculation of Profitability Index (PI):

P1=PV of cash inflow/PV of investment cost = 23, 56,116/26, 50,000 = 0.889

    = 0.89 (Approximated)

Ans:

i)      Pay Back Period 4.28 years

ii)      ARR= 6.37%

iii)    NPV= (-2,93,884)

iv)     PI = 0.89

Here,

A= Lower discounting rate

B= Higher discounting rate

C= NPV of lower discounting rate

D= NPV of higher discounting rate

 Comments: Out of 5 years project life, the investment will return within 4.28 years, ARR is 6.37% which is lower than cost of capital, PI is less than I and NPV value negative, So the project is not acceptable.

 

Problem-2: The Azom Int. Ltd. is contemplating to invest in a new project that would require procurement of a machine costing Tk. 21,00,000; and a working capital of Tk. 1,00,000. The project is expected to provide benefits for five years. The expected profit before depreciation and tax from the project is as below:

Year	Profit before Tax & Depreciation
1 S` year	7,50,000
2"d year	6,50,000
3`d year	5,50,000
4`" year	5,00,000
5`" year	4,50,000

 

(The policy of the company is to depreciate fixed assets on straight line basis over the period of the asset. Salvage value of the machine is expected to be Tk. 1,00,000. Assume a 50% tax rate and cost of capital of 10%.)

Required: Determine the financial viability of the project on the basis of (i) Payback period; (ii) ARR; (iii) NPV; (iv) IRR; (v) Profitability Index.

(The present values of Tk.1 for five years at 10% are 0.9001; 0.8264; 0.7513; 0.6830: 0.6209)

Solution:

Depreciation= Cost-Salvage value/No. of year in lifetime = 21,00,000-1,00,000/5 = 4,00,000

Statement of investment cost

Total investment= 21,00,000 (Cost of project)+1,00,000(Working capital)

= 22,00,000

Statement of cash inflow

Particular	1'` year	2"' year	3`d year	4`" year	5`" year
Profit before Tax & Depreciation Less Depreciation	7,50,000 4,00,000	6,50,000 4,00,000 _	5,50,000 4,00,000	5,00,000 4,00,000	4,50,000 4,00,000
Profit before Tax	3,50,000	2,50,000	1,50,000	1,00,000	50,000
Less Tax cr,50%	1,75,000	1,25,000	75,000	50,000	25,000
Profit after tax	1,75,000	1,25,000	75,000	50,000	25,000
Add depreciation	4,00,000	4,00,000	4,00,000	4,00,000	4,00,000
Cash before Terminal cash	5,75,000	5,25,000	4,75,000	4,50,000	4,25,000
inflow	-	-	-	-	1,00,000
Add Salvage value at 5`h year	-	-	-	-	1,00,000
Add Working capital
	5,75,000	5,25,000	4,75,000	4,50,000	6,25,000

 

Required -1:

Pay Back Period (PBP):

Year	Cash inflow	Cumulative cash inflow
1	5,75,000	5,75,000
2	5,25,000	11,00,000
3	4,75,000	15,75,000
4	4,50,000	20,25,000
5	6,25,000	26,50,000

 

PBP= 4+ (Total investment-4^th year cumulative cash inflow)/5 ^Ih year cash inflow = 4+ (22,000,000-20,25,000)/6,25,000 = 4.28 years

 

Required-2:

Average rate of return:

 

ARR= (Average annual profit/Average investment)x 100

= [{(I,75,000+1,25,000+75,000+50,000+25,000)/5}/(22,00,000+1,00,000)/2] x100  

= (90,000/11,50,000)X100

= 7.83%

Required-3:

Net Present Value(NPV) calculation:

Ye ar	Cash flow	Discount factor@ 10%	Present value
	5,75,000	0.9091	5,22,732
2	5,25,000	0.8264	4,33,860
3	4,75,000	0.7513	3,56,867
4	4,50,000	0.6830	3,07,350
5	6,25,000	0.6209	3,88,062
Present value of cash inflow                           = 20,08,871 Less, investment                                             =(22,00,000)
Net Present Value (NPV)                                  (1,91,129)

 

 

Required-4:

Internal Rate of Return (IRR):

Since the NPV at 10%, discounting rate is negative, let us take lower discounting rate 5%.

Therefore,

Present value= 5,75,000/(1+0.05)+5,25,000/(1+0.05)²+4,75,000/(1+0.05)³

 

So, NPV

 

+4,50,000/(1+0.05 )⁴+6,25,000/(1 +0.05)⁵

= (5,47,619+4,76,406+4,10,331+3,70,218+4,89,735) = 22,94,309

= 22,94,309-22,00,000

= 94,309.

IRR= A+C/C-D(B-A)

= 5%+94,309/94,309-(-1,19,129)X(10%-5%)

= 5%+94,309/2,85,138x5% = 0.05+ 0.0165                

=6.65%

 

Here,

A=Lower discounting rate

B= Higher discounting rate

C=NPV of lower discounting rate

D= NPV of higher discounting rate

Required-5:

Calculation of Profitability Index (PI):

P1=PV of cash inflow/PV of investment cost = 20,08,871/22,00,000 = 0.91 (Approximate)

Comments: Out of 5 years project life, the investment will return within 4.28 years, ARR is 7.83% which is lower than cost of capital, P1 is less than I and NPV value negative, So the project is not financially viable.

Problem-3: The `X' Int. Ltd. is contemplating to invest in a new project that would require procurement of a machine costing Tk.10,00,000; and no working capital. The project is expected to provide benefits for ten years. The expected profit before depreciation and tax from the project is as below:

 

Year	Profit before Tax & Depreciation
151 year	2,50,000
2"d year	4,00,000
3rd year	4,00,000
4`h year	4,00,000
5'n year	3,50,000
6"' year	3,00,000
7`n year	2,50,000
8th year	2,00,000
9th year	1,50,000
10`h year	1,00,000

 

(The policy of the company is to depreciate fixed assets on straight line basis over the period of the asset. No Salvage value of the machine is expected. Assume a 40% tax rate and cost of capital of 15%.)

Required: Determine the financial viability of the project on the basis of (i) Payback period; (ii) ARR; (iii) NPV; (iv) Profitability Index.

(The present values of Tk.l for five years at 15% are 0.87; 0.756; 0.658; 0.572; 0.497; 0.376; 0.432; 0.327; 0.284; 0.247.

Solution:

Depreciation= Cost-Salvage value/No. of year in lifetime

                = 10,00,000-0/10

= 1,00,000

Statement of investment cost

Total investment= 10,00,000 (Cost of project)+0 (Working Capital)= 10,00,000

(Fi ure in Lac)

1 Particulars	1 st year	' 2nd year	3rd year	' 4th year	5th year	6th year	' 7th year	8th year	' 9th year	1Oth year
Profit before Tax &	2.50	4.00	4.00	4.00	3.50	3.00	2.50	2.00	1.50	1.00
Depreciation Less Depreciation	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
Profit before Tax	1.50	3.00	3.00	3.00	2.50	2.00	1.50	1.00	0.50	-
Less Tax(a-b,40%	0.525	1.05	1.05	1.05	0.875	0.70	0.525	0.35	0.175
Profit after tax	0.975	1.95	1.95	1.95	1.625	1.30	0.975	0.65	0.325	-
Add des reciation	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
Cash before Terminal	-	-	-	-	-	-	-	-	-	-
cash inflow
Add Salvage value	-	-	-	-	-	-	-	-	-	-
Add working capital	-	-	-	-	-	-	-	-	-	-
Net cash inflow	1.975	2.95	2.95	2.95	2.625	2.30	1.975	1.65	1.325	1.00

 

Note- Please write full fiaure at exam script Required 1:

Pay Back Period (PBP):

Year	Cash inflow	Cumulative cash inflow
	1 ,97,500	1,97,000
	2,95,000	4,92,500
3	2,95,000	7,87,500
4	2,95,000	10,82,500
	2,62,500	13,45,000
	2,30,000	15,75,000

 

PBP   = 3 year+ (Total investment-3`<sup>d</sup> year cumulative cash inflow)/4`^h year cash inflow

= 3 year+ (10,00,000-7,87,500)/2,95,000

= 3 year+0.72 = 3.72 years

Required-2:

Avera2e rate of return

ARR   = (Average annual profit/Average investment)x100

= [{(97,500+1,95,000+1,95,000+1,95,000+1,62,500+1,30,000+97,500+65,000+32,500)/10} /(10,00,000/2)] x 100

=(1,17,000/5,00,000)x]00

=23.4%

 

Required-3:

Net Present Value (NPV) calculation

NPV =(1,97,SOOX0.87)+ (2,95,OOOX0.756)+ (2,95,OOOX0.658)+ (2,95,OOOX0.572)+ (2,62,SOOX0.497)+ (2,30,OOOX0.376)+ (1,97,SOOX0.432)+ (1,65,OOOX0.327)+ (I,32,SOOX0.284)+ (1,00,OOOX0.247)] -10,00,000 (total Investment)

= {( l ,71,825+2,23,020+1,94,110+1,68,740+ I ,30,463+99,360+74,260+53,955+3 7,630+24,700)

=11,78,460.50}-10,00,000 (total Investment)

So, NPV =1 1,78,460.50-10,00,000 (total Investment)

= 1,78,460.50

Reg u ired-4:

Calculation of Profitability Index (PI)

P(=PV of cash inflow/PV of investment cost

= 11,78,460.50/10,00,000

= 1.178486

= 1.18 (Approximate)

Statement of present value of payback period

Year	Cash flow	Discount factoroy 15%	Present value	Cumulative amount of PV~'
1	,97,500	0.87	1 71,825	1,71,825
_	2,95,000	0.756	2,23,020	3,94845
	2,95,000	0.658	1,94,110	5,88,955
	2,95,000	0.57?	1,68,740	7,57,695
	2,62,500	0.497	1,30,463	8,88,158
	2,30,000	0.376	99,360	9,87,518
7	1,97,500	0.432	74,260	10,61,778
~ 8	1 65,000	0.327	53,955	1 1,15,733
9	,32,500	0.284	37,630	11,53,366
10	1,00,000	0.247	__ 24,700	1 1,78,063                  ;

 

PVPE3P= 6 years+(Remaining amount)/PV of 7^1h year

 

Total Present value

=1 1,78,063

 

=	6 years+ (10,00,000-9,87,518)/74,260
=	6 years+ 0.168
=	6.168 years
=	6.17 years (approx)

 

Ans.:
v)		Pay Back Period 3.72 Years
vi)		ARR= 23.8%
vii)		NPV= 1,78,460.50
viii)		PI    = 1.18

 

Comments: Out of 10 years project life, the investment will return within 3.72 years, ARR is 23.8% which is higher than cost of capital, PI is greater than I and NPV value positive, So the project is acceptable.

Problem-4 (May11,12): The Chad Int. Ltd. is contemplating to invest in a new project that would require procurement of a machine costing Tk. 18,50,000; and a working capital of Tk. 1,50,000. The project is expected to provide benefits for nine years. The expected profit before depreciation and tax from the project is as below:

Year	Profit before Tax & Depreciation
ls year	3,50,000
2~ year	2,50,000
3" year	3,50,000
4`h year	3,00,000
5 year	2,50,000
6"' year	2,50,000
71h year	3,50,000
8 year	2,00,000
9th year	1,50,000

 

(The policy of the company is to depreciate fixed assets on straight line basis over the period of the asset. Salvage value of the machine is expected to be Tk50,000. Assume a 40% tax rate and cost of capital of 12%.)

Required: Determine the viability of the project on the basis of

(i) Payback period; (ii) ARR; (iii) NPV; (iv) Profitability Index.

(The present values of Tk.l for five years at 12% are 0.8929; 0.7972; 0.7181; 0.6355; 0.5674: 0.5066; 0.4523; 0.4039; 0.3606.

Solution:

 

Here. Depreciation= Cost-Salvage value/No. of year in lifetime - 18,50,000-50,000/9 = 2,00,000

 

Total investment = 18,50,000 (Machine price)+1,50,000(Working capital)

                                ⁼ 20,00.000

Statement of cash inflow

(Fi ure in Lac)

Particulars	1st year	2nd year	3rd year	4th year	5th year	6th year	7th year	8th year	9th year
Profit before Tax & Depreciation Less Depreciation	3.50 2.00	4.50 2.00	4.50 2.00	3.00 2.00	2.50 2.00	2.50 2.00	3.50 2.00	2.00 2.00	1.50 2.00
Profit before Tax Less Tax(&,40%	1.50 0.60	2.50 1.00	2.50 1.00	1.00 0.40	0.50 0.20	0.50 0.20	1.50 0.60	- -	(0.50) -
Profit after tax Add depreciation	0.90 2.00	1.50 2.00	1.50 2.00	0.60 2.00	0.30 2.00	0.30 2.00	0.90 2.00	- 2.00	(0.50) 2.00
Cash before Terminal cash inflow	2.90	3.50	3.50	2.60	2.30	2.30	2.90	2.00	1.50
Add Salvage value	-	-	-	-	-	-	-	-	0.50
Add working capital	-	-	-	-	-	-		-	1.50
Net cash inflow	2.90	3.50	3.50	2.60	2.30	2.30	2.90	2.00	3.50

 

Note- Please write full figure at exam script]

Required l:

Pay Back Period (PBP)

Year	Cash inflow	Cumulative cash inflow
I	2,90,000	2,90,000
	3,50,000	6,40,000
	3,50,000	9,90,000
	2,60,000	12,50,000
5	2,30,000	14,80,000
6	2,30,000	17,10,000
	2,90,000	20,00,000
8	2,00,000	22,00,000
	3,50,000	25,50,000

Pay Back Period= 7 Years Required-2:

Averaue rate of return

 

ARR= (Average annual profit/Average investment)X100

=[{(90,000+1,50,000+1,50,000+60,000+30,000+30,000+90,000-50,000)/9} /20,00,000/2] X100

= (61,1 1 1 / 10,00,000)X 100

= 6.11%

Required-3:

 

Required-3:

Net Present Value(NPV) calculation

Year	Cash flow	Discount factor@ 12%	Present value
1	2,90,000	0.8929	2,58,941
2	3,50,000	0.7972	2,79,020
3	3,50,000	0.7181	2,51,335
4	2,60,000	0.6355	1,65,230
5	2,30,000	0.5674	1,30,502
6	2,30,000	0.5066	1,16,518
7	2,90,000	0.4523	1,31,167
8	2,00,000	0.4039	80,780
9	3,50,000	0.3606	1,26,210
Present value of cash                               = 15,39,703 Less, investment                                      =(20,00,000)
Net Present Value (NPV)                           (4,60,297)

 

Required-4:

Calculation of Profitability Index (PI) P1=PV of cash inflow/PV of investment cost

= 15,39,703/20,00,000 = 0.7698
Ans.:
ix)		Pay Back Period 7 Year
x)		ARR= 6.11%
x0		NPV= (-460297)
xii)		P1 = 0.7698

 

 

Comments: Out of 9 years project life, the investment will return within 7 years, ARR is 6.11% which is lower than cost of capital, Pl is less than I and NPV value negative. So the project is not viable.

Problem-(Nov' 11): A large size Company is considering investment in a project that costs Tk. 4,00,000. The estimated salvage value is zero; tax rate is 35%. The company uses straight line depreciation and the proposed project has cash flows before tax (CFBT) as follows:

Year	Profit before Tax & Depreciation
1" vear	1,00,000
2n`' year	1,00,000                                          ,
3"d year	1 ,50,000
4th year	1,50,000
5`i' year	2,50,000

 

_Required: Determine the following:

(i) Payback period; (ii) ARK; (iii) NPV at 15% ; (iv) Profitability Index; (v) Comments on the basis of result.

PVF at 15% : 0.870; 0.756; 0.658; 0.572; 0.497) Solution:

Depreciation- Cost-Salvage value/No. of year in lifetime

= 4,00.000-0/5 = 80, 000/- Statement of cash inflow:
Particulars		1st Year		2nd year	3rd year       4th year		5th year
I Profit before tax & Depreciation		1_00,000		1.00,000	1.50.000	1.50.000	2.50.000
Less Depreciation		80.000		80,000	80.000	80.000	'   80.000
Profit before tax C Profit beliOrc Tax                                         ~		20.000		20,000	70.000	70.000	} 1.70.000
Less tax @ 35%		7.000		7,000	24.500	24.500	'_ 5 9.5 00
I Profit after tax		13,000		13,000	45,500	45.500	1,10,500
Add depreciation		80.000		80,000 '	80.000	80.000	80,000
cash inflow		93.000		93,000	1.25,500         125.500		1.90.500

 

Required 1:

Pav Back Period (PBP):

Year	Cash inflow	Cumulative cash inflow
1	93,000	93,000
2	93,000	1,86,000
3	1,25,500	3,11,500
4	1,25,500	4,37,000
5	1,90,500	6,27,500

 

 

PBP = 3+ (Total investment-3r^d year cumulative cash inflow)/4th year cash inflow

      = 3+ (4,00,000-3,11,500)/1,^;-5,500

= 3+0.705

               ⁼3.71

So,Pay Back Period = 3.71 years

 

Required-2:

Average rate of return:

ARR= (Average annual profit/Average investment)X 100

=({(13,000+13,000+45,500+45,500+1,10,500)/5,^1./(4,00,000)/2] x 100

 = (45,500/2,00,000)X 100

= 22.75%

Required-3:

Net Present Value (NPV) calculation:

Year	Cash flow	Discount factor( 15%	Present value
1	93,000	0.870	80,910
2	93,000	0.756	70,308       -
3	1,25.500	0.658	82,579
4	1,25,500	0.572                                 1	71,786
5   1,90,500       I		0.497                                 1	94,679
I Present value of cash                              = 4,00,262
Less investment                                                                                  = (4,00,000
Net present value (NPV)                                                                    = 262

 

Required-4:

Calculation of Profitabilitv Index (PI): P1-PV of cash intlo~e/PV of investment cost

-- 4.00?62/4,00,000 = 0.889 = 1.000655
Ans.:
i)		Pay Back Period 3.71 years
ii)		ARR=22.75%
iii)		NPV= 262
iv)		P1 =1.000655

 

Comments: Out of 5 years project life, the investment will return within 3.71 years, ARR is 22.75% which is higher than cost of capital, P1 is greater than I and NPV value positive. So the project is acceptable.

 

Problem-5: ABC Company has limited funds available for investment and must ration the funds among five competing projects. Selected information on the five projects are given below:

 

Project	Investmen t required	Net Present Value(NPV)	Life of the project(years)	Internal Rate of Return (%)
Project C	8,00,000	2,21,615		18
Project B	6,75,000	2,10,000	12	16
Project A	5,00,000	1,75,175	7	20
Project D	7,00,000	1,52,544	3	22
Project E	9,00,000	(52,176)	6	8

 

[The ABC company's cost of capital is 10% (the net present values above have been computed using a 10% discount rate.) The wants your assistance in determining which project to accept first which to accept second and so forth.]

 

Solution:

 

(1) Profitability Index Calculation

 

We know,

Profitability Index Calculation

PI=PV of cash inflow/PV of cash outflow

For project A:

Present value= NPV+Investment = 2,21,615+8,00,000 = 10,21,615

So, Pl= 10,21,615/8,00,000 = 1.27 > 1

For project B:

Present value= NPV+Investment = 2,10,000+6,75,000 = 8,85,000

So, Pl= 8,85,000/6,75,000 = 1.31> 1

For project C:

Present value= NPV+Investment = 1,75,175+5,00,000 = 6,75,175

 

So, PI= 6,75,175/5,00,000 = 1.35> 1

 

For project D:

 

Present value= NPV+Investment = 1,52,544+7,00,000 = 8,52,544

 

So, PI= 8,52,544/7,00,000 = 1.22 > 1

 

For project E:

 

Present value= NPV+Investment = 9,00,000+(-52,176) = 8,47,824

 

So, PI= 8,47,824/9,00,000 = 0.94< 1

 

Since ABC has limited funds. So, we have to choose the best alternative and the ranking of preference are:­

Project	Rating
Project A=135	1
Project B=1.31	2
Project C=1.27	_ 3
Project D=1.22	4
Pr~ect E=0.94	5

 

Project E should not be accepted because PI is than 1(<1)

(2) Net Present Value(NPV)

(i) Ranking of the 5(five) projects in terms of Net Present Value(NPV) are as follows:­

 

Project	NPV	Rating
Project A	2,21,615	1
Project B	2,10,000
Project C	1,75,175
Project D	1,52,544	4
Project E	(52,176)

 

 

(3) Profitability Index (PI)

(ii) Ranking of the 5(five) projects in terms of Profitability Index (PI) are as follows:­

Project	PI	Rating
Project C	1.35	1
Project B	1.31	2
Project A	1.27	3
Pro'ect D	1.22	4
, Pr~ject E	0.94	5

 

(i) Ranking of the 5(five) projects in terms of Internal Rate of Return(IRR) are as follows:­

Project	NPV	Rating
Project D	-22%	1
Project C	20%	2
Project A	18%	3
Project B	16%	4
Project E	8%	5

 

(4) The ranking in terms of Net Present Value (NPV) should be given preference. Because

(i)      NPV gives accurate results because of consider all cash flows,

(ii)     IRR gives misleading in non conventional investment project.

(iii)     IRR also gives multiple rates.

(iv)    Profitability Index(PI) is crude way to cope up the rate and it gives misleading if investment made reversal time.

 

(5) If capital rationing situation prevails in the company with a budget constraints of the 1.5 million, we should prefer project A and Project D

Because

(i)      Project A gives higher NPV

(ii)     Project D gives highest IRR

(iii)    Since Project B gives second highest NPV but it takes 12 years

(iv)    In considering PI the Project C is the best but some portion of our investment is

being idle if project C is chosen. SO project A and D would be best preference.

(6) The causes of difference in outcomes of the project under NPV and IRR methods are as follows:­

(i) NPV consider cash flows at the cost of capital rate over the year but IRR deals re-investment rate that may not prevail in the market.

(ii) If the outcome or inflows are great in recent year and smaller in later year than IRR gives misleading

(iii) For non conventional project, IRR gives misleading for that reason the difference is made.

Discuss the importance of capital budgeting for taking investment decision

 The importance of capital budgeting for taking! investment decision:

 1.As large sum of money is involved which influences the profitability of the firm making capital budgeting an important task.

 2.Long term investment once made can not be reversed without significance loss of invested capital. The investment becomes sunk and mistakes, rather than being readily rectified,must often be born until the firm can be withdrawn through depreciation charges or liquidation. It influences the whole conduct of the business for the years to come.

 3.Investment decision are the base on which the profit will be earned and probably measured through the return on the capital. A proper mix of capital investment is quite important to ensure adequate rate of return on investment, calling for the need of capital budgeting.

 4. The implication of long term investment decisions are more extensive than those of short run decisions because of time factor involved, capital budgeting decisions are subject to the higher degree of risk and uncertainty than short run decision.

Define capital budgeting. Discuss the techniques of capital budgeting.

 Capital budgeting: Capital budgeting is the planning process used to determine whether an organization's long term investments such as new machinery, replacement machinery, new plants, new products, and research development projects are worth pursuing. It is budget for major capital, or investment, expenditures.

 Many formal methods are used in capital budgeting, including the techniques such as:

 ·        Accounting rate of return

·       Payback period

·        Net present value

·        Profitability index

·        Internal rate of return

·        Modified internal rate of return

·        Equivalent annuity

·        Real Options Valuation

These methods use the incremental cash flows from each potential investment, or project. Techniques based on accounting earnings and accounting rules are sometimes used - though economists consider this to be improper - such as the accounting rate of return, and "return on investment." Simplified and hybrid methods are used as well, such as payback period and discounted payback period.

 Net present value

 Each potential project's value should be estimated using a discounted cash flow (DCF) valuation, to find its net present value (NPV). This valuation requires estimating the size and timing of all the incremental cash flows from the project. The NPV is greatly affected by the discount rate, so selecting the proper rate - sometimes called the hurdle rate - is critical to making the right decision. The hurdle rate is the Minimum acceptable rate of return on an investment. A common practice in choosing a discount rate for a project is to apply a WACC that applies to the entire firm, but a higher discount rate may be more appropriate whern a project's risk is higher than the risk of the firm as a whole.

Internal rate of return

The internal rate of return (IRR) is defined as the discount rate that gives a net present value (NPV) of zero. It is a commonly used measure of investment efficiency.

The IRR method will result in the same decision as the NPV method for projects in an unconstrained environment, in the usual cases where a negative cash flow occurs at the start of the project, followed by all positive cash flows. In most realistic cases, all independent projects that have an IRR higher than the hurdle rate should be accepted.

In a budget-constrained environment, efficiency measures should be used to maximize the overall NPV of the firm. Some managers find it intuitively more appealing to evaluate investments in terms of percentage rates of return than dollars of NPV.

 

Equivalent annuity method

 

The equivalent annuity method expresses the NPV as an annualized cash flow by dividing it by the present value of the annuity factor. It is often used when assessing only the costs of specific projects that have the same cash inflows. In this form it is known as the equivalent annual cost (EAC) method and is the cost per year of owning and operating an asset over its entire lifespan.

 The use of the EAC method implies that the project will be replaced by an identical project.

 The assumption of the same cash flows for each link in the chain is essentially an assumption of zero inflation, so a real interest rate rather than a nominal interest rate is commonly used in the calculations.

 Profitability index

 Profitability index (PI), also known as profit investment ratio (PIR) and value investment ratio (VIR), is the ratio of payoff to investment of a proposed project. It is a useful tool for ranking projects because it allows you to quantify the amount of value created per unit of investment.

 The ratio is calculated as follows:

Profit abilit v index - PV of future cash flows Initial investment

 Assuming that the cash flow calculated does not include the investment made in the project, a profitability index of 1 indicates breakeven. Any value lower than one would indicate that the project's PV is less than the initial investment. As the value of the profitability index increases, so does the financial attractiveness of the proposed project.

 Rules for selection or rejection of a project:

 ·         If PI > 1 then accept the project

·         If PI < 1 then reject the project

Illustrate Break even point with Break even Chart

 Break even point can also be computed graphically. This is known as Break even Chart (BEC). It portrays view of the relationship between cost, output and profit. The Break even point indicated in the chart will be one at which total cost line and total revenue line (sales line) intersects. To illustrate Break even point with the help of Break even Chart the data given in the table earlier have been used:

 Fig. Break even point with Break even Chart

 

Units

Output (000 Units)

Illustrate about Contribution Margin (CM) Ratio with example

 A relationship between the cost, volume and profit is the contribution margin. The contribution margin is the revenue excess from sales over variable costs. The following chart shows the income statement of a company X, which has been prepared to show its contribution margin:

Sales	$1,000,000
(-) Variable Costs	$600,000
Contribution Margin	$400,000
(-) Fixed Costs	$300,000

 

Income from Operations $100,000

Uses: The concept of contribution margin is particularly useful in the planning of business because it gives an insight into the potential profits that can generate a business.

 

Contribution MarZin (CM) Ratio: The margin contribution can also be expressed as a percentage. The contribution margin ratio, which is sometimes called the profit-volume ratio, indicates the percentage of each sales dollar available to cover fixed costs and to provide operating revenue. For the company Fusion, Inc. the contribution margin ratio is 40%, which is computed as follows:

 Contribution Margin Ratio = (Sales - Variable Costs)/Sales

 The contribution margin ratio measures the effect on operating income of an increase or a decrease in sales volume. For example, assume that the management of Fusion, Inc. is studying the effect of adding $80,000 in sales orders. Multiplying the contribution margin ratio (40%) by the change in sales volume ($80,000) indicates that operating income ~\ ill increase $32,000 if additional orders are obtained. To validate this analysis the table below shows the income statement of the company including additional orders:

Sales	$1,080,000
(-) Variable Costs	$648,000	(1,080,000 x 60%)
Contribution Margin	$432,000	(1,080,000 x 40%)
(-) Fixed Costs	$300,000

 Income from Operations $132,000

Variable costs as a percentage of sales are equal to 100% minus the contribution margin ratio. Thus, in the above income statement, the variable costs are 60% (100% - 40%) of sales, or $648,000 ($1'080,000 X 60%). The total contribution margin $432,000, can also be computed directly by multiplying the sales by the contribution margin ratio ($ I'080,000 X 40%).

Application/Necessities of Break even analysis, Write some terms relating to Break even analysis

 Application/Necessities of Break even analysis: The break-even point is one of the simplest yet least used analytical tools in management.

(1) It helps to provide a dynamic view of the relationships between sales, costs and profits.

(2) A better understanding of break-even, for example, is expressing break-even sales as a percentage of actual sales-can give managers a chance to understand when to expect to break even.

(3) The break-even point is a special case of Target Income Sales, where Target Income is 0 (breaking even). This is very important for financial analysis.

 Q. Write some terms relating to Break even analysis.  Ans:

  For understanding the calculation of Break even point, the following terms should be kept at the back of one's mind:

 FC= Fixed Cost

VC=Variable Cost

TC=Total Cost

TR=Total Revenue

TS=Total sales

CM=Contribution Margin

P= Profit

TC=FC+VC

P =TR - TC or TS -TC or S- TC

Contribution Margin (CM)= Selling price per unit - Variable cost per unit.

 Formula-1:

Break even point=Total fixed cost/Unit contribution

Or

Break even point=Fixed cost/ (Selling price per unit - Variable cost per unit).

Formula-2:

Fixed Cost

Total Sales - Variable cost

Total Sales

Or _BEP=       Fixed Cost     

          Contribution Margin ratio

CMR = Contribution Margin ratio

Sales price per unit

Define margin of safety, What is Contribution Margin

 Ans: Margin of Safety:Margin of safety represents the strength of the business. It enables 1 business to know what is the exact amount it has gained or lost and whether they are ova or below the break even point.

Margin of safety = (current output - breakeven output)

Margin of safety% = (current output - breakeven output)/current output x 100

0. What is Contribution Margin (CM)? Ans.:

Contribution Margin:

 Units

 

.The Unit Contribution Margin (CM) is the quantity of unit sales price (P) minus the quantity of unit variable cost (V ) is of interest in its own right, it is the marginal profit per unit, or alternatively the portion of each sale that contributes to Fixed Costs. The Break-Even Point can alternatively be computed as the point where Contribution equals Fixed Costs. Thus the break-even point can be more simply computed as the point where Total Contribution = Total Fixed Cost.

Total Contribution = Total Fixed Costs

Unit Cotttributiou x Number of Units = Total Fixed Costs

Total Fixed Costs

Number of Units =       Unit  Contribution

In currency units (sales proceeds) to reach break-even, one can use the above calculation and multiply by Price, or equivalently use the Contribution Margin Ratio (Unit Contribution Margin over Price) to compute it as:

                                                                      Fixed Costs /

Break-even(in Sales}                                       C/P

R=C,

Where R is revenue generated,

C is cost incurred i.e. Fixed costs + Variable Costs or Q * P(Price per unit) = TFC + Q VC(Price per unit), Q * P - Q * VC = TFC, Q * (P - VC) = TFC, or, Break Even Analysis Q = TFC/c/s ratio=Break Even