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IPCC_34e_F.M_ Capital Budgeting_Assignment Solutions ________________1
No.1 for CA/CWA & MEC/CEC MASTER MINDS
2. CAPITAL BUDGETING
SOLUTIONS TO ASSIGNMENT PROBLEMS
Problem No.1 W.N.-1: Calculation of depreciation per annum
Depreciation p.a. =
Life
ValueScrap - Cost510,00080,000 = Rs.14,000 p.a.
W.N.-2: Calculation of PAT p.a.
Year PBDT Depreciation PBT / PAT (PBDT – Dep.)
1 20,000 14,000 6,000
2 40,000 14,000 26,000
3 30,000 14,000 16,000
4 15,000 14,000 1,000
5 5,000 14,000 (9,000)
Since Income tax rate is not given in the problem, PBT = PAT.
Calculation of ARR
Step-1: Calculation of Average Profit after Tax
Average Profit after tax=5
000,9000,10000,16000,26000,6 = Rs. 8,000 p.a
Step-2: Calculation of Average Investment
Average investment = (21
Initial Cost - Salvage Value) + Salvage Value
= (21
80,000 - 10,000) + 10,000 = Rs.45,000
Step-3: Calculation of Accounting Rate of Return (ARR) (Return on Avg. Capital Employed)
ARR = 45,0008,000x100
investmentAverageAveragePAT = 17.77%
Step-4: Return on Original Capital employed
Return on Original Capital employed = x100InvestmentOrginal
PATAverage= 100x
000,80000,8
= 10%
Problem No.2
Payback reciprocal = %20000,20
100X000,4
The above payback reciprocal provides a reasonable approximation of the internal rate of return, i.e. 19%.
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Problem No.3
(i) Payback Period of Projects
Particulars C0 C1 C2 C3
A (10,000) 6,000 2,000 2,000 3 years
B (10,000) 2,500 2,500 5,000 3 years
C (3,500) 1,500 2,500 1 year and 9.6 months
D (3,000) 0 0 3,000 3 years
i.e. 000,2x500,212
(ii) If standard payback period is 2 years, Project C is the only acceptable project. But if standard payback period is 3 years, all the four projects are acceptable.
(iii) Discounted Payback Period (Cash flows discounted at 10%)
A 10,000 + 5,454.6 + 1,652.8 + 1,502.6 + 8,196
390,1x196,812years3 = 3 years and 2 months
B 10,000 + 2,272.75 + 2,066 + 3,756.5 + 5,122.50
75.904,1x55.122,5
12years3 = 3 years and 4.6 months
C 3,500 + 1,363.65 + 2,066 + 375.65 + 3,415
35.70x65.375
12years2 =2 years and 2.25 months
D 3,000 + 0 + 0 + 2,253.9 + 4,098
10.746x098,412years3 =3 years and 2.18 months
If standard discounted payback period is 2 years, no project is acceptable on discounted payback period criterion.
If standard discounted payback period is 3 years, Project ‘C’ is acceptable on discounted payback period criterion.
Problem No.4
W.N. 1: Calculation of depreciation per annum
Depreciation p.a. =
Life
ValueScrap - Cost =
50000,80
= Rs.16,000 p.a.
Calculation of NPV using Incremental approach Step-1: Calculation of Present Value of Cash Outflows:
Particulars Amount
Investment in new equipment 80,000
Additional working capital 1,50,000
Total 2,30,000
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Step-2: Calculation of Present Value of Operating Cash Inflows:
Particulars Amount Rs. Amount Rs.
Incremental net cash in flow Less: additional wages Depreciation(w.n.1) Incremental PBT Less: Tax @ 40 % Incremental PAT Add: depreciation Incremental CFAT p.a
40,000 16,000
1,00,000
56,000 44,000 17,600 26,400 16,000 42,400
Therefore, Present Value of Operating Cash Inflows = 42,000 X PVAF(13%,5)
= 42,400 X 3.517
= 1,49,120 Step 3: Present Value of Terminal Cash Inflows =
Gsp or Nsp on sale of initial equipment = 0
Recovery of additional working capital = 1,50,000 1,50,000
PV there off = 1,50,000 * PVF (13%, 5)
= 1,50,000 X 0.543
= 81,450 Step 4: Calculation of NPV
NPV = PV of cash inflows – PV of cash outflows
= PV of Operating Cash Inflows +PV of Terminal Cash Inflows – PV of cash outflows.
= 1,49,120 + 81,450-2,30,000
= Rs.570 Conclusion: Since NPV is positive it is advisable to accept.
Problem No.5 W.N – 1: Calculation of depreciation p.a. (Rs. in Lakhs)
Depreciation p.a. =
Life
ValueScrap - Cost=
80140
= Rs. 17.5 lakhs p.a.
On supplementary equipment =6
110 = 1.5 lakhs pa
Calculation of NPV using Incremental approach
Step-1: Calculation of Present Value of Cash Outflows:
Particulars Amount
Cost of initial equipment Cost of additional working capital Less: tax free subsidy from government
140 15
155 20
135
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Add: cost of supplementary equipment - 10 Present value there off - 10* pvf ( 12% , 2 ) - 10* 0.797 Present value of cash out flows
7.97 142.97
Step-2: Calculation of Present Value of Operating Cash Inflows
Selling price per unit = 100
Less: - variable cost @ 40% = 40
Contribution per unit = 60
Particulars Y1 Y2 Y3 to 5 Y6 to 8
a. Sales volume (lakhs of unit) 0.8 1.2 3.0 2.0
b. Total contribution ( a * Rs. 60 per unit) 48 72 180 120
c. Fixed cost 16 16 16 16
d. Advertisement cost 30 15 10 4
e. Depreciation (WN – 1) 17.5 17.5 19(17.5+1.5) 19
f. PBF (b-c-d-e) (loss) (15.5) 23.5 135 81
g. Tax @ 50% (7.75) 11.75 67.5 40.5
h. PAT (f-g) (7.75) 11.75 67.5 40.5
i. CFAT (h+e) 9.75 29.25 86.5 59.5
j. PVF @ 12 % 0.893 0.797 1.915 1.363
k. Present value 8.706 23.31 165.64 278.765
Therefore, Present Value of Operating Cash Inflows = Rs.278.765 Present value factor for years 3 to 5 = PVF (12% , 3) + PVF (12%, 4) + PVF (12%, 5)
= 0.712+0.636+0.567
= 1.915
(or)
PVAF (12%, 5) - PVAF (12%, 2)
= 3.605 - 1.690
= 1.915 Present value factor for years 6 to 8 = PVF ( 12% , 6) + PVF (12%, 7) + PVF (12%, 8)
= 0.507+0.452+0.404
= 1.363
(or)
PVAF(12% , 8) - PVAF (12%, 5)
= 4.968 - 3.605
= 1.363 Step-3: Present Value of Terminal Cash Inflows =
Gsp or Nsp on sale of initial equipment - 0
Gsp or Nsp on sale of supplementary equipment - 1
Recovery of working capital - 15
16 Pv there off = 16 * PVF (12%, 8)
= 16 * 0.404
= 6.464
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Step-4: Calculation of NPV
NPV = PV of cash inflows – PV of cash outflows
= PV of Operating Cash Inflows +PV of Terminal Cash Inflows – PV of cash outflows.
= 278 + 65 – 6.464 = Rs. 142.97 Conclusion: Since NPV is positive it is advisable to accept the project. Note: It is given that the company has other profitable businesses and the loss from one business can be set off against profit of other business. Alternatively it can also be assumed that the loss is carried forward and setoff against future profit.
Problem No.6
Calculation of NPV
a. Step 1: Calculation of Present Value of Cash Outflows:
Particulars Amount
Cost of machinery 4,00,000
Present Value of Cash Outflows 4,00,000
Step 2: Calculation of Present Value of Operating Cash Inflows:
Particulars Amount
a. Sales volume b. Contribution per unit (10-6) c. Total contribution (axb) d. Fixed cost e. CFAT (c-d)
40,000 units Rs.4
1,60,000 20,000
1,40,000 p.a
PV thereof = 1,40,000 X PVAF(15%,6)
= 1,40,000 X 3.784 = 5,29,760
Step-3: Present Value of Terminal Cash Inflows
G.S.P/N.S.P on sale of machinery = 20,000
PV thereof = 20,000 X PVF(15%,6)
= 20,000 X 0.432
= 8,640
Step-4: Calculation of NPV
NPV = PV of cash inflows – PV of cash outflows
= PV of Operating Cash Inflows +PV of Terminal Cash Inflows – PV of cash outflows.
= 5,29,760+8,640-4,00,000
= 1,38,400
Conclusion: Since NPV is positive it is advisable to accept the project.
b. Let, x represents the sale volume required to justify the project. The project is acceptable if NPV is at least equal to zero
Step-1: same as above – 4,00,000.
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Step-2: present value of operating cash inflows
Particulars Amount (Rs.)
a. Sales volume X unit
b. Contribution per unit (10 – 6) 4
c. Total contribution 4X
d. Fixed cost 20,000
e. CFAT (c-d) 4X-20,000
Present value there of = (4X – 20,000) * PVAF (15%, 6 years)
= (4X – 20,000) *3.784 Step-3: same as above – 8,640 Step-4: Finding the value of X Since NPV is ‘0’ then present value of cash inflows = present value of cash outflows present value of operating cash inflows + present value of terminal cash inflows = present value of cash out flows
(4X – 20,000) * 3.784 + 8,640 = 4,00,000
(4X – 20,000) = 1,03,424
4X = 1,23,424
X = 30,856 units pa
Problem No.7 Given information:
Project Investment NPV
A 1,00,000 1,25.000
B 1,50,000 45,000
A&B 2,50,000 2,00,000
C 1,50,000 90,000
a. Selection of the projects if the firm has no budget constraint: Given that all the projects have positive NPV therefore it is beneficial to select all the projects I.e A,B & C.
b. Selection of projects if there is a budget constraint of 2,50,000:
Combination NPV
A&B 2,00,000
A&C 2,15,000(1,25,000+90,000)
Since NPV is more in case of projects A&C, it is beneficial to invest in project A&C.
Problem No.8
W.N - 1: Calculation of depreciation per annum
Cost of Machinery 2,50,000
Less: Salvage value 30,000
Depreciable amount 2,20,000
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Sum of the years digits = 1 + 2 + 3 + …….. + 10 = 55.
Dep. for 1st year = 10x
55000,20,2
= Rs.40,000 2nd
year = 9x55
000,20,2 = Rs.36,000
3rd
year = 8x55
000,20,2 = Rs. 32,000 4
th year = 7x
55000,20,2
= Rs. 8,000
5th
year = 6x55
000,20,2 = Rs.24,000
W.D.V at the end of 5th year = Cost – depreciation = 2,50,000 – 1,60,000 = Rs. 90,000
Book value of machine after capital expenditure = 90,000 + 60,000 = Rs. 1,50,000
Depreciable amount from 6th to 10th year = 1,50,000 – 30,000 = Rs. 1,20,000 Sum of the years digits = 1 + 2 + 3 + 4 + 5 = 15
Dep. for 6th year = 5x
15000,20,1
= Rs. 40,000 7th year = 4x
15000,20,1
= Rs. 32,000
8th year = 3x
15000,20,1
= Rs. 24,000 9th year = 2x
15000,20,1
= Rs. 16,000
10th year = 1x
15000,20,1
= Rs. 8,000
Calculation of NPV
Step-1: Calculation of Present Value of Cash Outflows
Particulars Amount
Cost of Machinery Add: Working capital Add: Cost of Additional equipment [60,000 x PVF (20%, 5y)]
2,50,000 50,000 24,120
Present value of Cash Outflows 3,24,120
Step-2: Calculation of Present Value of Operating Cash Inflows. (Rs. in Lakhs)
Particulars Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10
PBDT Less: Dep.(W.N-1)
1.0 0.4
1.0 0.36
1.0 0.32
1.0 0.28
1.0 0.24
1.0 0.40
1.0 0.32
1.0 0.24
1.0 0.16
1.0 0.08
P.B.T Less: Tax @ 40%
0.6 L 0.24 L
0.64 0.256
0.68 0.272
0.72 0.288
0.76 0.304
0.60 0.24
0.68 0.272
0.76 0.304
0.84 0.336
0.92 0.368
P.A.T Add:Depreciation
0.36 0.4
0.384 0.36
0.408 0.32
0.432 0.28
0.456 0.24
0.36 0.40
0.408 0.32
0.456 0.24
0.504 0.16
0.552 0.08
C.F.A.T. X P.V.F (20%, n)
0.76 0.833
0.744 0.694
0.728 0.579
0.712 0.482
0.696 0.402
0.76 0.335
0.728 0.279
0.696 0.233
0.664 0.194
0.632 0.162
P.Value 0.634 0.516 0.422 0.343 0.279 0.255 0.203 0.162 0.128 0.102
Therefore, Present Value of operating cash inflows = Rs.3,04,498
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Step-3: Calculation of Present Value of Terminal Cash Inflows (At the end of the project)
Particulars Amount
G.S.P/N.S.P on sale of machinery Add: Recovery of working capital
30,000 50,000
Total of Terminal Cash Inflows 80,000
Present Value thereof = 80,000 X PVF (20%, 10y) = 80,000 X 0.162 = Rs.12,960
Step-4: Calculation of NPV
NPV = PV of cash inflows – PV of cash outflows
= PV of Operating Cash Inflows + PV of Terminal Cash Inflows – PV of Cash Outflows
= 3,04,498 + 12,960 – 3,24,120 = - Rs. 6662 Conclusion: Since NPV is negative it is not advisable for the company to accept the project. Assumptions:
Cash flows are assumed to accrue at the end of each year.
Interim cash inflows at the end of each year are assumed to be reinvested at the rate of cost of capital.
Cash flows given in the problem are assumed to be certain.
Problem No.9
Step 1: Calculation of Present value of Net Cash outflows.
Machine – A:
Year Particulars Cash flow PVF @ 14% PV
0 Purchasing Cost 7,50,000 1 7,50,000
1-3 Running Cost p.a. 2,00,000 2.5313 (PVAF@9%, 3y)
5,06,260
PV of Net cash outflows 12,56,260
Machine – B:
Year Particulars Cash flow PVF @ 14% PV
0 Purchasing Cost 5,00,000 1 6,00,000
1-3 Running Cost p.a. 3,00,000 1.7591
(PVAF@9%, 2y) 5,27,730
PV of Net cash outflows 10,27,730
Step 2: Calculation of Equivalent Present Value of Annual Net Cash outflows.
1. Machine A )PVAF(9%,3y
12,56,2602.5313
260,56,12 =4,96,290
2. MachineB )PVAF(9%,2y
10,27,7301.7591
10,27,730 =5,84,236
Conclusion: Since Equivalent Present Value of Net Cash Outflow is less, it is beneficial to purchase Machine A.
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Problem No. 10
Step-1: Calculation of CFAT p. a
Particulars Machine X Machine Y
Estimated savings in cost Estimated savings in Wages
500 6,000
800 8,000
Less: Additional cost of maintenance Additional cost of supervision
800 1,200
1,000 1,800
CFAT p.a 4,500 6,000
Step-2: Calculation of Pay back period
Particulars Machine X Machine Y
Payback period = CFAT
InvestmentInitial
4500
9000 = 2yrs.
6000
18000= 3 yrs.
Assumption: The two machines are mutually exclusive.
Conclusion: It is beneficial to select the machine with least pay back period i.e. Machine X.
Problem No.11
Calculation of IRR:
(Single out flow & multiple even cash inflows)
From the given information,
PVA = 36,000 periodic payment = 11,200 term of annuity = 5 years
We know that, PVA = P.P X PVAF (r%, 5 yrs)
36,000 = 11,200 X PVAF
PVAF = 3.214
Trace the PVAF in the PVAF table against 5 years
Therefore IRR = 17% approximately
Problem No.12
Calculation of NPV & IRR:
Using interpolation,
IRR = )ll(l@NPVl@NPV
l@NPVl 1221
11
= 12% + %)12%13(500,88000,74
= 12.836%
Since NPV is positive, it is beneficial for the company to accept the proposal.
Since IRR is > cost of capital, it is beneficial for the company to accept the proposal.
Year Cash flow NPV at the rate of 12% NPV at the rate of 13%
PVF @12% PV PVF @13% PV
0 (35,00,000) 1 (35,00,000) 1 (35,00,000)
1-4 10,00,000 3.037 30,37,000 2.974 29,74,000
5 5,00,000 0.567 2,83,500 0.543 2,71,500
6 5,00,000 0.507 2,53,500 0.48 2,40,000
NPV 74,000 (14,500)
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Problem No.13
1. Computation of Net Present Values of Projects:
Year
Cash flows Discounting Discounted
Factor @ 16% Cash flow
Project A Rs. (1)
Project B Rs. (2)
(3)
Project A Rs. (3) x (1)
Project B Rs. (3) x (2)
0 1,35,000 2,40,000 1.000 1,35,000 2,40,000
1 - 60,000 0.862 - 51,720
2 30,000 84,000 0.743 22,290 62,412
3 1,32,000 96,000 0.641 84,612 61,536
4 84,000 1,02,000 0.552 46,368 56,304
5 84,000 90,000 0.476 39,984 42,840
Net present value 58,254 34,812
2. Computation of Cumulative Present Values of Projects Cash inflows:
Year
Project A Project B
PV of cash inflows
Cumulative PV
PV of Cumulative
cash inflows PV
Rs. Rs. Rs. Rs.
1 - - 51,720 51,720
2 22,290 22,290 62,412 1,14,132
3 84,612 1,06,902 61,536 1,75,668
4 46,368 1,53,270 56,304 2,31,972
5 39,984 1,93,254 42,840 2,74,812
(i) Discounted payback period: (Refer to Working note 2)
Cost of Project A = Rs.1,35,000
Cost of Project B = Rs.2,40,000
Cumulative PV of cash inflows of Project A after 4 years = Rs.1,53,270
Cumulative PV of cash inflows of Project B after 5 years = Rs.2,74,812
A comparison of projects cost with their cumulative PV clearly shows that the project A’s cost will be recovered in less than 4 years and that of project B in less than 5 years. The exact duration of discounted pay back period can be computed as follows:
Project A Project B
Excess PV of cash inflows over the
18,270 34,812
Project cost (Rs.) (Rs.1,53,270 – Rs.1,35,000) (Rs.1,53,270 – Rs.1,35,000)
Computation of period required
0.39 year 0.81 years
To recover excess amount of cumulative PV over project cost
(Rs.18,270 / Rs.46,368) (Rs.34,812 / Rs.42,840)
(Refer to Working note2)
Discounted payback period 3.61 year 4.19 years
(4 – 0.39 years (5 – 0.81) years
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(ii) Profitability Index : =houtlayinitiancas
lowsinfuntcashSumofdisco
Profitability Index (for Project A) = 000,35,1.Rs254,93,1.Rs
= 1.43
Profitability Index (for Project B) = 000,40,2.Rs812,74,2.Rs
= 1.15
(iii) Net present value (for Project A) = Rs.58,254 (Refer to Working note 1) Net present value (for Project B) = Rs.34,812
Problem No.14
Advise to the Hospital Management:
Determination of Cash inflows Amount
Sales Revenue Less: Operating Cost Less: Depreciation (80,000 – 6,000)/8 Net Income Tax @ 30% Earnings after Tax (EAT) Add: Depreciation Cash inflow after tax per annum Less: Loss of Commission Income Net Cash inflow after tax per annum In 8th Year : New Cash inflow after tax Add: Salvage Value of Machine Net Cash inflow in year 8
40,000 7,500
32,500 9,250
23,250 6,975
16,275 9,250
25,525 12,000 13,525
13,525 6,000
19,525
Calculation of Net Present Value (NPV):
Year CFAT PV Factor @10% Present Value of
Cash inflows
1 to 7 8 Less: Cash Outflows
13,525 19,525
NPV
4.867 0.467
65,826.18 9,118.18
74,944.36 80,000.00 (5,055.64)
outflows cash of value Presentinflows cash discounted of SumIndexity Profitabil
000,8036.944,74 =0.937
Advise: Since the net present value is negative and profitability index is also less than 1, therefore, the hospital should not purchase the diagnostic machine. Note: Since the tax rate is not mentioned in the question, therefore, it is assumed to be 30 percent in the given solution.
Problem No.15
Recommendations regarding Two Alternative Proposals: (i) Net Present Value Method:
Computation of Present Value
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Project A = Rs.4,00,000 x 3.791 = Rs.15,16,400
Project B = Rs.5,80,000 x 3.791 = Rs.21,98,780
Computation of Net Present Value:
Project A = Rs.15,16,400 – 12,00,000 = Rs.3,16,400
Project B = Rs.21,98,780 – 18,00,000 = Rs.3,98,780
Advise: Since the net present value of Project B is higher than that of Project A, therefore, Project B should be selected.
(ii) Present Value Index Method:
Present Value Index = estmentInitialInv
lowinfofCashesentValuePr
Project A = 000,00,12400,16,15
= 1.264
Project B = 000,00,18780,98,21
= 1.222
Advise: Since the present value index of Project A is higher than that of Project B, therefore, Project A should be selected.
(iii) Internal Rate of Return (IRR): Project A:
P.V. Factor = 000,00,4000,00,12
InflowAnnualCashestmentInitialInv = 3
PV factor falls between 18% and 20%
Present Value of cash inflow at 18% and 20% will be:
Present Value at 18% = 3.127 x 4,00,000 = 12,50,800 Present Value at 20% = 2.991 x 4,00,000 = 11,96,400
IRR = 18 + )1820(x400,96,11800,50,12000,00,12800,50,12
= 18 + 2x400,54800,50
= 18 + 1.8676 = 19.868% Project B:
P.V. Factor = 103.3000,80,5000,00,18
Present Value of cash inflow at 18% and 20% will be:
Present Value at 18% = 3.127 x 5,80,000 = 18,13,660 Present Value at 20% = 2.991 x 5,80,000 = 17,34,780
IRR = 18 + )1820(x780,34,17660,13,18000,00,18660,13,18
= 18 + 2x880,78660,13
= 18 + 0.3463 = 18.346% Advise: Since the internal rate of return of Project A is higher than that of Project B, therefore, Project A should be selected.
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Problem No.16 Working notes:
Depreciation on machine. X =
Life
ValueScrap - Cost =
5000,50,1
= Rs.30,000
Depreciation on machine. Y =
Life
ValueScrap - Cost =
6000,40,2
= Rs.40,000
Particulars Machine X Machine Y
Annual savings: Wages Scrap Total savings(A)
90,000 10,000
1,00,000
1,20,000 15,000
1,35,000
Annual estimated cash cost: Indirect material Supervision Maintenance Total cash cost(B)
6,000
12,000 7,000
25,000
8,000 16,000 11,000 35,000
Annual cash savings(A-B) Less: depreciation Annual savings before tax Less: tax @ 30 % Annual profit after tax Add: depreciation Annual cash in flows
75,000 30,000
1,00,000 40,000
45,000 13,500
60,000 18,000
31,500 30,000
42,000 40,000
61,500 82,000
Evaluation of alternatives: (i) ARR = average annual net savings
Average investment
Machine X = 100x000,75500,31
= 42%
Machine Y = 100x000,20,1000,42
= 35%
Decision: Machine X is better. [Note: ARR can be computed alternatively taking initial investment as the basis forcomputation (ARR = Average Annual Net Income/Initial Investment). The value ofARR for Machines X and Y would then change accordingly as 21% and 17.5%respectively] (ii) Present Value Index Method
Present Value of Cash Inflow = Annual Cash Inflow x P.V. Factor @ 10%
Machine X = 61,500 x 3.79
= Rs.2,33,085
Machine Y = 82,000 x 4.354
= Rs.3,57,028
P.V index = present value of cash inflow
Investment
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Machine X = 5539.1000,50,1085,33,2
Machine Y = 4876.1000,40,2028,57,3
Decision: Machine X is better.
Problem No.17
PART – A
Project Present Value of Cash Inflows Initial cash
outlay NPV P.I
Ranking as per NPV
Ranking as per
P.I
A 1,87,600 x PVAF (12%, 2y ) = 317044 3,00,000 17,044 1.057 IV V
B 66,000 x PVAF (12%, 5y ) = 2,37,930 2,00,000 37,930 1.19 III III
C 1,00,000 x PVAF (12%, 3y) = 2,40,200 2,00,000 40,200 1.201 II II
D 20,000 x PVAF (12%, 9y) = 1,06,560 1,00,000 6,560 1.066 V IV
E 66,000 x PVAF (12%, 10y) = 3,72,900 3,00,000 72,900 1.243 I I
PART – B
All the projects have positive NPV. So, we can accept all the projects subject to availability of funds. It is also given that the company is having limited funds of Rs.4,00,000 and we need Rs.11,00,000 to invest in all the projects. So, it is required to do capital rationing.
Capital Rationing, assuming that the projects are divisible
Project Cash Outflow NPV Surplus funds
E 3,00,000 72,900 1,00,000
C 1,00,000 20,100
000,00,1x
000,00,2200,40
-
Total 93,000 -
PART - C
All the projects have positive NPV. To accept all the projects we need initial investment of Rs.11,00,000. But the available funds are just Rs.5,00,000. Therefore, it is necessary to do capital rationing.
Capital Rationing, assuming that the projects are divisible
Project Cash outlay NPV Surplus funds
E 3,00,000 72,900 2,00,000
C 2,00,000 40,200 ---
Total 1,13,100
Assumptions:
Perfect linear relationship is assumed to exist between inflows and outflows. In other words, NPV changes proportionately to changes in investment.
It is assumed that there is scarcity of funds in the current year only. In other words, there is no scarcity of funds in subsequent years.
The given projects are mutually independent.
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A project can be accepted only once.
A project can either be accepted now or rejected. In other words, there is no question of postponement.
Problem No. 18
Part: A – Calculation of NPV
Step 1:Calculation of Present Value of Cash Outflows
Particulars Amount
a) Initial investment b) Working capital
600 80
Present Value of Cash Outflows 680
Step 2:Calculation of Depreciation p.a.
Depreciation life
scraptcos5
0000,00,6 =1,20,000
Step 3:Calculation of Present Value of Operating cash inflows
Particulars Y1 Y2 Y3 Y4 Y5
a) PBDT 240 275 210 180 160
b) Depreciation (120) (120) (120) (120) (120)
c) PBT 120 155 90 60 40
d) Tax @35% (42) (54.25) (31.5) (21) (14)
e) PAT 78 100.75 58.5 39 26
f) CFAT (e+b) 198 220.75 178.5 159 146
g) Pvf@12% 0.8929 0.7972 0.7118 0.6355 0.5674
h) PV of cashinflow 176.7942 175.98 127.0563 101.0445 82.8404
Therefore, Present Value of Operating Cash Inflows = Rs.663.71 Step 4: Calculation of PV of Terminal Cash inflows
PV of TMCI = 80 x PVF (12%, 5y)
= 80 x 0.5674
= 45.39
Step 4: Calculation of NPV
NPV = PV of Operating Cash Inflows + PV of Terminal Cash Inflows – PV of Cash Outflows
= 663.71+ 45.39 – 680
= 29.1
Part: B – Calculation of IRR
year Cash flow PVF @ 12% Present Value PVF @ 14% Present Value
0 (680) 1 (680) 1 (680)
1 198 0.8929 176.7 0.8772 173.68
2 220.75 0.7972 175.9 0.7695 169.86
3 178.5 0.7118 127.6 0.6750 120.48
4 159 0.6355 101.5 0.5921 94.1
5 226 0.5674 123.24 0.5195 117.38
NPV29.1 (4.43)
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Using interpolation
)LL(L@NPVL@NPV
L@NPVLIRR 1221
11
%735.13
)2(5.331.2912
)2(43.41.29
1.2912
Part: C – Discounted payback period
Year Discounted cash flow Cumulative
1 176.7 176.7
2 175.9 352.6
3 127.6 480.2
4 101.2 581.4
5 128.24 709.6
Discounted payback period 24.128
4.5816.7094
24.12819.1284
years9.4
Part: D – Payback period
Year Discounted cash flow Cumulative
1 198 198
2 220.75 418.75
3 178.5 597.25
4 159 756.25
5 226 982.25
Payback period 159
25.59725.7563
1591593
= 4
Problem No.19
(a) Payback Period Method:
A = 5 + (500/900) = 5.5 years
B = 5 + (500/1200) = 5.4 years
C = 2 + (1000/2000) = 2.5 years Net Present Value:
ANPV= (- 5000) + (900 - 6.145) = (5000) + 5530.5 = Rs.530.5
BNPV is calculated as follows:
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Year Cash flow (Rs.) 10% discount factor Present value (Rs.)
0 (5,000) 1.000 (5,000)
1 700 0.909 636
2 800 0.826 661
3 900 0.751 676
4 1,000 0.683 683
5 1,100 0.621 683
6 1,200 0.564 677
7 1,300 0.513 667
8 1,400 0.467 654
9 1,500 0.424 636
10 1,600 0.386 618
1591
NPVC = (-5000) + (2000×2.487) + (1000×0.683) = Rs.657
Internal Rate of Return
If ANPV= 0, present value factor of IRR over 10 years = 5000/900 = 5.556
From tables, AIRR = 12 per cent.
IRRB
Year Cash flow
(Rs.) 10% discount
factor Present
value (Rs.)
20% discount
factor
Present value (Rs.)
0 (5,000) 1.000 (5,000) 1.000 (5,000)
1 700 0.909 636 0.833 583
2 800 0.826 661 0.694 555
3 900 0.751 676 0.579 521
4 1,000 0.683 683 0.482 482
5 1,100 0.621 683 0.402 442
6 1,200 0.564 677 0.335 402
7 1,300 0.513 667 0.279 363
8 1,400 0.467 654 0.233 326
9 1,500 0.424 636 0.194 291
10 1,600 0.386 618 0.162 259
1,591 (776)
Interpolating: IRRB = )776591,1(
10x591,110
= 10+6.72 = 16.72 per cent
IRRC
Year Cash flow
(Rs.)
15% discount
factor
Present value (Rs.)
18% discount
factor
Present value (Rs.)
0 (5,000) 1.000 (5,000) 1.000 (5,000)
1 2,000 0.870 1,740 0.847 1,694
2 2,000 0.756 1,512 0.718 1,436
3 2,000 0.658 1,316 0.609 1,218
4 1,000 0.572 572 0.516 516
140 136
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Interpolating: IRRC = 52.115)136140(
3x14015
= 16.52 per cent
Accounting Rate of Return
ARRA: Average capital employed = 2000,5
= Rs.2,500
Average accounting profit = 10
)000,5000,9( = Rs.400
ARRA = 500,2
)100x400( = 16 per cent
ARRB: Average accounting profit = 10
)000,5500,11( = Rs.650
ARRB = 500,2
)100x650( = 26 per cent
ARRC = Average accounting profit = 4
)000,5000,7( = Rs.500
ARRC = 500,2
)100x500( = 20 per cent
(b)
Summary of Results
Project A B C
Payback (years) 5.5 5.4 2.5
ARR (%) 16 26 20
IRR (%) 12.4 16.7 16.5
NPV (Rs.) 530.5 1,591 657
Comparison of Rankings
Method Payback ARR IRR NPV
1 C B B B
2 B C C C
3 A A A A
Problem No. 20 (Rs. In Lakhs) Step-1: Calculation of Pay Back Period
Year Machine – A Machine – B
CFAT Accumulated CFAT CFAT Accumulated CFAT
1 2 3 4 5
1.5 2.0 2.5 1.5 1.0
1.5 3.5 6.0 7.5 8.5
0.5 1.5 2.0 3.0 2.0
0.5 2.0 4.0 7.0 9.0
Pay Back Period 2 +
2.53.55.0
= 2.6 Years 3 + 3.0
0.45.0 = 3.33 years
Since Pay Back Period is less for Machine – A, it is beneficial to purchase Machine – A.
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Step-2: Present Value of Cash Out flows
Particulars Amount
Cost of Machinery Present Value of Cash Outflows
5,00,000
5,00,000
Step-3: Present Value of Operating Cash Inflows
Year Machine – A Machine – B
Y1 Y2 Y3 Y4 Y5 Y1 Y2 Y3 Y4 Y5
CFAT PVF @ 10% PV
1.5 0.909 1.3635
2.0 0.826 1.652
2.5 0.751 1.8775
1.5 0.683 1.0245
1.0 0.621 0.621
0.5 0.909 0.4545
1.5 0.826 1.239
2.0 0.751 1.502
3.0 0.683 2.049
2.0 0.621 1.242
Present Value there of for Machine – A= 6.5385 Present Value there of for Machine – B= 6.4865
Step-4: Present Value of Terminal Cash Inflows - Nil
Step-5: Calculation of NPV and Profitability Index
Particulars Machine A Machine B
Present Value of cash inflows Present Value of cash outflows NPV @ 10% Profitability Index (P.V of Cash Inflows / Cash Outflows)
6.5385 (5.0)
6.4865 (5.0)
1.5385 1.31
1.4865 1.30
Since NPV and P.I. are higher for Machine – A, it is beneficial to purchase Machine – A. Step-6: Calculation of I.R.R for Machine – A
Year Cash flow NPV @ 20% NPV @ 24%
PVF P V PVF P V
0 1 2 3 4 5
5.0 1.5 2.0 2.5 1.5 1.0
1.0 0.833 0.694 0.579 0.482 0.402
(5.0) 1.25 1.39 1.45 0.72 0.40
1.0 0.806 0.650 0.524 0.423 0.341
(5.0) 1.21 1.30 1.31 0.63 0.34
NPV 0.21 (0.21)
Using Interpolation
IRR = Ll +
2L NPV@1L NPV@1L NPV@
(L2 – L1) = 20 + 4
21.00.210.21
= 22%.
Step-7: Calculation of IRR for Machine – B
Year Cash flow NPV @ 18% NPV @ 20%
PVF P V PVF P V
0 1 2 3 4 5
5.0 0.5 1.5 2.0 3.0 2.0
1.0 0.847 0.718 0.609 0.516 0.437
(5.0) 0.42 1.08 1.22 1.55 0.87
1.0 0.833 0.694 0.579 0.482 0.402
(5.0) 0.42 1.04 1.16 1.45 0.80
0.14 (0.13)
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Using Interpolation
IRR = Ll +
2L NPV@1L NPV@1L NPV@
(L2 – L1)
= 18 + 0.13 0.14
0.14
× 2 = 18 + 1.012 = 19.04%
= 19.04% Since IRR is high for Machine – A, it is beneficial to purchase Machine – A. Step-8: Calculation of Average Rate of Return
Particulars Machine– A Machine – B
1. Depreciation
LifeScrapCost
1,00,000 1,00,000
2. Average Investment =
Add.W/capScrapScrapInvestmentInitial21
2,50,000 2,50,000
3. Average PAT. p.a. (Avg CFAT – Depreciation)
70,000
15
11.52.521.5
80,000
15
2321.50.5
4. Average Rate of Return (3) / (2) 0.28 (70,000/2,50,000) 0.32 (80,000/2,50,000)
Since machines are mutually exclusive and A.R.R. is high for Machine – B, it is beneficial to purchase Machine – B. Conclusion: In all the above cases except in the case of A.R.R - purchase of Machine - A is beneficial. Assumptions: 1. For Pay back period: Cash flows are assumed to accrue evenly throughout the year. 2. For NPV
Cash flows are assumed to accrue at the end of each year.
Interim cash inflows at the end of each year are assumed to be reinvested at the rate of cost of capital.
Cash flows given in the problem are assumed to be certain. 3. For IRR
Cash flows are assumed to accrue at the end of each year.
Interim cash inflows at the end of each year are assumed to be reinvested at the rate of IRR.
Cash flows given in the problem are assumed to be certain.
Problem No.21
(a)
(i) Payback Period
Project A: 10,000/10,00 = 1 year
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Project B: 10,000/7,500 = 1 1/3 years.
Project C: 2 years + 312
000,12000,6000,10
years
Project D: 1 year.
(ii) ARR
Project A: 02/1)000,10(
2/1)000,10000,10(
Project B: %50000,5500,2
2/1)000,10(2/1)000,10000,15(
Project C: %53000,5667,2
2/1)000,10(3/1)000,10000,18(
Project D: %40000,5000,2
2/1)000,10(3/1)000,10000,16(
Note: This net cash proceed includes recovery of investment also. Therefore, net cash earnings are found by deducting initial investment.
(iii) IRR
Project A: The net cash proceeds in year 1 are just equal to investment.
Therefore, r = 0%
Project B: This project produces an annuity of Rs.7,500 for two years. Therefore, the required PVAF is: 10,000/7,500 = 1.33. This factor is found under 32% column. Therefore, r = 32%
Project C: Since cash flows are uneven, the trail and error method will be followed. Using 20% rate of discount the NPV is + Rs.1,389. At 30% rate of discount, the NPV is –Rs.633. The true rate of return should be less than 30%. At 27% rate of discount it is found that the NPV is –Rs.86 and at 26% + Rs.105. Through interpolation, we find r = 26.5%
Project D: In this case also by using the trail and error method, it is found that at 37.6% rate of discount NPV becomes almost zero.
Therefore, r = 37.6%
(iv) NPV
Project A: at 10% -10,000+10,000x0.909 = -910 at 30% -10,000+10,000x0.769 = -2,310
Project B: at 10% -10,000+7,500(0.909+0.826) = 3,013 at 30% -10,000+7,500(0.769+0.592) = +208
Project C: at 10% -10,000+2,000x0.909+4,000x0.826+12,000x0.751 = +4,134 at 30% -10,000+2,000x0.769+4,000x0.592+12,000x0.455 = -633
Project D: at 10% -10,000+10,000x0.909+3,000x(0.826+0.751) = +3,821 at 30% -10,000+10,000x0.769+3,000x(0.592+0.4555) = +831
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The Project are ranked as follows according to the various methods:
Ranks
Projects PB ARR IRR NPV (10%) NPV (30%
A 1 4 4 4 4
B 2 2 2 3 2
C 3 1 3 1 3
D 1 3 1 2 1
(b) Payback and ARR are theoretically unsound method for choosing between the investment projects.
Between the two time-adjusted (DCF) investment criteria, NPV and IRR, NPV gives consistent results. If the projects are independent (and there is no capital rationing), either IRR or NPV can be used since the same set of projects will be accepted by any of the methods. In the present case, except Project A all the three projects should be accepted if the discount rate is 10%. Only Projects B and D should be undertaken if the discount rate is 30%. If it is assumed that the projects are mutually exclusive, then under the assumption of 30% discount rate, the choice is between B and D (A and C are unprofitable). Both criteria IRR and NPV give the same results – D is the best. Under the assumption of 10% discount rate, ranking according to IRR and NPV conflict (except for Project A). If the IRR rule is followed, Project D should be accepted. But the NPV rule tells that Project C is the best. The NPV rule generally gives consistent results in conformity with the wealth maximization principle. Therefore, Project C should be accepted following the NPV rule.
PROBLEM NO. 22 Step 1:Calculation of Present Value of Cash Outflows
Particulars Machine -1 Machine -2
Cost of Machine 15,00,000 20,00,000
Step 2:Calculation of Depreciationp.a
Depreciation life
scraptcos
a) Machine 15000,00,15 = 3,00,000
b) Machine 2 5000,00,20 =4,00,000
Step 3:Calculation of Present Value of Operating Cash inflow
Particulars Machine 1 Machine 2
a) PBDT 6,25,000 8,75,000
b) Depreciation 3,00,000 4,00,000
c) PBT 3,25,000 4,75,000
d) Tax @30% 97,500 1,42,500
e) PAT 2,27,500 3,32,500
f) CFAT (e+b) 5,27,500 7,32,500
P.V of operating cashinflow
Machine 1 = 5,27,500 x PVAF (12%, 5y) Machine 2 = 7,32,500 x PVAF (12%, 5y) = 5,27,500 x 3.605 = 7,32,500 x 3.605 = 19,01,637.5 = 26,40,662.5
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Step 4: Present Value of Terminal Cash inflow = 0
Part A: Calculation of NPV
NPV =PV of Operating Cash Inflows + PV of Terminal Cash Inflows – PV of Cash Outflows
a) Machine 1
NPV = 19,01,637 + 0 –15,00,000
= 4,01,637.5 b) Machine 2
NPV = 26,40,662.5 – 20,00,000
=6,40,664
Part B: Calculation of Profitability Index
Profitability index outflows cash ofPV inflows cash ofPV
a) Machine 1
Profitability index 268.115,00,00019,01,639
b) Machine – II
Profitability index 320.115,00,00026,40,664
Part C: Calculation of Discounted Pay Back Period
Step:1 Calculation of cumulative cash inflows
Machine – I Machine – II
Year PVF @ 2%
Cash flow
PV Cumulative PV
Cash flow
PV Cumulative PV
1 0.893 5,27,500 4,71,058 4,71,058 7,32,500 6,54,123 6,54,123
2 0.797 5,27,500 4,20,418 8,91,476 7,32,500 5,83,803 12,37,926
3 0.712 5,27,500 3,75,580 12,67,056 7,32,500 5,21,540 17,59,466
4 0.636 5,27,500 3,35,490 16,02,546 7,32,500 4,65,870 22,25,336
5 0.567 5,27,500 2,99,093 19,01,639 7,32,500 4,15,328 26,40,664
Step 2: Calculation of Discounted Pay Back Period Machine 1
Discounted Pay Back Period490,35,3
)056,67,12000,00,15(3
490,35,3944,32,23 = 3+0.6943 = 3.69 years
Machine – II
870,65,4)466,59,17000,00,20(3periodpaybackDiscounted
870,65,4534,40,23
= 3 + 0.5163
= 3.52 years or 3 years 6.24 months
THE END