MASTER MINDS
No.1 for CA/CWA & MEC/CEC
2. CAPITAL BUDGETING
SOLUTIONS TO ASSIGNMENT PROBLEMS
Problem No.1
Payback reciprocal =
4,000 X100
= 20%
20,000
The above payback reciprocal provides a reasonable approximation of the internal rate of return, i.e.
19%.
Problem No.2
W.N.-1: Calculation of depreciation per annum
 Cost - Scrap Value  80,000 − 10,000
= Rs.14,000 p.a.
Depreciation p.a. = 
=
5
Life


W.N.-2: Calculation of PAT p.a.
Year
PBDT
Depreciation
PBT / PAT (PBDT – Dep.)
1
2
3
20,000
40,000
30,000
14,000
14,000
14,000
6,000
26,000
16,000
4
5
15,000
5,000
14,000
14,000
1,000
(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=
6,000 + 26,000 + 16,000 + 10,000 − 9,000
= Rs. 8,000 p.a
5
Step-2: Calculation of Average Investment
1
Average investment = ( Initial Cost - Salvage Value) + Salvage Value
2
1
= ( 80,000 - 10,000) + 10,000 = Rs.45,000
2
Step-3: Calculation of Accounting Rate of Return (ARR) (Return on Avg. Capital Employed)
ARR =
AveragePAT
8,000
= 17.77%
x100 =
Average investment
45,000
Step-4: Return on Original Capital employed
Return on Original Capital employed =
8,000
Average PAT
x100 =
x100 = 10%
Orginal Investment
80,000
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Problem No.3
W.N. 1: Calculation of depreciation per annum
 Cost - Scrap Value 
80,000 − 0
= Rs.16,000 p.a.
 =
5
Life


Depreciation 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
Step-2: Calculation of Present Value of Operating Cash Inflows:
Particulars
Amount Rs.
Amount Rs.
1,00,000
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
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
=
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81,450
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MASTER MINDS, Guntur
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.
IPCC_33e_F.M_ Capital Budgeting_Assignment Solutions ________________2
MASTER MINDS
No.1 for CA/CWA & MEC/CEC
Problem No.4
W.N – 1: Calculation of depreciation p.a.
Depreciation p.a. =
(Rs. in Lakhs)
 Cost - Scrap Value  140 − 0
= Rs. 17.5 lakhs p.a.

=
8
Life


On supplementary equipment =
10 − 1
= 1.5 lakhs pa
6
Calculation of NPV using Incremental approach
Step-1: Calculation of Present Value of Cash Outflows:
Particulars
Amount
140
15
155
20
135
Cost of initial equipment
Cost of additional working capital
Less: tax free subsidy from government
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
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
=
100
Less: - variable cost @ 40% =
40
Contribution per unit
60
=
Particulars
Sales volume (lakhs of unit)
Total contribution ( a * Rs. 60 per unit)
Fixed cost
Advertisement cost
Depreciation (WN – 1)
PBF (b-c-d-e) (loss)
Tax @ 50%
PAT (f-g)
CFAT (h+e)
PVF @ 12 %
Present value
Y1
0.8
48
16
30
17.5
(15.5)
(7.75)
(7.75)
9.75
0.893
8.706
Y2
1.2
72
16
15
17.5
23.5
11.75
11.75
29.25
0.797
23.31
Y3 to 5
3.0
180
16
10
19(17.5+1.5)
135
67.5
67.5
86.5
1.915
165.64
Y6 to 8
2.0
120
16
4
19
81
40.5
40.5
59.5
1.363
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
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MINDS, Guntur
PVAF (12%, 5) - PVAF (12%, 2)
= 3.605 - 1.690
= 1.915
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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)
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= 16 * 0.404
=
6.464
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.5
Calculation of NPV
a.
Step 1: Calculation of Present Value of Cash Outflows:
Particulars
Cost of machinery
Present Value of Cash Outflows
Amount
4,00,000
4,00,000
Step 2: Calculation of Present Value of Operating Cash Inflows:
Particulars
a.
b.
c.
d.
e.
Sales volume
Contribution per unit (10-6)
Total contribution (axb)
Fixed cost
CFAT (c-d)
Amount
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
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MASTER MINDS
No.1 for CA/CWA & MEC/CEC
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.
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)
Present value there of
4X-20,000
= (4X – 20,000) * PVAF (15%, 6 years)
= (4X – 20,000) *3.784
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Step-3: same as above – 8,640
To
MASTER MINDS, Guntur
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.6
Given information:
Project
A
B
A&B
C
Investment
1,00,000
1,50,000
2,50,000
1,50,000
NPV
1,25.000
45,000
2,00,000
90,000
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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
A&B
A&C
NPV
2,00,000
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.7
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.
st
Dep. for 1 year =
rd
3 year =
th
5 year =
2, 20, 000
x 10 = Rs.40,000
55
2, 20, 000
x 8 = Rs. 32,000
55
2, 20, 000
x 6 = Rs.24,000
55
nd
2
year
th
4 year =
2, 20, 000
x 9 = Rs.36,000
55
2, 20, 000
x 7 = Rs. 8,000
55
=
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
th
Dep. for 6 year =
th
8 year =
th
10 year =
1, 20, 000
x 5 = Rs. 40,000
15
th
7 year =
1, 20, 000
x 3 = Rs. 24,000
15
th
1, 20, 000
x 4 = Rs. 32,000
15
9 year =
1, 20, 000
x 2 = Rs. 16,000
15
1, 20, 000
x 1 = Rs. 8,000
15
Calculation of NPV
Step-1: Calculation of Present Value of Cash Outflows
Particulars
Cost of Machinery
Add: Working capital
Add: Cost of Additional equipment [60,000 x PVF (20%, 5y)]
Present value of Cash Outflows
Amount
2,50,000
50,000
24,120
3,24,120
IPCC_33e_F.M_ Capital Budgeting_Assignment Solutions ________________6
MASTER MINDS
No.1 for CA/CWA & MEC/CEC
Step-2: Calculation of Present Value of Operating Cash Inflows.
Particulars
Y1
(Rs. in Lakhs)
Y2
Y3
Y4
Y5
Y6
Y7
Y8
Y9
Y10
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 0.84
0.304 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 0.504
0.24 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
0.76
0.402 0.335
0.728
0.279
0.696 0.664
0.233 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
PBDT
Less: Dep.(W.N-1)
Therefore, Present Value of operating cash inflows = Rs.3,04,498
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.8
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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
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Problem No. 9
(Rs. In Lakhs)
Step-1: Calculation of Pay Back Period
Machine – A
Year
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+
= 2.6 Years
3+
5.0 − 3.5
2.5
5.0 − 4.0
3.0
= 3.33 years
Since Pay Back Period is less for Machine – A, it is beneficial to purchase Machine – A.
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
Y1
CFAT
PVF @ 10%
PV
1.5
0.909
1.3635
Machine – A
Y2
Y3
Y4
Y5
Y1
2.5
0.751
1.8775
1.0
0.621
0.621
0.5
0.909
0.4545
2.0
0.826
1.652
1.5
0.683
1.0245
Machine – B
Y2
Y3
Y4
2.0
0.751
1.502
1.5
0.826
1.239
Y5
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
Present Value of cash inflows
Present Value of cash outflows
NPV @ 10%
Profitability Index (P.V of Cash Inflows / Cash Outflows)
Machine B
6.5385
(5.0)
1.5385
1.31
6.4865
(5.0)
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
0
1
2
5.0
1.5
2.0
NPV @ 20%
NPV @ 24%
PVF
PV
PVF
PV
1.0
0.833
0.694
(5.0)
1.25
1.39
1.0
0.806
0.650
(5.0)
1.21
1.30
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No.1 for CA/CWA & MEC/CEC
3
4
5
2.5
1.5
1.0
NPV
0.579
0.482
0.402
1.45
0.72
0.40
0.21
0.524
0.423
0.341
1.31
0.63
0.34
(0.21)
Using Interpolation
IRR = Ll +
NPV@ L1
NPV@ L1 − NPV@ L 2
(L2 – L1)
=
20 +
0.21
(4) = 22%.
0.21 + 0.21
Step-7: Calculation of IRR for Machine – B
Year
NPV @ 18%
Cash flow
5.0
0.5
1.5
2.0
3.0
2.0
0
1
2
3
4
5
NPV @ 20%
PVF
PV
PVF
PV
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)
Using Interpolation
IRR
NPV@ L1
=
Ll +
=
18 +
=
19.04%
NPV@ L1 − NPV@ L 2
(L2 – L1)
0.14
× 2 = 18 + 1.012 = 19.04%
0.14 + 0.13
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Since IRR is high for Machine – A, it is beneficial to purchase Machine – A.
Step-8: Calculation of Average Rate of Return
1. Depreciation
Particulars
Machine– A
Machine – B
 Cost − Scrap 


Life


1,00,000
1,00,000
2,50,000
2,50,000
2. Average Investment =
1
2
(Initial Investment − Scrap ) + Scrap + Add.W/cap
3. Average PAT. p.a.
(Avg CFAT – Depreciation)
4. Average Rate of Return (3) / (2)
70,000
80,000
 1.5 + 2 + 2.5 + 1.5 + 1

− 1

5



 0.5 + 1.5 + 2 + 3 + 2
− 1

5


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.
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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.
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3. For IRR
MASTER MINDS,
• 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. 10
Step-1: Calculation of CFAT p. a
Particulars
Machine X
Estimated savings in cost
Estimated savings in Wages
Less: Additional cost of maintenance
Additional cost of supervision
CFAT p.a
Machine Y
500
6,000
800
1,200
4,500
800
8,000
1,000
1,800
6,000
Step-2: Calculation of Pay back period
Particulars
Payback period =
Machine X
Initial Investment
9000
CFAT
4500
= 2yrs.
Machine Y
18000
= 3 yrs.
6000
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
(a)
(i) Payback Period
Project A: 10,000/10,00
= 1 year
Project B: 10,000/7,500
= 1 1/3 years.
Project C: 2 years +
10,000 − 6,000
1
= 2 years
12,000
3
Project D: 1 year.
(ii) ARR
(10,000 − 10,000)1/ 2
=0
Project A:
(10,000)1/ 2
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(15,000 − 10,000)1/ 2 2,500
=
= 50%
(10,000)1/ 2
5,000
(18,000 − 10,000)1 / 3 2,667
=
= 53%
Project C:
(10,000)1 / 2
5,000
(16,000 − 10,000)1/ 3 2,000
=
= 40%
Project D:
(10,000)1/ 2
5,000
Project B:
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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%
at 30%
-10,000+10,000x0.909 = -910
-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
The Project are ranked as follows according to the various methods:
Ranks
Projects
A
B
C
D
PB
1
2
3
1
ARR
4
2
1
3
IRR
4
2
3
1
NPV (10%)
4
3
1
2
NPV (30%
4
2
3
1
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(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.12
(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:
NPVA = (- 5000) + (900 - 6.145) = (5000) + 5530.5 = Rs.530.5
NPVB is calculated as follows:
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 NPVA = 0, present value factor of IRR over 10 years = 5000/900 = 5.556
From tables, IRR A = 12 per cent.
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IPCC_33e_F.M_ Capital Budgeting_Assignment Solutions ________________12
MASTER MINDS
No.1 for CA/CWA & MEC/CEC
IRRB
Year
Cash flow
(Rs.)
10% discount
factor
Present
value (Rs.)
0
1
2
3
4
5
6
7
8
9
10
(5,000)
700
800
900
1,000
1,100
1,200
1,300
1,400
1,500
1,600
1.000
0.909
0.826
0.751
0.683
0.621
0.564
0.513
0.467
0.424
0.386
(5,000)
636
661
676
683
683
677
667
654
636
618
1,591
Interpolating: IRRB = 10 +
20%
discount
factor
1.000
0.833
0.694
0.579
0.482
0.402
0.335
0.279
0.233
0.194
0.162
Present
value (Rs.)
(5,000)
583
555
521
482
442
402
363
326
291
259
(776)
1,591x10
= 10+6.72 = 16.72 per cent
(1,591 + 776)
IRRC
15%
discount
factor
Present
value (Rs.)
18%
discount
factor
Present
value (Rs.)
(5,000)
1.000
2,000
0.870
(5,000)
1.000
(5,000)
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
Year
Cash flow
(Rs.)
0
1
140
136
140x3
= 15 + 1.52 = 16.52 per cent
(140 + 136)
Accounting Rate of Return
5,000
ARRA: Average capital employed =
= Rs.2,500
2
(9,000 − 5,000 )
Average accounting profit =
= Rs.400
10
( 400x100)
ARRA =
= 16 per cent
2,500
(11,500 − 5,000 )
= Rs.650
ARRB: Average accounting profit =
10
(650x100)
ARRB =
= 26 per cent
2,500
(7,000 − 5,000 )
= Rs.500
ARRC = Average accounting profit =
4
(500 x100)
ARRC =
= 20 per cent
2,500
Interpolating: IRRC = 15 +
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(b)
Summary of Results
Project
A
5.5
16
12.4
530.5
Payback (years)
ARR (%)
IRR (%)
NPV (Rs.)
B
5.4
26
16.7
1,591
C
2.5
20
16.5
657
Comparison of Rankings
Method
1
2
3
Payback
C
B
A
ARR
B
C
A
IRR
B
C
A
NPV
B
C
A
Problem No.13
Calculation of NPV & IRR:
Year
NPV at the rate of 12%
Cash flow
0
PVF @12%
PV
NPV at the rate of 13%
PVF @13%
PV
(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)
Using interpolation,
IRR = l1 +
NPV @ l1
(l2 − l1 )
NPV @ l1 − NPV @ l2
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74,000
(13% − 12%)
=12% +
88,500
= 12.836%
To
MASTER MINDS, Guntur
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.
Problem No.14
1. Computation of Net Present Values of Projects:
Cash flows
Year
0
1
2
Project A
Rs. (1)
1,35,000
30,000
Project B
Rs. (2)
2,40,000
60,000
84,000
Discounting
Discounted
Factor @ 16%
Cash flow
Project A
Project B
(3)
Rs. (3) x (1)
Rs. (3) x (2)
1.000
1,35,000
2,40,000
0.862
51,720
0.743
22,290
62,412
IPCC_33e_F.M_ Capital Budgeting_Assignment Solutions ________________14
MASTER MINDS
No.1 for CA/CWA & MEC/CEC
3
4
5
Net present value
1,32,000
84,000
84,000
96,000
1,02,000
90,000
0.641
0.552
0.476
84,612
46,368
39,984
58,254
61,536
56,304
42,840
34,812
2. Computation of Cumulative Present Values of Projects Cash inflows:
Year
Project A
PV of cash
Cumulative
inflows
PV
Rs.
1
2
3
4
5
Project B
PV of
Cumulative
cash inflows
PV
Rs.
Rs.
51,720
51,720
62,412
1,14,132
61,536
1,75,668
56,304
2,31,972
42,840
2,74,812
Rs.
22,290
84,612
46,368
39,984
22,290
1,06,902
1,53,270
1,93,254
(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
18,270
34,812
(Rs.1,53,270 – Rs.1,35,000)
(Rs.1,53,270 – Rs.1,35,000)
period
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)
3.61 year
4.19 years
(4 – 0.39 years
(5 – 0.81) years
Excess PV of cash inflows
over the
Project cost (Rs.)
Computation
required
of
(Refer to Working note2)
Discounted payback period
(ii) Profitability Index : =
Sumofdisco untcash inf lows
initiancas houtlay
Profitability Index (for Project A)
=
Profitability Index (for Project B)
=
(iii) Net present value (for Project A)
(Refer to Working note 1)
Net present value (for Project B)
=
Rs.1,93,254
= 1.43
Rs.1,35,000
Rs.2,74,812
= 1.15
Rs.2,40,000
Rs.58,254
=
Rs.34,812
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Problem No.15
Advise to the Hospital Management:
Determination of Cash inflows
Amount
Sales Revenue
Less: Operating Cost
40,000
7,500
32,500
9,250
23,250
6,975
16,275
9,250
25,525
12,000
13,525
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
13,525
6,000
19,525
Calculation of Net Present Value (NPV):
Year
CFAT
13,525
19,525
1 to 7
8
Present Value of
Cash inflows
PV Factor @10%
4.867
0.467
Less: Cash Outflows
NPV
65,826.18
9,118.18
74,944.36
80,000.00
(5,055.64)
Sum of discounted cash inflows 74,944.36
=
=0.937
Present value of cash outflows
80,000
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.
Profitability Index =
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.16
(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
D
(3,000)
0
0
1 year and 9.6 months
3,000
3 years
12
x2,000
i.e.
2,500
(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.
IPCC_33e_F.M_ Capital Budgeting_Assignment Solutions ________________16
MASTER MINDS
No.1 for CA/CWA & MEC/CEC
(iii) Discounted Payback Period (Cash flows discounted at 10%)
A 10,000 + 5,454.6 + 1,652.8 + 1,502.6 + 8,196
3years +
12
x1,390 = 3 years and 2 months
8,196
B 10,000 + 2,272.75 + 2,066 + 3,756.5 + 5,122.50
3years +
12
x1,904.75 = 3 years and 4.6 months
5,122.55
C 3,500 + 1,363.65 + 2,066 + 375.65 + 3,415
2years +
12
x70.35 =2 years and 2.25 months
375.65
D 3,000 + 0 + 0 + 2,253.9 + 4,098
3years +
12
x746.10 =3 years and 2.18 months
4,098
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.17
Recommendations regarding Two Alternative Proposals:
(i) Net Present Value Method:
Computation of Present Value
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 =
Pr esentValue ofCash inf low
InitialInv estment
15,16,400
= 1.264
12,00,000
21,98,780
= 1.222
Project B =
18,00,000
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Project A =
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MASTER MINDS, Guntur
Advise: Since the present value index of Project A is higher than that of Project B, therefore,
Project A should be selected.
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(iii) Internal Rate of Return (IRR):
Project A:
P.V. Factor =
InitialInvestment
12,00,000
=
=3
AnnualCashInflow
4,00,000
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
12,50,800 − 12,00,000
x(20 − 18)
IRR
= 18 +
12,50,800 − 11,96,400
50,800
x2
54,400
= 18 + 1.8676 = 19.868%
= 18 +
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Project B:
P.V. Factor =
18,00,000
= 3.103
5,80,000
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
18,13,660 − 18,00,000
x(20 − 18)
IRR = 18 +
18,13,660 − 17,34,780
13,660
x2
= 18 +
78,880
= 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.
Problem No.18
Working notes:
 Cost - Scrap Value 
1,50,000
= Rs.30,000
 =
5
Life


Depreciation on machine. X = 
2,40,000
 Cost - Scrap Value 
= Rs.40,000
 =
6
Life


Depreciation on machine. Y = 
Particulars
Annual savings:
Wages
Scrap
Total savings(A)
Annual estimated cash cost:
Indirect material
Supervision
Maintenance
Total cash cost(B)
Machine X
Machine Y
90,000
10,000
1,00,000
1,20,000
15,000
1,35,000
6,000
12,000
7,000
25,000
8,000
16,000
11,000
35,000
IPCC_33e_F.M_ Capital Budgeting_Assignment Solutions ________________18
MASTER MINDS
No.1 for CA/CWA & MEC/CEC
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
31,500
x100 = 42%
Machine X =
75,000
42,000
x100 = 35%
Machine Y =
1,20,000
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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
Machine X
=
2,33,085
= 1.5539
1,50,000
Machine Y
=
3,57,028
= 1.4876
2,40,000
Decision: Machine X is better.
Problem No.19
PART – A
Project
Present Value of Cash Inflows
A
B
C
D
E
1,87,600 x PVAF (12%, 2y ) = 317044
66,000 x PVAF (12%, 5y ) = 2,37,930
1,00,000 x PVAF (12%, 3y) = 2,40,200
20,000 x PVAF (12%, 9y) = 1,06,560
66,000 x PVAF (12%, 10y) = 3,72,900
Initial
cash
outlay
3,00,000
2,00,000
2,00,000
1,00,000
3,00,000
NPV
P.I
17,044
37,930
40,200
6,560
72,900
1.057
1.19
1.201
1.066
1.243
Ranking
as per
NPV
IV
III
II
V
I
Ranking
as per
P.I
V
III
II
IV
I
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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
E
Cash Outflow
3,00,000
C
1,00,000
NPV
72,900
20,100
Total
Surplus funds
1,00,000
 40,200

x 1,00,000 

 2,00,000

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
E
C
Cash outlay
3,00,000
2,00,000
NPV
72,900
40,200
1,13,100
Total
Surplus funds
2,00,000
---
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.
• 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.
THE END
IPCC_33e_F.M_ Capital Budgeting_Assignment Solutions ________________20