K.J.SOMAIYA COLLEGE OF SCEINCE AND COMMERCE T.Y.B.M.S.
CHAPTER 1 CAPITAL BUDGETING PART 1
Q.1 A company proposes to install a machine involving a capital cost of Rs. 3,60,000.
The life of the machines is 5 years and its salvage value at the end of the life is Nil. The
machine will produce the net operating income after depreciation of Rs. 68,000 per
annum. The company’s tax rate is 45%. The present value factors for 5 years are as
under:
Discounting Rate 14% 15% 16% 17% 18%
Cumulative Factors 3.43 3.35 3.27 3.20 3.13
You are required to calculate the internal rate of return of the proposal:
Solution:
Computation of Cash Inflow
A. Net operating income Per annum 68,000
B. Less: Tax @ 45% (30,600)
C. Profit after tax 37,400
D. Add: Depreciation (Rs. 3,60,000/ 5 years) 72,000
E. Cash inflow p.a. 1,09,400
The IRR of the investments can be found as follows:
NPV = - Rs. 3,60,000 + Rs. 1,09,400 (PVAF5,r) =0
𝑅𝑠.3,60,000
Or, PAVF5r (cumulative factors) = 𝑅𝑠.1,09,400 = 3.29
Computation of internal Rate of return
A. Discounting rate 15% 16%
B. Cumulative factors 3.35 3.27
C. Total cash inflow 3,66,490 3,57,738
(Rs. 1,09,400×3,350) (Rs.1,09,400×3.27)
D. Initial Outlay (Rs.) 3,60,000 3,60,000
E. NPV (Rs) [C – D] 6,490 (2,262)
6,490
IRR = 15% +[6,490+2,262] = 15% + 0.74% = 15.74%
Alternatives Method
𝑃𝑉𝐴𝐹 𝑎𝑡 𝑙𝑜𝑤𝑒𝑟 𝑟𝑎𝑡𝑒−𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜𝑑
IRR = Lower Rate + 𝑃𝑉𝐴𝐹 𝑎𝑡 𝑙𝑜𝑤𝑒𝑟 𝑟𝑎𝑡𝑒−𝑃𝑉𝐴𝐹 𝑎𝑡 ℎ𝑖𝑔ℎ𝑒𝑟 𝑟𝑎𝑡𝑒
3.35−3.29
= 15% + 3.35−3.27 = 15.75%.
Q.2 A company is considering the proposals of takings up a new projects which
requires an investments of Rs. 400 lakhs on machinery and other assets. The projects is
expected to yield the followings earnings (before depreciation and taxes) over the
next five years.
Year 1 2 3 4 5
Earnings (Rs.in lakhs) 160 160 180 180 150
The cost of raising the additional capital is 12% and assets have to be
depreciation at 20% on Written Down value bases. The scrap value at the end of the
five years. Period may be taken as zero income tax applicable to the company is 50%.
Required: Calculate the net present value of the project and advise the
managements to take appropriate decision. Also calculate the internal Rate of
Return of the project.
Page | 1
,K.J.SOMAIYA COLLEGE OF SCEINCE AND COMMERCE T.Y.B.M.S.
Note: Present value of Re. 1 at different rates of interest are as follows.
Year 10% 12% 14% 16%
1 0.91 0.89 0.88 0.86
2 0.83 0.80 0.77 0.74
3 0.75 0.71 0.67 0.64
4 0.68 0.64 0.59 0.55
5 0.62 0.57 0.52 0.48
Solution:
Statements Showing The Computation Of Cash Inflows After Tax [CFAT]
Particulars Year 1 Years 2 Year 3 Year 4 Year 5
Earnings before depreciation% 16,000 16,000 18,000 18,000 15,000
tax (8,000) (6,400) (5,120) (4,096) (3,277)
Less: Depreciation 8,000 9,600 12,880 13,904 11,723
Earnings before tax (4,000) (4,800) (6,440) (6,952) (5,862)
Less: Tax @ 50% 4,000 4,800 6,440 6,952 5,861
Earnings after tax 8,000 6,400 5,120 4,096 3,277
Add: Depreciation 12,000 11,200 11,560 11,048 9,138
Cash flow after taxes (CFAT)
Add: Tax savings on loss - - - 6,554
[50% of (Rs. 13,107 – 0 ) 15,692
Statements Showing The Computation of Net Present Value
Particulars Year Amt. PV PV PV PV PV factor PV
Factor Factor At 16%
at 12% At 14%
Purchase price of 0 40,000 1 40,000 1 40,000 1 40,000
New machinery
CFAT of year 1 12,000 0.89 10,680 0.88 10,580 0.86 10,320
CFAT of year 2 11,200 0.80 8,960 0.77 8,624 0.74 8,288
CFAT of year 3 11,560 0.71 8,208 0.67 7,745 0.64 7,398
CFAT of year 4 11,048 0.64 7,071 0.59 6,518 0.55 6,076
CFAT of year 5 15,692 0.57 8,944 0.52 8,160 0.48 7,532
NPV 3,863 1,607 (386)
Recommendation: Company should accept the projects at 12% since NPV is potive.
(ii)Calculation of internal Rate of Return (IRR)
1,607
IRR = 14% + 1,607+386 × (16% − 14%)
IRR = 14% + 1.61% = 15.61%.
Page | 2
,K.J.SOMAIYA COLLEGE OF SCEINCE AND COMMERCE T.Y.B.M.S.
Q.3 XYZ Ltd. is planning to introduce a new product with a project life of 8 years. The
projects is to be set up in special Economic Zone (SEZ), qualifies for one time (at starting
) tax free subsidy from the state Goverment of Rs. 25,00,000 on Capital investments.
Initial equipments cost will be Rs. 1.75 crores. Additional equipments costing Rs.
12,50,000 will be purchase at the end of the third year from the cash inflow of thisyears.
At the end of 8 years, the original equipments will have no resale value, but additional
equipments can be sold for Rs. 1,25,000. A working capital Of Rs. 20,00,000 will be
needed and it will be released at the end of eighth years. The projects will be financed
with sufficient amt. of Equity capital . The sales volumes over eight years have been
estimated as follows:
Years 1 2 3 4th 5
Units 72,000 1,08,000 2,60,000 2,70,000 1,80,000
A selling price of Rs. 120 per unit is expected and variable expenses will amount
to 60% of sales revenue. Fixed cash operating Costs will amount rs. 1,80,000 per years.
The loss of any year will be set off from the profits of subsequent two years. The
company is subjects to 30 per cent tax rate and considers 12 per cent to be an
appropriates after tax costs of capital for this projects. The company follows straight
line method of depreciation.
Required: Calculate the net present value of the project and advise the
managements to take appropriate decision.
(Figures should be rounded off in the multiple of 1,000)
Note: The present value factors @ 12% discount rate are as follows,
Year 1 2 3 4 5 6 7 8
Present value factor 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404
Solution:
Computation of Cash Inflows After Tax (CFAT) in ooo’s
Particulars Year 1 Year 2 Year 3 Year Year
4/5 6to 8
yrs
A.Sales Units 72 108 260 270 180
B. selling price per unit (Rs.) 120 120 120 120 120
C. Sales [A – B] 8,640 12,960 31,200 32,400 21,600
D. Less: Total cost:
Variable costs @ 60% of sale 5,184 7,776 18,720 19,440 12,960
Depreciation 2,188 2,188 2,188 2,413 2,413
Other fixed costs 1,800 1,800 1,800 1,800 1,800
Total cost 9,172 11,764 22,708 (23,653) (17,173)
E. Earnings before tax (532) 1,196 8,492 8,747 4,427
F. less: Tax @ 30% - (199) 2,548 (2,624) (1,328)
G. Earnings after tax (532) 997 5,944 6,123 3,099
H. Add: Depreciation 2,188 2,188 2,188 2,413 2,413
I. Cash flow after taxes (CFAT 1,656 3,185 8,132 8,536 5,512
(for year other than last year
J. Add: release of working capital 2,000
K. Add: cash Salvage value of asset 125
L. Total CFAT for the last years. 7,637
Computation of Net Present Value
Particulars Year PV factor Amount PV
Purchase price of New machinery 0 1 (17,500) (17,500)
Page | 3
, K.J.SOMAIYA COLLEGE OF SCEINCE AND COMMERCE T.Y.B.M.S.
Subsidy from Govt. 0 1 2,500 2,500
Working Capital 0 1 (2,000) (2,000)
Additional Equipments 3 0.712 (1,250) (890)
CFAT of year 1 1 0.893 1,656 1,479
CFAT of Year 2 2 0.797 3,185 2,538
CFAT of year 3 3 0.712 8,132 5,790
CFAT of Year 4 4 0.636 8,536 5,429
CFAT of Year 5 5 0.567 8,536 4,840
CFAT of Year 6 6 0.507 5,512 2,795
CFAT of Year 7 7 0.452 5,512 2,491
CFAT of Year 8 8 0.404 7,637 3,085
NPV 10,557
Recommendation : The company Should accept the projects since NPV is positive.
Note: The tax for the second years has been calculated after set off of brought
forward loss of the first years. [I.e. 30% of (Rs. 1,196 – Rs. 532)].
Q.4 Consider the following mutually exclusive projects.
Projects Cash flow (Rs.)
C0 C1 C2 C3 C4
A -10,000 6,000 2,000 2,000 12,000
B -10,000 2,500 2,500 5,000 7,500
C -3,500 1,500 2,500 500 5,000
D -3,000 0 0 3,000 6,000
Required:
(i)Calculate the payback period for each project:
(ii)If the standard payback period is 2 years, which project will you select ? will your
answer differ, if standard payback period is 3 years?
(iii)If the cost Of capital is 10%. Compute the discounted payback period for each
projects Which projects, will you recommend if standard discounted payback period
is (i)2 years ; (ii)3 years?
(iv)Compute NPV of each projects, which projects will you recommends on the NPV
criterion? The cost of capital is 10%. What will be the appropriate choice criteria in the
case? The PV factors at 10% are:
Years 1 2 3 4
PV Factors at 10% 0.9091 0.8264 0.7513 0.6830
Solution:
(i)Payback Period
Years Projects A Project B Project C Project D
CI Cum. CI CI Cum. CI Cum.CI CI Cum.Ci
CI
1 6,000 6,000 2,500 2,500 1,500 1,500 0 0
2 2,000 8,000 2,500 5,000 2,500 4,000 0 0
3 2,000 10,000 5,000 10,000 500 4,500 3,000 3,000
4 12,000 22,000 7,500 17,500 5,000 9,500 6,000 9,000
(ii) If the standard payback period is 2 years only projects C can be selected.
If the standard payback period is 3 years , all the 4 projects can be selected.
(iii)Discounted payback Period
PVF @ Project A Project B Project C Project D
Page | 4
CHAPTER 1 CAPITAL BUDGETING PART 1
Q.1 A company proposes to install a machine involving a capital cost of Rs. 3,60,000.
The life of the machines is 5 years and its salvage value at the end of the life is Nil. The
machine will produce the net operating income after depreciation of Rs. 68,000 per
annum. The company’s tax rate is 45%. The present value factors for 5 years are as
under:
Discounting Rate 14% 15% 16% 17% 18%
Cumulative Factors 3.43 3.35 3.27 3.20 3.13
You are required to calculate the internal rate of return of the proposal:
Solution:
Computation of Cash Inflow
A. Net operating income Per annum 68,000
B. Less: Tax @ 45% (30,600)
C. Profit after tax 37,400
D. Add: Depreciation (Rs. 3,60,000/ 5 years) 72,000
E. Cash inflow p.a. 1,09,400
The IRR of the investments can be found as follows:
NPV = - Rs. 3,60,000 + Rs. 1,09,400 (PVAF5,r) =0
𝑅𝑠.3,60,000
Or, PAVF5r (cumulative factors) = 𝑅𝑠.1,09,400 = 3.29
Computation of internal Rate of return
A. Discounting rate 15% 16%
B. Cumulative factors 3.35 3.27
C. Total cash inflow 3,66,490 3,57,738
(Rs. 1,09,400×3,350) (Rs.1,09,400×3.27)
D. Initial Outlay (Rs.) 3,60,000 3,60,000
E. NPV (Rs) [C – D] 6,490 (2,262)
6,490
IRR = 15% +[6,490+2,262] = 15% + 0.74% = 15.74%
Alternatives Method
𝑃𝑉𝐴𝐹 𝑎𝑡 𝑙𝑜𝑤𝑒𝑟 𝑟𝑎𝑡𝑒−𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜𝑑
IRR = Lower Rate + 𝑃𝑉𝐴𝐹 𝑎𝑡 𝑙𝑜𝑤𝑒𝑟 𝑟𝑎𝑡𝑒−𝑃𝑉𝐴𝐹 𝑎𝑡 ℎ𝑖𝑔ℎ𝑒𝑟 𝑟𝑎𝑡𝑒
3.35−3.29
= 15% + 3.35−3.27 = 15.75%.
Q.2 A company is considering the proposals of takings up a new projects which
requires an investments of Rs. 400 lakhs on machinery and other assets. The projects is
expected to yield the followings earnings (before depreciation and taxes) over the
next five years.
Year 1 2 3 4 5
Earnings (Rs.in lakhs) 160 160 180 180 150
The cost of raising the additional capital is 12% and assets have to be
depreciation at 20% on Written Down value bases. The scrap value at the end of the
five years. Period may be taken as zero income tax applicable to the company is 50%.
Required: Calculate the net present value of the project and advise the
managements to take appropriate decision. Also calculate the internal Rate of
Return of the project.
Page | 1
,K.J.SOMAIYA COLLEGE OF SCEINCE AND COMMERCE T.Y.B.M.S.
Note: Present value of Re. 1 at different rates of interest are as follows.
Year 10% 12% 14% 16%
1 0.91 0.89 0.88 0.86
2 0.83 0.80 0.77 0.74
3 0.75 0.71 0.67 0.64
4 0.68 0.64 0.59 0.55
5 0.62 0.57 0.52 0.48
Solution:
Statements Showing The Computation Of Cash Inflows After Tax [CFAT]
Particulars Year 1 Years 2 Year 3 Year 4 Year 5
Earnings before depreciation% 16,000 16,000 18,000 18,000 15,000
tax (8,000) (6,400) (5,120) (4,096) (3,277)
Less: Depreciation 8,000 9,600 12,880 13,904 11,723
Earnings before tax (4,000) (4,800) (6,440) (6,952) (5,862)
Less: Tax @ 50% 4,000 4,800 6,440 6,952 5,861
Earnings after tax 8,000 6,400 5,120 4,096 3,277
Add: Depreciation 12,000 11,200 11,560 11,048 9,138
Cash flow after taxes (CFAT)
Add: Tax savings on loss - - - 6,554
[50% of (Rs. 13,107 – 0 ) 15,692
Statements Showing The Computation of Net Present Value
Particulars Year Amt. PV PV PV PV PV factor PV
Factor Factor At 16%
at 12% At 14%
Purchase price of 0 40,000 1 40,000 1 40,000 1 40,000
New machinery
CFAT of year 1 12,000 0.89 10,680 0.88 10,580 0.86 10,320
CFAT of year 2 11,200 0.80 8,960 0.77 8,624 0.74 8,288
CFAT of year 3 11,560 0.71 8,208 0.67 7,745 0.64 7,398
CFAT of year 4 11,048 0.64 7,071 0.59 6,518 0.55 6,076
CFAT of year 5 15,692 0.57 8,944 0.52 8,160 0.48 7,532
NPV 3,863 1,607 (386)
Recommendation: Company should accept the projects at 12% since NPV is potive.
(ii)Calculation of internal Rate of Return (IRR)
1,607
IRR = 14% + 1,607+386 × (16% − 14%)
IRR = 14% + 1.61% = 15.61%.
Page | 2
,K.J.SOMAIYA COLLEGE OF SCEINCE AND COMMERCE T.Y.B.M.S.
Q.3 XYZ Ltd. is planning to introduce a new product with a project life of 8 years. The
projects is to be set up in special Economic Zone (SEZ), qualifies for one time (at starting
) tax free subsidy from the state Goverment of Rs. 25,00,000 on Capital investments.
Initial equipments cost will be Rs. 1.75 crores. Additional equipments costing Rs.
12,50,000 will be purchase at the end of the third year from the cash inflow of thisyears.
At the end of 8 years, the original equipments will have no resale value, but additional
equipments can be sold for Rs. 1,25,000. A working capital Of Rs. 20,00,000 will be
needed and it will be released at the end of eighth years. The projects will be financed
with sufficient amt. of Equity capital . The sales volumes over eight years have been
estimated as follows:
Years 1 2 3 4th 5
Units 72,000 1,08,000 2,60,000 2,70,000 1,80,000
A selling price of Rs. 120 per unit is expected and variable expenses will amount
to 60% of sales revenue. Fixed cash operating Costs will amount rs. 1,80,000 per years.
The loss of any year will be set off from the profits of subsequent two years. The
company is subjects to 30 per cent tax rate and considers 12 per cent to be an
appropriates after tax costs of capital for this projects. The company follows straight
line method of depreciation.
Required: Calculate the net present value of the project and advise the
managements to take appropriate decision.
(Figures should be rounded off in the multiple of 1,000)
Note: The present value factors @ 12% discount rate are as follows,
Year 1 2 3 4 5 6 7 8
Present value factor 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404
Solution:
Computation of Cash Inflows After Tax (CFAT) in ooo’s
Particulars Year 1 Year 2 Year 3 Year Year
4/5 6to 8
yrs
A.Sales Units 72 108 260 270 180
B. selling price per unit (Rs.) 120 120 120 120 120
C. Sales [A – B] 8,640 12,960 31,200 32,400 21,600
D. Less: Total cost:
Variable costs @ 60% of sale 5,184 7,776 18,720 19,440 12,960
Depreciation 2,188 2,188 2,188 2,413 2,413
Other fixed costs 1,800 1,800 1,800 1,800 1,800
Total cost 9,172 11,764 22,708 (23,653) (17,173)
E. Earnings before tax (532) 1,196 8,492 8,747 4,427
F. less: Tax @ 30% - (199) 2,548 (2,624) (1,328)
G. Earnings after tax (532) 997 5,944 6,123 3,099
H. Add: Depreciation 2,188 2,188 2,188 2,413 2,413
I. Cash flow after taxes (CFAT 1,656 3,185 8,132 8,536 5,512
(for year other than last year
J. Add: release of working capital 2,000
K. Add: cash Salvage value of asset 125
L. Total CFAT for the last years. 7,637
Computation of Net Present Value
Particulars Year PV factor Amount PV
Purchase price of New machinery 0 1 (17,500) (17,500)
Page | 3
, K.J.SOMAIYA COLLEGE OF SCEINCE AND COMMERCE T.Y.B.M.S.
Subsidy from Govt. 0 1 2,500 2,500
Working Capital 0 1 (2,000) (2,000)
Additional Equipments 3 0.712 (1,250) (890)
CFAT of year 1 1 0.893 1,656 1,479
CFAT of Year 2 2 0.797 3,185 2,538
CFAT of year 3 3 0.712 8,132 5,790
CFAT of Year 4 4 0.636 8,536 5,429
CFAT of Year 5 5 0.567 8,536 4,840
CFAT of Year 6 6 0.507 5,512 2,795
CFAT of Year 7 7 0.452 5,512 2,491
CFAT of Year 8 8 0.404 7,637 3,085
NPV 10,557
Recommendation : The company Should accept the projects since NPV is positive.
Note: The tax for the second years has been calculated after set off of brought
forward loss of the first years. [I.e. 30% of (Rs. 1,196 – Rs. 532)].
Q.4 Consider the following mutually exclusive projects.
Projects Cash flow (Rs.)
C0 C1 C2 C3 C4
A -10,000 6,000 2,000 2,000 12,000
B -10,000 2,500 2,500 5,000 7,500
C -3,500 1,500 2,500 500 5,000
D -3,000 0 0 3,000 6,000
Required:
(i)Calculate the payback period for each project:
(ii)If the standard payback period is 2 years, which project will you select ? will your
answer differ, if standard payback period is 3 years?
(iii)If the cost Of capital is 10%. Compute the discounted payback period for each
projects Which projects, will you recommend if standard discounted payback period
is (i)2 years ; (ii)3 years?
(iv)Compute NPV of each projects, which projects will you recommends on the NPV
criterion? The cost of capital is 10%. What will be the appropriate choice criteria in the
case? The PV factors at 10% are:
Years 1 2 3 4
PV Factors at 10% 0.9091 0.8264 0.7513 0.6830
Solution:
(i)Payback Period
Years Projects A Project B Project C Project D
CI Cum. CI CI Cum. CI Cum.CI CI Cum.Ci
CI
1 6,000 6,000 2,500 2,500 1,500 1,500 0 0
2 2,000 8,000 2,500 5,000 2,500 4,000 0 0
3 2,000 10,000 5,000 10,000 500 4,500 3,000 3,000
4 12,000 22,000 7,500 17,500 5,000 9,500 6,000 9,000
(ii) If the standard payback period is 2 years only projects C can be selected.
If the standard payback period is 3 years , all the 4 projects can be selected.
(iii)Discounted payback Period
PVF @ Project A Project B Project C Project D
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