Definition:
Capital budgeting is the process of making investment decisions in long-term assets or projects that are expected to generate returns over an extended period, typically more than one year. These investment decisions play a crucial role in a company's growth and profitability, as they involve significant financial commitments and have long-term implications.
Objective:
The main objective of capital budgeting is to determine which investment opportunities are worth pursuing, given a company's limited resources, to maximize the value of the firm. The process typically involves the following steps:
Project Identification:
Identifying potential investment opportunities or projects that align with the company's strategic objectives and business goals.
Project Evaluation:
Evaluating the potential benefits and costs associated with each project. This includes estimating cash flows over the project's life and discounting them to their present value using an appropriate discount rate.
Capital Budgeting Techniques:
There are several capital budgeting techniques used to assess the viability of projects. The most common ones are:
01. Net Present Value (NPV):
NPV calculates the present value of expected future cash inflows minus the initial investment. A positive NPV indicates that the project is expected to increase the company's value.
02. Internal Rate of Return (IRR):
IRR is the discount rate at which the NPV of the project becomes zero. It represents the project's expected rate of return. If the IRR is greater than the company's cost of capital, the project is considered acceptable.
03. Payback Period:
Payback period calculates the time required to recover the initial investment from the project's cash flows. Shorter payback periods are generally preferred, as they indicate quicker recovery of the investment.
04. Profitability Index (PI):
PI is the ratio of the present value of cash inflows to the initial investment. A PI greater than 1 suggests that the project is profitable.
Abbreviation
01. PBP = payback period
02. NCO =Net cash outlay
03. NCB = Net cash benefit
04. CFBT(Cash flow before tax)
05. EBT = Earnings before tax
06. EAT =Earnings after tax
07. CFAT/NCB=Cash flow after tax
08. C=Cumulative cash flows near to NCO
09. D = Cash flow of the following year
10. A =Year of cumulative cash flow near to NCO
11. ARR = Average rate of return
12. ROI = Return on investment
13. PBR = pay back reciprocal
14. PI =Profitability index
15. TPV =Total present value
16. IRR = Internal rate of return
17. SV = salvage value/ Scroll value/ Residual value
18. WC = working capital
19. PV.PBP = Present value payback period
20. DF= Discount factor{1/(1+r)n}
21. D.PBP= Discount payback period
22. ARR = Accounting Rate of return
Lets start with some Important formula
Payback period:(PBP)
There are four (04) steps to calculate PBP (payback period)
When cash flows Even
1. without tax
2. with tax
When cash flows uneven
3. without tax
4. with tax
01. PBP =NCO/NCB [When cash flows is even)
02. PBP =A+NCO-C/D [When cash flows is uneven)
03. CFBT (Cash flow before tax) **** [When tax rate exist] ([When cash flows is uneven)
(Less)Depreciation ****
Result creates EBT ****
(Less)Tax (EBT*Tax rate) ****
Result creates EAT ****
(Add)Depreciation ****
Result creates CFAT/NCB ****
04. Depreciation =Cost-SV (Salvage value)/Life of the Assets
05. ARR= AV.EAT /AV.Investment (100)
06. AV.EAT= Total EAT/ Total year
07. AV.Investment= Cost/02
or AV.Investment =SV+WC+(Cost-SV)/ 02[When mention SV+WC in the question]
08. ROI = AV.EAT / NCO (100)
09. PBR = 1 / PBP (100) [When cash flow uneven]
10. PBR = NCB /NCO (100) [When cash flow even]
11. Surplus life=Useful life-PBP
12. NPV=TPV-PV of NCO
13. PI= TPV / NCO (100)
14. NPI =PI-100%
15. PV.PBP /D.PBP = A+ PV of NCO-C /D
16. IRR = A+ C/C-D (B-A)
[When calculate IRR we need two NPV & Two discount factor (DF) one is positive another is negative, if one DF-14% another may be, 18% for negative reason (it is depend on your assumption)
Where, A=Lower discount rate (14) %,( if)
B = Higher discount rate (18%), (if)
C = positive value of NPV,
D = Negative value of NPV.]
17. AV Investment= SV + WC + Cost- SV/02
[Where mention in the question SV+WC the total balance would be consider in CFAT calculation in the last column. also working capital added in to the new NCO.
18.ARR = (Average Accounting profit /Average annual investment)*100
18. (Average Accounting profit= Total of Net cash inflow /no of years cash flows in total
19.Average annual investment = ( Initial Investment / 2)
Determination of number of row (When cash flow uneven & no tax effect %)
When calculate only PBP +NPV+PI+NPI +PV.PBP Row will be 6 column
(Years + CFAT + C.CFAT + D.F + PV + C.PV)
Determination of number of row (When cash flow uneven & Retain tax %)
When calculate only NPV& PI & NPI & DPBP Row will be 10 column
(Years + CFBT + DEP + EBT + TAX +EAT + CFAT +D.F+PV+C.PV)
When calculate only PBP & NPV& PI & NPI &PV.PBP Row will be11 column
(Years + CFBT + DEP + EBT + TAX +EAT + CFAT + C.CFAT+D.F+PV+C.PV)
Practical Example (01).
MR. Karim investment in project Tk.1,20,000. life of this project 10 years. Annual cash inflow in every year Tk.30,000.
Calculate- pay back period (PBP ).
Ans:
PBP = NCO/NCB [When cash flows is even)
= TK.120000/30000
= 4 yearsPractical Example (02).
Investment in a project TK.1,20,000. Life of this project 10 years.Annual cash flows in every year Tk.30,000. If tax rate for the company is 30%. Calculate payback period.
Ans:
Depreciation =Cost-SV /Life of the Assets
=Tk.(120000-0) /10 years
=Tk.12000
Table for calculation of CFAT (Year-1-10) ( Since cash flow is even)
CFBT (Cash flow before tax) TK.30 ,000 [When tax rate exist] ([When cash flows is uneven)
(Less)Depreciation = TK.12000
Result creates EBT =TK.18000
(Less)Tax (18000*30%) = Tk.(5400)
Result creates EAT = Tk.12600
(Add)Depreciation =Tk.12000
Result creates CFAT/NCB = Tk.24600
PBP = NCO/NCB [When cash flows is even)
= 120000/24600
= 4.88years
Practical Example (03). [ when cash flows is uneven)
The capital expenditure of a company is 11,000. Scrap value is 4,000 having a life of the company is 5 years. Cash flows after tax (CFAT) is as follows.
Year CFAT
1 4000
2 4000
3 4000
4 3000
5 2000
Required Payback period
Ans:
Table for calculation of PBP
Year
CFAT
Cumulative(CFAT)
1
4000
4000
2(A)
4000
8000(C)
3
4000(D)
12000
4
3000
15000
5
2000
17000
We know that,
PBP = A+NCO-C/D [When cash flows is uneven)
= 2+11000-8000/4000
=2.75 years
Practical Example (04).
Wimax company LTD. Plans to a machine which cost Tk.3,00,000. the estimated salvage value is Zero. Tax rate is 50%. The company usages straight line depreciation method and proposed project has cash flow before tax as follows
Year CFBT
1 70000
2 90000
3 80000
4 75000
5 65000
Required
1.PBP
2.ARR
3.ROI
4.PBR
Ans:
Depreciation =Cost-SV (Salvage value)/Life of the Assets
=Tk.(300000-0)/5years
=Tk.60,000
Table for calculation of PBP, ARR, ROI, PBR
Year-
1
CFBT
2
Dep
3
EBT
4=(2-3)
TAX
5= (4*50%)
EAT
6=(4-5)
CFAT
7=(3+6)
Cumulative
(CFAT)
8
1
70000
60000
10000
5000
5000
65000
65000
2
90000
60000
30000
15000
15000
75000
140000
3
80000
60000
20000
10000
10000
70000
210000
4 ( A)
75000
60000
15000
7500
7500
67500
277500 (C)
5
65000
60000
5000
2500
2500
62500(D)
340000
We know that,
PBP = A+ NCO-C /D [When cash flows is uneven)
= 4+300000-27750/62500
= 4.36 years
ARR= AV.EAT/AV Investment(100) AV.EAT= = 5000+15000+10000+7500+2500/5
= (8000/150000)(100) = 8000
= 5.33% AV.investment = 300000/02 =150000
ROI = (AV.EAT/NCO) (100)
= (8000/300000) (100)
= 2.67%%
PBR = 1/PBP (100)
= 1/4.36 (100)
= 22.93%
Practical Example (05).
Wimax Company is thinking of a new project. A machine cost,Tk.50,000 has to be procured to implement this project. The estimated life of this machine would be 5 years having no salvage value. The tax rate of that company is 55% and does not get any investment allowance. Discount rate 10%. The company charges depreciation on straight line basis. Cash flow before tax(CFBT) would be as follows.
At the end of Year CFBT
1 10000
2 11000
3 14000
4 15000
5 25000
You’re required to calculate
1. PBP
2. ARR
3. ROI
4. PBR
5. NPV
6. PI
7. NPI
8. PV
Ans:
Note-01 Depreciation =Cost-SV (Salvage value)/Life of the Assets
=Tk.(50000-0)/05years
=Tk.10000
Year-
1
CFBT
2
Dep
3
EBT
4=(2-3)
TAX
5= (4*50%)
EAT
6=(4-5)
CFAT
7=(3+6)
Cumulative
(CFAT)
8
Discount
factor(9)
PV
10=7*9
Cu.PV
11
1
10000
10000
0
0
0
10000
10000
0.909
9090
9090
2
11000
10000
1000
550
450
10450
20450
0.826
8632
17722
3
14000
10000
4000
2200
1800
11800
32250
0.751
8862
26584
4(A)
15000
10000
5000
2750
2250
12250
44500(C)
0.683
8367
34951
5
25000
15000
8250
6750
16750(D)
61250
0.621
10402
45353
Total PV= 45353 We know that,
01. PBP = A+NCO-C/D [When cash flows is uneven)
=4+50000-44500/16750
=4.33 years
2. ARR= AV EAT/AV.Investment (100)
= 2250/50000 (100)
=4.50%
3. ROI = AV.EAT/NCO (100)
= 2250/50000 (100)
= 4.50%%
4. PBR = 1/PBP (100)
= 1/4.33 (100)
= 23.09%
5. NPV=TPV-NCO
=45353-50000
= (4547)
6. PI= TPV/NCO(100)
= 45353/50000(100)
=90.71%
7. NPI =PI-100
=90.71%-100%
= 9.29%
8. PV.PBP
= A+PV of NCO-C/D
=5 +50000-45353/10402
=5.45 Years
Practical Example (06).
You are a financial analysis of Tamanna electronic company .The director of capital budgeting has asked you to analysis two proposed capital investment, project -A & Project- B. Each project 12% cost of capital. The project expected net cash flows are as follows;
Year
Project -A
Project-B
0
(10000)
(10000)
1
6500
3500
2
3000
3500
3
3500
3000
4
1500
2500
Required:
1. Calculate each project s PBP, NPV, & PI
2. Which project should be accepted if they are independent?
3. Which project should be accepted if they are mutually exclusive?
Table for necessary calculation
Project-A
Project-A
Year
CFAT
C.CFAT
D.F12%
PV
CFAT
C.CFAT
D.F12%
PV
1
6500
6500
0.893
5805
3500
3500
0.893
3126
2A
3000
9500C
0.797
2391
3500
7000C
0.797
2790
3
3500(D)
13000
0.712
2492
3000D
10000
0.712
2136
4
1500
14500
0.636
954
2500
12500
0.636
1590
TPV
11642
TPV
9642
Project-A
1. PBP = A+NCO-C/D [When cash flows is uneven)
= 2+10000-9500/3500
= 2.14 years
Project-B
2. PBP = A+NCO-C/D [When cash flows is uneven)[When cash flows is uneven)
= 2+10000-7000/3000
= 3 years
Project -A
NPV=TPV-NCO
= 11642-10000
= 1642
PI = Total PV/NCO (100)
= 11642/10000 (100)
= 116.42 %
Project -B
NPV=TPV-NCO
= 9642-10000
= (358)
6. PI = Total PV/NCO (100)
= 9642/10000 (100)
= 96.42 %
Comments-A
Since project A of PBP=2.14 years <useful life ,NPV= Tk.1642 is positive .PI=116.42%>100 , hence project A should be accepted.
Comments-B
Since project B of PBP=3 years <useful life, NPV= Tk.(358) is Negative .PI=96.42%<100 , hence project A should be rejected.
Decision Table:
Details
Project- A
Project-B
Decision
PBP
2.14 years
3 years
Project A accepted
NPV
Tk.11642
Tk.(358)
Project A accepted
PI
116.4%
96.42%
Project A accepted
Practical Example (07).
Sharmin company expects to save Tk.56,000 a year in cash operating expense for the next 10 years, if it buys a new machine at cost of Tk.2,20,000. Salvage value is expected at the end of 10 years. The company is satisfied with a 14% rate of return. Ignore tax impact. The present value of Tk.1.00 required for the purpose of this example is given below
Year
14%
20%
22%
1st
0.877
0.833
0.820
5th
3.433
2.991
2.864
10th
5.216
4.192
3.923
You’re required to calculate
1. PBP
2. ARR
3. ROI
4. NPV
5. Internal rate of return (IRR)to comment on the acceptability of the project.
Ans:
Depreciation = 2,20,000/10 years
= Tk.22,000
1. PBP = NCO/NCB [When cash flows is uneven
= 2,20,000/56000
= 3.93 years
2. ARR = AV EAT/AV Investment (100)
= 34000/11000 (100)
= 30.91%%
3. ROI = AV EAT/NCO (100) (100)
= 34000/22000(100)
= 15.45%%
Table for calculation of NPV
Year
CFAT
D.F(14%)
TPV
1-10
56000
5.216
292096
1. NPV=TPV-NCO
= 292096-220000
= TK.72096
Table for calculation of IRR
Year
CFAT
D.F (20%)
PV/TVP
D.F (22%)
PV/TVP
1-10
56000
4.192
234752
3.923
219688
-NCO
220000
-NCO
220000
NPV
+14752
NPV
-312
IRR = A+ C/C-D (B-A)
= 20+14752/14752-(-312) (22-20)
= 21.96%
Practical Example (08).
An enterprise is consider a new product line .the details of the investment proposal are follows
Initial out lay tk.100000
Estimated life =5 years
Scroll value=TK.10000
Working capital=Tk.20000
Year
Cash flow (Tk.)
1
25000
2
30000
3
32000
4
35000
5
40000
Project cost of capital is 10% and tax rate 45%. Depreciation will be Straight line basis. Your are required to calculate
1. PBP
2. ARR
3. ROI
4. PBR
5. NPV
6. PI
7. NPI
8. IRR
Ans:
Depreciation= Cost-Salvage value/useful life
= 100000-10000/5 years
=Tk.18000
Table for necessary calculation
Year-
1
CFBT
2
Dep
3
EBT
4=(2-3)
TAX
5= (4*45%)
EAT
6=(4-5)
CFAT
7=(3+6)
Cumulative
(CFAT)
8
Discount
Factor
9
PV
10=7*9
Cu.PV
11
1
25000
18000
7000
3150
3850
21850
21850
0.909
19862
9090
2
30000
18000
12000
5400
6600
24600
46450
0.826
20320
17722
3
32000
18000
14000
6300
7700
25700
72150
0.751
19301
26584
4(A)
35000
18000
17000
7650
9350
27350
99500C
0.683
18680
34951
5
40000
18000
22000
9900
(SV+WC)
12100
30100
30000D
159100
0.621
18692
18630
45353
Total=39600 =115485
1. PBP= A+NCO-C/D [When cash flows is uneven)
=A+120000-99500/60100
=4.34 years
2. ARR= AV.EAT/AV. Investment (100)
= 7920/75000 (100)
=10.56%
3. ROI = AV.EAT/NCO (100)
= 7920/120000(100)
= 6.60%%
4. PBR =1/PBP (100)
= 1/4.34 (100)
= 23.04%
5. NPV=TPV-NCO
=115485-120000
= (4515)
6. PI= TVP/NCO (100)
= 115485/120000 (100)
=96.24%
7. NPI =PI-100
=96.24%-100%
= 3.76%
Table for calculation of IRR
Year-1
CFAT-2
D.F-14%
3
PV
4=2*3
D.F18%
5
PV
6=2*5
1
21850
0.909
19862
0.952
20801
2
24600
0.826
20320
0.907
22312
3
25700
0.751
19301
0.864
22205
4
27350
0.683
18680
0.823
22509
30100
30000
0.621
18692
18630
0.784
23598
23520
TPV= 115485 TPV=134945
8. IRR = A+C/C-D (B-A)
= 5+14945/14945- (-4515) (10-5)
= 8.84
Practical Example (09).
Using a 14% cost of capital, calculate the PI & NPI from the following project
Year
Cash flow (Tk.)
0
(500000)
1
100000
2
120000
3
140000
4
160000
5
180000
6
200000
Table for calculation of PI &NPI
Year
CFAT
D factor
PV(CFAT*D.F)
1
100000
1/(1+0.14)1=0.877
87700
2
120000
0.769
92280
3
140000
0.675
94500
4
160000
0.592
94720
5
180000
0.519
93420
6
200000
0.456
91117
TPV=553737
6. PI= TPV/NCO (100)
= 553737/500000 ( (100)
=111%
7. NPI =PI-100
=111%-100%
= 11%