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Column1 Column2 Subsequent Cash Inflows Column1 Column2 Column3 Column4 Column5 Column6 Column7 Column8
Cost of new Machine Particulars 1Year 2Year 3Year 4year 5Year 6Year 7year 8Year 📒 1. CASH FLOW ESTIMATION
Installation Charges sales ✅ A) Non-Replacement Case
Working Capital Variable cost
Salvage value of new asset Fixed cost (New product / new machine / new project)
Life in years CFBT
Tax Rate Depreciation Step 1: Operating Data
Sales per unit PBT
variable cost per unit Tax Sales = SP per unit × Units sold
fixed cost PAT Variable Cost = VC per unit × Units sold
Number of units sold Depreciation Fixed Cost = Given
CFAT
Cash Outflow Column1 Step 2: Profit Calculation
Cost of new Machine Depreciation = (cost + installation charges - salvage value)/life of asset
Installation Expenses CFBT = Sales − Variable Cost − Fixed Cost
Working Cap Depreciation = (Cost + Installation − Salvage) ÷ Life
Net Cash Outflow PBT = CFBT − Depreciation
Tax = PBT × Tax Rate (If PBT < 0 → Tax = 0)
Terminal Cash Inflows Column1 PAT = PBT − Tax
Additional Working cap CFAT = PAT + Depreciation
Salvage Value of new asset
Tax paid or saved if nothing is mentioned , Salvage value (book value) is sale value.
Total Terminal Cash Inflow Step 3: Initial Cash Outflow
Net Cash Outflow = Machine + Installation + Working Capital
Step 4: Terminal Cash Flow
Book Value = Cost + Installation − (Depreciation × Life)
Tax on Sale = (Sale value − Book value) × Tax rate
Terminal CF = Salvage value + WC recovery −/+ Tax effect
REPLACEMENT CASE
Subsequent Cash Inflows
Column1 Column2 Column1 Column2 Column3 Column4 Column5 Column6 Column7 Column8 Column9 Column10 Column11
Cost of new Machine B) Replacement Case
Installation Charges Particulars 1Year 2Year 3Year 4year 5Year 6Year 7Year 8Year 9Year 10Year
Working Capital Cost saving- new machine /CFBT (Replace old machine with new)
Life in years Dep of New Asset
Tax Rate Dep of old Asset Operating Differences
Book Value of old Asset today Incremental Dep
sale value of old asset today PBT CFBT = Cost saving from new machine
Salvage value of new asset Tax Dep(New) = (New cost + Install − Salvage new) ÷ Life
PAT Dep(Old) = Old book value ÷ Remaining life
Cost saving due to new machine incremental Depreciation Incremental Dep = Dep(New) − Dep(Old)
CFAT
Cash Outflow Column1
Cost of new Machine Profit Calculation
Installation Expenses Depreciation = (cost + installation charges- salvage value)/life of asset
Working Cap PBT = CFBT − Incremental Dep
Sale value of old asset today Tax = PBT × Tax Rate
Capital loss PAT = PBT − Tax
Tax saved on Capital Gains CFAT = PAT + Incremental Dep
Net Cash Outflow
Terminal Cash Inflows Column1 Initial Outflow
Additional Working cap
Salvage Value of new asset Capital Gain/Loss = Sale value old − Book value old
Tax paid or saved if nothing is mentioned , Salvage value (book value) is sale value. Tax effect = Capital gain/loss × Tax rate
Total Terminal Cash Inflow Net Outflow = New cost + Install + WC − Sale value ± Tax effect
Terminal Flow
Terminal CF = Salvage of new + WC recovery −/+ Tax
PAYBACK PERIOD: 📒 2. CAPITAL BUDGETING METHODS
✅ Payback Period
PROBLEM 1 : A project requires an outflow of Rs.40,000 and the expected inflows generated from the project are Rs.10,000, Rs.12,000, Rs.10,000, Rs. 7,000 and Rs. 5,000 for the next 5 years. Calculate Payback period.
Equal Cash Flows
SOLUTION INITIAL CASH OUTFLOW
YEAR CASH INFLOWS CUMULATIVE CASH INFLOWS Payback = Initial Investment ÷ Annual Cash Inflow
1 10000
2 12000 Equal cash inflows case => pb period = Initial cash outflow/amount of Equal cash inflow
3 10000 Unequal Cash Flows
4 7000 Unequal Cash Inflows case => pb period = P+(B/C)
5 5000 here , P = no. of years immediately preceeding the year of final recovery PB = P + (B ÷ C)
B = balance amount to be recovered in the year of final recovery P = Years before recovery
PAYBACK PERIOD = C = cash inflow in the year of final recovery B = Balance left
C = Cash flow in recovery year
AVERAGE RATE OF RETURN:
ARR = Avg. annual PAT *100 / Avg. investment ✅ ARR (Average Rate of Return)
•Average Investment = ½ {(Initial cost + Installation cost – Salvage value)} + Salvage value + working capital Average Profit = Total PAT ÷ Years
Avg annual PAT = Sum of annual PAT of all years / life span of project Average Investment = (Initial − Salvage) ÷ 2
ARR (%) = (Avg Profit ÷ Avg Investment) × 100
PROBLEM 2: ABC Ltd. is planning to purchase a machine costing Rs. 60,000 and having a salvage value of Rs. 8,000. The economic life of the machine is 5 years and it is likely to give following earnings after tax
YEAR 1 2 3 4 5 ✅ NPV
PAT 6000 7000 5000 6000 8000 NPV = PV of Inflows − Initial Outflow
Excel =NPV(rate, cashflows) − Initial investment
SOLUTION: COST OF MACHINE SALVAGE VALUE
✅ Profitability Index
YEAR PAT PI = PV of Inflows ÷ PV of Outflows
1 Decision: PI > 1 → Accept
2
3 ✅ IRR
4 IRR = Rate at which NPV = 0
5 Excel =IRR(cashflow range)
AVERAGE PROFITS
AVERAGE INVESTMENT
ARR
NET PRESENT VALUE (NPV) and Probitability index
NPV(RATE,RANGE OF CASH INFLOWS)+(-CASH OUTFLOW)
PROBLEM 3: RS Ltd. is planning to buy a machine for Rs. 1,00,000. The cash flows after tax from this machine in next 5 years will be as follows:
YEAR 1 2 3 4 5
CFAT 26000 29000 32000 35000 38000
Using NPV method, give your advice whether the machine should be purchased if cost of capital is 10%
SOLUTION: CASH OUTFLOW
COST OF CAPITAL
YEAR CFAT
1
2
3
4
5
NPV
PROFITABILITY INDEX
pi= pv of CI/pv of CO
INTERNAL RATE OF RETURN
IRR(range of cash inflow and rate)
PROBLEM 4: SR Ltd. is considering investing in a project requiring a capital outlay of Rs. 1,00,000. Forecast for cash flows are:
YEAR 1 2 3 4 5
CFAT 40000 40000 20000 40000 40000
Project salvage value is zero. Calculate IRR and advice the company whether to invest in project if desirable rate of return is 20%.
SOLUTION: CASH OUTFLOW
COC
YEAR CFAT
0
1
2
3
4
5
IRR
COST OF CAPITAL
ISSUED AT PAR => NP = FV - ISSUED EXPENSE
ISSUED AT PREMIUM => FV + PREMIUM - ISSUED EXPENSE % 📒 3. COST OF CAPITAL
ISSUED AT DISCOUNT => NP = FV - DISCOUNT -ISSUED EXPENSE % ✅ Debt (Debentures)
DEBENTURES (IRREDEMABLE) DEBENTURE (REDEEMABLE) Net Proceeds
PROBLEM 1. A Company issues Rs.10,00,000, 12% debentures of Rs.100 each. . PROBLEM 2 A Company issues Rs.10,00,000, 12% debentures of Rs.100 each. The debentures are redeemable after the expiry of fixed period of 7 years.
The company is in 35% tax bracket. Calculate: The company is in 35% tax bracket. Calculate: NP (Par) = FV − Expenses
(1) Cost of debt after tax, if debentures are issued (a) at Par, (b) 10% discount ,(c) 10% premium (1) Cost of debt after tax, if debentures are issued (a) at Par, (b) 10% discount ,(c) 10% premium NP (Premium) = FV + Premium − Expenses
(2) If brokerage is paid at 2%what will be cost of debentures, if issue is at par. (2) If brokerage is paid at 2%what will be cost of dedentures, if issue is at par. NP (Discount) = FV − Discount − Expenses
(I*(1-t)+((RV-NP)/N))/((RV+NP)/2) REDEEMABLE
int*(1-tax)/np or mp Irredeemable
0.12 Debentures Tax YEARS (N)
IRREDEEMABLE INTEREST Brokerage Kd (Before tax) = I ÷ NP
RV Kd (After tax) = I(1 − T) ÷ NP
0.12 Debentures Tax
INTEREST SOLUTION (a) When debentures are issued at Par ANSWER NP
RV Redeemable
SOLUTION (1) (a) When debentures are issued at Par ANSWER NP
Kd = [I + (RV − NP)/N] ÷ [(RV + NP)/2]
SOLUTION (1) (b) When debentures are issued at discount ANSWER NP DISCOUNT After tax: replace I with I(1 − T)
RV
SOLUTION (1) (b) When debentures are issued at discount ANSWER NP DISCOUNT ✅ Equity Shares
D1 = D0 (1 + g)
SOLUTION (1) (c) When debentures are issued at premium ANSWER NP PREMIUM Ke = (D1 ÷ MP) + g
RV
SOLUTION (1) (c) When debentures are issued at premium ANSWER NP PREMIUM ✅ Preference Shares
NP = FV − Discount − Expenses
SOLUTION (2) When debentures are issued at par ANSWER NP ISSUED EXPENSE Kp (Irredeemable) = (PD ÷ NP) × 100
RV Kp (Redeemable) = [PD + (RV − NP)/N] ÷ [(RV + NP)/2] × 100
SOLUTION (2) When debentures are issued at par ANSWER NP ISSUED EXPENSE
✅ WACC
Weight = Book value ÷ Total capital
Weighted cost = Weight × Specific cost
WACC = Sum of weighted costs
Homework
EQUITY SHARES DIVIDEND PRICE PLUS GROWTH CASE WEIGHTED AVERAGE COST OF CAPITAL 📒 3. COST OF CAPITAL
PROBLEM 3: A company shares are quoted in the market at Rs.20 currently. The company pays a dividend of Rs.1 per share and PROBLEM 5: A Ltd. has the following capital structure: ✅ Debt (Debentures)
the investor's market expects a growth rate of 5% per year. You are required to compute: Equity Share Capital (2,00,000 shares) 4000000
(i) Equity cost of capital, 6% Preference Share Capital @ Rs.100 1000000 Net Proceeds
8% Debentures 3000000
NP (Par) = FV − Expenses
D1=D0*(1+g) The market price of the company's Equity share is Rs.20. It is expected that company will pay current dividend of Rs.2 per share. NP (Premium) = FV + Premium − Expenses
SOLUTION: It will grow at 7% forever. The tax may be presumed at 50%. You are required to compute the following: NP (Discount) = FV − Discount − Expenses
Market Price (i) A weighted average cost of capital based on existing capital structure.
Dividend D0 (ii) The new weighted average COC if the company raises additional Rs.20,00,000 debt by issuing 10% debentures. This would
Growth result in increasing the expected dividend to Rs.3 and leave the growth unchanged but the price of share will fall to Rs.15 per share. Irredeemable
D1
SOLUTION: EXISTING CAPITAL STRUCTURE = BOOK VALUE METHOD Kd (Before tax) = I ÷ NP
ANSWER Ke=(D1/MP)+g (i) Kd (After tax) = I(1 − T) ÷ NP
Equity Share Capital
6% Preference Share Capital Source of capital Specific cost Book value WEIGHTS Weighted cc
8% Debenture Equity Share Capital @Rs.20 Redeemable
PREFERENCE SHARES Tax 6%Preference Share capital
PROBLEM 4: K Ltd. is planning to raise Rs.1 crore by the issue of 12% Preference Shares of Rs.100 each at 10% discount. 8%Debentures Kd = [I + (RV − NP)/N] ÷ [(RV + NP)/2]
The underwriting expenses are expected to be 2%. Find out the cost of preference share capital in each of the following cases: Equity Share Price After tax: replace I with I(1 − T)
(i) If preference shares are irredeemable, Equity Dividend (D1) Total
(ii) If preference share are redeemable at the end of 10th year at 15% premium. Use shortcut method. Growth rate ✅ Equity Shares
Ke Ke=(D1/MP)+g WACC WACC = SUM OF WEIGHTED COST OF CAPITAL /SUM OF WEIGHTS D1 = D0 (1 + g)
Ke = (D1 ÷ MP) + g
SOLUTION: (i) Preference Shares are irredeemable preference div
0.12 Preference shares NP = FACE VALUE - DISCOUNT - ISSUED EXPENSES NP ✅ Preference Shares
Discount rate PD NP = FV − Discount − Expenses
Underwriting exp (100-10%)-2% Kp Kp=PD*100/NP Kp (Irredeemable) = (PD ÷ NP) × 100
No.of shares TOTAL VALUE Kp (Redeemable) = [PD + (RV − NP)/N] ÷ [(RV + NP)/2] × 100
PD RATE deb interest
PREFERENCE DIVIDEND NP ✅ WACC
NP Kd Kd=I*(1-Tax)/NP or MP Weight = Book value ÷ Total capital
Weighted cost = Weight × Specific cost
Kp Kp=PD*100/NP WACC = Sum of weighted costs
(ii) Preference shares are redeemable at the end od 10th year at premium of 15%
Preference Dividend (ii)
Premium FOR RV Price of Equity share Source of capital Specific cost Book value Weighted cc
RV Equity Dividend (D1) Equity Share Capital @Rs.15
YEARS Growth rate 6%Preference Share capital
NP Ke Ke=(D1/MP)+g 8%Debentures
10% Debentures
Kp (PD+(RV-NP)/N)/((RV+NP)/2) deb interest Total
NP
Kd Kd=I*(1-Tax)/NP or MP WACC WACC = SUM OF WEIGHTED COST OF CAPITAL /SUM OF WEIGHTS
WALTER AND GORDON MODEL
Following are the details regarding 3 companies
A Ltd B Ltd C Ltd
IRR (r) 0.1 0.08 📒 4. DIVIDEND THEORIES
Cost of Capital (Ke) 0.1 0.1 0.1 ✅ Walter Model
Earning Per share 10 10 10 P = [D + (r/Ke) × (EPS − D)] ÷ Ke
Using Walter model, calculate the effect of dividend payment on the value of share of the above companies under:
Rule:
i) When no dividend is paid
ii) When dividend is paid @8Rs per share r > Ke → Low dividend better
ii) When dividend is paid @10Rs per share r = Ke → No effect
r < Ke → High dividend better
Calculate Market price of the share as per Walter Model:
✅ Gordon Model
(Div + ( r /Ke)*(EPS-Div))/Ke b = 1 − payout ratio
HOMEWORK g = b × r
D1 = EPS × (1 − b)
A Ltd. B Ltd C Ltd P0 = D1 ÷ (Ke − g)
A Ltd B Ltd C Ltd
D/P Ratio IRR (r) ✅ MM Model
0 Price = Cost of Capital (Ke) Ke = 1 ÷ P/E ratio
Earning Per share P1 = P0(1 + Ke) − D1
m (no dividend) = I
0.8 Price = m (with dividend) = I − (E − N×D1)
New shares = m ÷ P1
V0 = [(N + m) × P1 + E] ÷ (1 + Ke)
1 Price =
r>ke , lower the D/P ratio maximum the price price will be same at any D/p ratio r<ke , maximum the D/P ratio , maximum will the price
A' Ltd. is a "growth company". The price of share is maximum with zero payout ratio B' Ltd. is a normal firm. The price of the share is unaffected by the divident decision. C' Ltd. is a "declining company". The price increases with the increase in payout ratio
Assuming that the rate of return expected by investors is 11%, internal rate of return is 12% and earning per share is 15. Calculate price per share by Gordon Model if D/P ratio is 10% and 30%
Scenario 1 Scenario 2
EPS 15 15
Ke 0.11 0.11
r 0.12 0.12
D/p ratio 0.1 0.3
b (retention)
b*r DIVIDEND IN RS = D/P ratio*EPS
Price per share as per Gordon Model: (EPS*(1-b))/(Ke-b*r)
Price =
MM MODEL
P/E Ratio 10
No. of Outstanding shares (N) 50000
Price per share 100 📒 4. DIVIDEND THEORIES
Expected Net Income (E) 500000 ✅ Walter Model
New Investment (I) 1000000 P = [D + (r/Ke) × (EPS − D)] ÷ Ke
Dividend intended to be paid 8
Ke = 1 Rule:
P/E Ratio
r > Ke → Low dividend better
i) Price of the share at the end of the year if r = Ke → No effect
P1=P0*(1+ke)-D1 r < Ke → High dividend better
a) dividend is not declared P0
P1 ✅ Gordon Model
b) dividend is declared P1 b = 1 − payout ratio
g = b × r
ii.a) Amount to be raised through issue of new equity shares when dividend is not paid: m = I-(E-n*D1) D1 = EPS × (1 − b)
P0 = D1 ÷ (Ke − g)
Number of new shares to be issued : ✅ MM Model
Ke = 1 ÷ P/E ratio
P1 = P0(1 + Ke) − D1
ii.b)Amount to be raised through issue of new equity shares when dividend is paid:
m (no dividend) = I
m (with dividend) = I − (E − N×D1)
Number of new shares to be issued :
New shares = m ÷ P1
V0 = [(N + m) × P1 + E] ÷ (1 + Ke)
iii) Value of Firm: (1/(1+ke))*((n+m)*P1-I +E)
a) when no dividend is declared:
rP0 =
b) when dividend is declared
rP0 =
Therefore, Value of firm remains unaffected irrespective of the fact whether company pays dividend or not
WORKING CAPITAL REQUIREMENT
A performa cost sheet of a company provide you with the following particulars: Additional information:
Estimated Cost per unit: Selling Price 400 per unit 📒 5. WORKING CAPITAL ESTIMATION
Cost elements Amount per unit Level of activity 104000 units of production ✅ Step-wise Format
Raw materials 160 Raw materials in stock 4 average weeks
Direct Labour 60 Work in progress 2 average weeks Production
Overheads 120 Finished goods in stock 4 average weeks
340 Credit allowed by suppliers 4 average weeks Cost per unit = RM + Labour + Overheads
Credit allowed to debtors 8 average weeks Units per week = Annual production ÷ 52
Solution STATEMENT OF WORKING CAPITAL ESTIMATION Lag in payment of wages 1.5 average weeks
a) Current assets: cash 50000
1/4 of Sales is on cash basis Current Assets
Raw material Lag in payment of overheads 4 average weeks
Work in progress Safety margin 0.1 RM stock = RM/unit × units/week × weeks
Finished Goods WIP (RM) = RM/unit × units/week × WIP weeks
Debtors RM WIP FG DEBTOR WIP (Labour) = Labour × units/week × WIP weeks × % completion
Desired cash balance RM WIP (OH) = OH × units/week × WIP weeks × % completion
LABOUR Finished goods = Total cost/unit × units/week × FG weeks
Total Current assets (A) OVERHEADS Debtors = Selling price/unit × units/week × credit weeks
TOTAL Cash = Given
b) Current Liabilities:
creditors Total Current Assets (A)
wages Total Production per week =
overheads
Total Current liabilities (B) Current Liabilities
Net working capital requirement (A-B) Creditors = RM × units/week × credit weeks
Safety margin (10%) Outstanding wages = Labour × units/week × lag weeks
Total Working Capital Requirement Outstanding overheads = OH × units/week × lag weeks
Total Current Liabilities (B)
Final Working Capital
Net WC = A − B
Safety Margin = Net WC × 10%
Total WC Required = Net WC + Safety Margin
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