Chapter 4
Financial Statement Analysis
Net profit
1.
Return on equity =
Equity
=
Net profit
Total revenues
x
Total assets
x
Total revenues
Total assets
Equity
1
=
0.05
x
1.5
x
= 0.25 or 25 per cent
0.3
Debt
Note :
Equity
= 0.7
So
Total assets
= 1-0.7 = 0.3
Total assets
Hence Total assets/Equity = 1/0.3
2.
PBT
= Rs.40 million
PBIT
Times interest earned =
= 6
Interest
So PBIT = 6 x Interest
PBIT – Interest = PBT = Rs.40 million
6 x Interest = Rs.40 million
Hence Interest = Rs.8 million
3.
Sales = Rs.7,000,000
Net profit margin = 6 per cent
Net profit = Rs.7000000 x 0.06 = 420,000
Tax rate = 60 per cent
420,000
So, Profit before tax =
= Rs.1,050,000
(1-.6)
Interest charge = Rs.150,000
So Profit before interest and taxes = Rs.1,200,000
Hence
1,200,000
Times interest earned ratio =
= 8
150,000
4.
CA = 1500
CL = 600
Let BB stand for bank borrowing
CA+BB
= 1.5
CL+BB
1500+BB
=
1.5
600+BB
BB = 1200
1,000,000
5.
Average daily credit sales =
= 2740
365
160000
ACP =
= 58.4
2740
If the accounts receivable has to be reduced to 120,000 the ACP must be:
120,000
x 58.4 = 43.8days
160,000
Current assets
6.
Current ratio =
= 1.5
Current liabilities
Current assets - Inventories
Acid-test ratio =
= 1.2
Current liabilities
= 800,000
Sales
Inventory turnover ratio =
= 5
Inventories
Current assets - Inventories
Acid-test ratio =
Current liabilities
Current liabilities
= 1.2
Current assets
Inventories
This means
Current liabilities
= 1.2
Current liabilities
Inventories
1.5
-
= 1.2
800,000
Inventories
= 0.3
800,000
Inventories = 240,000
Sales
=5
So Sales = 1,200,000
2,40,000
7.
Debt/equity = 0.60
Equity = 50,000 + 60,000 = 110,000
So Debt = Short term bank borrowing = 0.6 x 110,000 = 66,000
Hence Total assets = 110,000+66,000 = 176,000
Total assets turnover ratio = 1.5
So revenue from operations = 1.5 x 176,000 = 264,000
Cost of goods sold as a percentage of total revenues = 80 per cent
So Cost of goods sold = 0.8 x 264,000 = 211,200
Days’ sales outstanding in trade receivables = 40 days
revenue from operations
So trade receivables =
x 40
360
264,000
=
x 40
= 29,333
360
Cost of goods sold
Inventory turnover ratio =
211,200
=
Inventory
= 5
Inventory
So Inventory = 42,240
As short-term bank borrowing is a current liability as well,
Cash and cash equivalents + trade receivables
Acid-test ratio =
Current liabilities
Cash and cash equivalents + 29,333
=
= 1.2
66,000
So Cash and cash equivalents = 49867
Plant and equipment = Total assets - inventories – trade s receivables – cash and cash equivalents
= 176,000 42240
29333
–
49867
= 54560
Putting together everything
Balance Sheet
Equity capital
50,000
Retained earnings
60,000
Short-term bank borrowing 66,000
176,000
Plant & equipment
Inventories
Cash and cash equivalents
Trade receivables
54,560
42,240
49,867
29,333
176,000
Sales
264,000
Cost of goods sold
211,200
8.
(i) Current ratio
= Current assets/ Current liabilities
45,000,000
=
=
1.5
30,000,000
Note: Please note that for the purpose of calculation of current ratio and acid –test ratio, we have
to include short-term bank borrowings in current liabilities.
Current assets – Inventories
(ii) Acid-test ratio =
25,000,000
=
= 0.83
Current liabilities
30,000,000
Long-term debt + Short-term bank borrowings+Trade creditors+Provisions
(iii) Debt-equity ratio =
Equity capital + Reserves & surplus
12,500,000 + 15,000,000+10,000,000+5,000,000
=
=1.31
10,000,000 + 22,500,000
Profit before interest and tax
(iv) Times interest coverage ratio =
Interest
15,100,000
=
= 3.02
5,000,000
Cost of goods sold
(v) Inventory turnover period
=
72,000,000
=
Inventory
365
= 3.6
20,000,000
(vi) Average collection period =
Net sales/Accounts receivable
365
= 57.6 days
95,000,000/15,000,000
=
(vii)
Net sales
Total assets turnover ratio
95,000,000
=
75 ,000,000
=
Total assets
Profit after tax
(ix) Net profit margin
5,100,000
=
95,000,000
=
Net sales
PBIT
(x) Earning power =
= 1.27
= 5.4%
15,100,000
=
Total assets
Equity earning
(xi) Return on equity =
Net worth
= 20.13 %
75,000,000
5,100,000
=
32,500,000
The comparison of the Omex’s ratios with the standard is given below
= 15.7%
Omex
1.5
0.8
1.3
3.02
3.6
57.6 days
1.27
5.4%
20.1%
15.7%
Current ratio
Acid-test ratio
Debt-equity ratio
Times interest covered ratio
Inventory turnover ratio
Average collection period
Total assets turnover ratio
Net profit margin ratio
Earning power
Return on equity
Standard
1.5
0.8
1.5
3.5
4.0
60 days
1.0
6%
18%
15%
9.
.
Current ratio
Debt-equity ratio
Total assets turnover
ratio
Net profit margin(%)
Earning power (%)
Return on equity (%)
20X1
1.68
1.23
5.00
20X2
1.47
1.32
20X3
1.37
1.61
20X4
1.36
1.77
20X5
1.53
1.70
0.84
6.56
15.07
12.50
0.84
3.85
10.75
8.00
0.79
5.49
11.35
11.76
0.87
6.25
15.56
14.89
Chapter 5
Funds Flow Analysis
1
(Rs in million)
Equity and Liabilities
Share Capital
Equity
Preference
Reserve and Surplus
Long-term Debt
Debentures
Term Loan
Current Liabilities and Provisions
Source
of
funds
20X0
20X1
50
10
60
50
10
70
10
40
60
50
70
10
10
Use of
funds
Loans and Advances
Trade payables
Short-term provisions
Total
Assets
Fixed Assets (net)
Gross Block
Accumulated Depreciation
Long-term Investments
Current Assets
Cash and cash equivalents
Current investments
Trade receivables
Inventories
Other current assets
Pre-paid Expenses
Other Assets
Total
10
5
100
70
30
420
110
75
25
460
240
400
160
10
260
440
180
10
20
40
20
10
2
70
72
15
2
65
86
5
6
10
420
10
12
460
5
5
14
4
2
2
Changes which increased net working capital
Increase in current investments
Increase in inventories
Decrease in short-term provisions
Total
95
Changes which decreased net working capital
Decrease in trade receivable
50
25
60
10
Increase in short-term Bank Loan
Increase in trade payables
Total
Since the net working capital increased by 10,
cash and cash equivalents decreased by 5.
15
15
80
3
Sources of cash
Trade receivables
Accumulated depreciation
Trade payables
Net Profit
Uses of cash
400
800
400
400
Inventory
Gross fixed assets
Accruals
Long - term Loans
Dividends
500
1500
200
400
200
4
(a)
Funds Flow Statement (Total Resources Basis) for Saraswati Company for the Year Ended 20X1
Rs in
million
Sources of funds
Uses of funds
Profit before Tax
50
Taxes
20
Depreciation and
amortisation charges
Increase in Liabilities
Trade payables
Short-term bank borrowing
Decrease in Assets
Inventories
Cash and cash equivalents
Total
20
20
Dividends
Decrease in Liabilities
Long-term debt
Short-term provisions
Increase in Assets
Fixed assets
Trade receivables
Other current assets
Total
10
10
15
10
5
105
20
20
15
5
45
30
10
5
(b )Funds Flow Statement (Working Capital Basis) for the Year Ended 20X1
Rs in million
Sources of Working Capital
Operations
50
Profit after tax
30
Depreciation and amortisation charges
20
Total Working Capital Generated
50
Uses of Working Capital
Dividends
20
Long - term debt repayment
15
Purchase of fixed assets (gross)
30
Total Working Capital Used
65
Net Change in Working Capital
-15
(c)
Sources and Uses of Funds (Cash Basis) for the Year
20X1
Sources of Cash
Operations
50
Profit after tax
30
Depreciation and amortisation charges
20
Increases in current liabilities
Short-term bank borrowings
20
10
105
Trade payables
Decreases in current assets
Inventories
Total Cash Generated
Uses of Cash
Payment of dividends
Repayment of long-term debt
10
10
80
20
15
Purchase of fixed assets
30
Increase in current assets, other than
cash and cash equivalents
15
Trade receivables
Other current assets
Decrease in current liabilities
Short-term provisions
Total cash used
10
5
5
5
85
Net change in cash position
-5
(d)
Cash Flow Statement
Rs. in million
A. CASH FLOW FROM OPERATING ACTIVITIES
PROFIT BEFORE TAX
50
Adjustments for:
Depreciation and amortisation
20
Finance costs
30
Interest income
OPERATING PROFIT BEFORE WORKING CAPITAL CHANGES
100
Adjustments for changes in working capital:
Trade receivables
-10
Inventories
10
Other current assets
-5
Trade payables and short-term provisions
5
CASH GENERATED FROM OPERATIONS
100
Direct taxes paid
-20
NET CASH FROM OPERATING ACTIVITIES
80
B.CASH FLOW FROM INVESTING ACTIVITIES
Purchase of fixed assets
-30
Interest income
NET CASH USED IN INVESTING ACTIVITIES
-30
C.CASH FLOW FROM FINANCING ACTIVITIES
Decrease in long- term debt
-15
Increase in short-term bank borrowings
10
Dividend paid
-20
Finance costs
-30
NET CASH FROM FINANCING ACTIVITIES
-55
NET CASH GENERATED
(A+B+C)
-5
CASH AND CASH EQUIVALENTS AT THE BEGINNING OF PERIOD
20
CASH AND CASH EQUIVALENTS AT THE END OF PERIOD
15
5
Cash Flow Statement for the period of 1.4.20X0 to 31.3.20X1
Rs. in million
A. CASH FLOW FROM OPERATING ACTIVITIES
PROFIT BEFORE TAX
90
Adjustments for:
Depreciation and amortization
30
Finance costs
30
Interest income
OPERATING PROFIT BEFORE WORKING CAPITAL CHANGES
150
Adjustments for changes in working capital:
Trade receivables
-20
Inventories
-20
Trade payables
20
CASH GENERATED FROM OPERATIONS
130
Direct taxes paid
-30
NET CASH FROM OPERATING ACTIVITIES
100
B.CASH FLOW FROM INVESTING ACTIVITIES
Purchase of fixed assets
-50
Interest income
NET CASH USED IN INVESTING ACTIVITIES
-50
C.CASH FLOW FROM FINANCING ACTIVITIES
Increase in share capital
20
Decrease in long- term debt
-10
Increase in short-term debt
20
Dividend paid
-40
Finance costs
-30
NET CASH FROM FINANCING ACTIVITIES
-40
NET CASH GENERATED
10
(A+B+C)
CASH AND CASH EQUIVALENTS AT THE BEGINNING OF PERIOD
20
CASH AND CASH EQUIVALENTS AT THE END OF PERIOD
30
Chapter 6
Break – Even Analysis And Leverages
1.
(a) EBIT = Q (P – V) – F = 20,000( 10-6) – 50,000 = Rs. 30,000
(b) EBIT = Q (P – V) – F = 12,000( 50-30) – 200,000 = Rs. 40,000
2. EBIT = Q (P – V) – F
30,000 = 5,000( 30 – 20 ) – F
F = 50,000 – 30,000 = Rs. 20,000
3. DOL = Contribution/ EBIT –
= [Q (P - V)] /[ Q (P - V) – F] =[ 400 x 400] / [ 400x400 – 100,000] = 2.67
If the quantity manufactured and sold rises to 600 units, the DOL will be:
= [ 600 x 400] / [ 600x400 – 100,000] = 1.71
4.
We have DOL = [Q (P - V)] /[ Q (P - V) – F]
2.5 = 15,000 x (P-V) / 300,000
So, ( P-V) = 2.5 x 300,000/ 15,000 = Rs. 50
Also, Q (P - V) – F = 15,000 x 50 –F =300,000
So, F = 750,000 -300,000 = 450,000
At the lower range, the output will be = 15,000 x 0.90 = 13,500
At the higher range, the output will be = 15,000 x 1.05 = 15,750
The corresponding EBITs will be
EBIT ( minimum) = Q (P – V) – F = 13,500 x 50 – 450,000 = Rs. 225,000
EBIT ( maximum) = Q (P – V) – F = 15,750 x 50 – 450,000 = Rs. 337500
The range of forecast errors for EBIT in percentage terms, would be:
[( 300,000 – 225,000)/300,000] x 100 below to[ ( 337,500 -300,000) /300,000]x100 above the
forecast value.
i.e, 25 percent below to 12.5 percent above the forecast value.
5.
Break-even point in units:
F
Q=
= 50,000 /(12- 7) = 10,000
P-V
F
Break-even sales in rupees =
=
50,000 / [1-7/12] = Rs. 120,000
1–V/P
Sales (in units) are required to earn a pre-tax income of Rs 60,000 is
= (60,000 + 50,0000)/(12 -7 ) = 22,000
Sales (in units) are required to earn an after-tax income of Rs 60,000 is:
=(60,000 /0.60 + 50,0000/(12 -7 ) = 30,000
6.
BEP in units = F /(P-V) = 20,000 / 6 = 3,333
BEP in rupees = F /Contribution margin = 20,000 /(0.3) = 66,667
To calculate sales we proceed as follows:
We have P –V = 6 …. (1) and V/P =1- 0.3 = 0.7 i.e. V = 0.7P
Substituting this value in eqn.1, we get P -0.7 P = 6 or P =6/0.3 = 20
Also, Q(P-V) –F =60,000
i.e. 6 Q – 20,000 = 60,000 or Q = 80,000/6
Sales = QP = (80,000/6) x 20 = Rs.266,667
7.
(a) Break-even quantity = 10,000 / (30 -16) = 715
(b) Current level of profit = 3000( 30-16) – 10,000 = Rs. 32,000
A 10 percent increase in production will raise the profit to
3300 ( 30 -16) – 10,000 = Rs. 36,200
Hence the percentage increase in profit =[( 36,200 – 32,000) /32,000] x 100
= 13.13 percent.
(c) With a 10 percent increase in selling price, the new break-even point will be
10,000 / ( 30 x 1.1 – 16) = 589
(d) Break – even point = ( 10,000 x 1.5) / ( 30 -16) = 1072
(e) Break – even point = 10,000 / ( 30 – 20) = 1000
8.
Case A
Case B
Selling Price per Unit
10
16.67
Variable Cost per Unit
6
8.33
Contribution Margin per Unit
4
8.33
Fixed Costs per Unit
1.39
4.63
Contribution Margin Ratio
0.4
0.5
Total Fixed Costs
16,000 Rs 100,000
Break-even Point in Units
4,000
12,000
Break-even Rupees in Sales 40,000
200,000
Margin of Safety in Units
7,500
9,608
Net Income (Loss) before TaxRs 30,000Rs 80,000
Number of Units Sold
11,500
21,608
Case C
Rs 20
12
8
10.67
0.4
Rs 160,000
20,000
400,000
(5,000)
Rs (40,000)
15,000
Case D
8
5
3
2
0.375
Rs60,000
20,000
160,000
10,000
30,000
30,000
9
(a)
Break-even point for P = 30,000 / (30-20) = 3,000
Break-even point for Q = 100,000 / (50-30) = 5,000
Break-even point for R = 200,000 / (80-40) = 5,000
Break-even point for the company as a whole = 330,000 / (160-90) = 4715
(b) The combined contribution margin ratio is = 1-V/P = 1-(20+30+40)/(30+50+80) = 0.4375
10.
EBIT = [Q(P-V)-D –F] = 20,0000( 40-24)-10,000- 80,000 = 230,000
DFL = EBIT / (EBIT – I ) = 230,000 / (230,000 – 30,000) = 1.15
11
Firm
A
B
C
EBIT
EPS
BEP
DOL
DFL
20,000(20-15)-40,000
10,000(50-30)-70,000
3000(100-40)-100,000
=60,000
=130,000
=80,000
[(60,000-10,000)x0.6
-5,000] / 10,000
[(130,000-20,000)x0.5-5,000]/
12,000
[(80,000-40,000)x0.4-10,000]/15,000
= 2.5
=4.17
(40,000+10,000)/(2015) = 10,000
(70,000+20,000)/(50-30)
(100,000+40,000)/(100-40)
=4,500
=2,334
[20,000(20-5)]/60,000
=1.67
[10,000(50-30)]/130,000
[(3,000(100-40)/80,000
=1.54
=2.25
60,000/(60,00010,000)
130,000/(130,000-20,000)
80,000/(80,000-40,000)
=1.18
=2.0
1.54x1.18=1.82
2.25x2.0=4.5
=0.4
=1.2
DTL
1.67 x 1.2 =2.00
Minicase
(Fixed costs (F) + interest(I)) /contribution = BEP
F + I = BEP x contribution = 7500 x (500 – 500 x 0.6) = 7500 x 200 = Rs. 15,00,000
a)
As there is no incidence of tax in the first year the unit’s PBT = PAT
PBT = 10,00,000 x 0.20 = Rs.2,00,000
Quantity required to be manufactured = [(F+ I) + PBT]/contribution
= 15,00,000/200 + 200000/200 = 8500
b)
If a PBT of Rs.200,000 is to be achieved:
Quantity (Selling price per unit - Variable cost per unit) – (Fixed cost + Interest) = 2,00,000
7500 x (0.4 x unit selling price) – 15,00,000 = 2,00,000
0.4 x unit selling price = (2,00,000+ 15,00,000)/7500
Unit selling price = [(2,00,000+ 15,00,000)/7500]/0.4 = Rs.567
Chapter 7
Financial Planning And Forecasting
1
Pro forma Income Statement for Modern Electronics for Year 3
Historical data
Year 1
Revenues from Operations
Expenses
Material expenses
Employee benefit expenses
Finance costs
Depreciation and amortisation
expenses
Other expenses
Total expenses
Profit before exceptional items and
other income
Exceptional Items
Profit before Extraordinary Items
and Tax
Extraordinary Items
Profit Before Tax
Tax Expense
Profit (Loss) for the period
Dividends
Retained earnings
Average
per cent
of sales
Year 2
Pro forma
income statement for year 3
800
890
100.00
1020
407
203
10
453
227
11
50.89
25.44
1.24
519
259
13
50
64
6.72
69
120
790
117
872
14.07
98.36
144
1003
10
18
1.64
17
8
10
1.06
11
18
28
2.70
28
18
7
11
28
10
18
2.70
1.00
1.70
28
10
17
8
9
6
5
7
11
2
Pro forma Income Statement for Modern Electronics for Year 3
Historical data
Average
per cent
Year 1
Year 2
of sales
Revenues from Operations
Expenses
Material expenses
Employee benefit expenses
Finance costs
Depreciation and amortisation
expenses
Other expenses
Total expenses
Profit before exceptional items and
other income
Exceptional Items
Profit before Extraordinary Items
and Tax
Extraordinary Items
Pro forma
income statement for year 3
800
890
100.00
1020
407
203
10
453
227
11
50.89
25.44
Budgeted
519
259
12
50
64
Budgeted
60
120
790
117
872
Budgeted
98.36
124
974
10
18
1.64
46
8
10
1.06
11
18
28
2.70
57
Profit Before Tax
Tax Expense
Profit (Loss) for the period
Dividends
Retained earnings
18
7
11
6
5
28
10
18
7
11
2.70
1.00
1.70
Budgeted
57
10
47
9
38
3
Pro forma Balance Sheet for Modern Electronics for Year 3
Historical data
Average
per cent
Year 1
Year 2
of sales
Revenue from operations
EQUITY AND LIABILITIES
Shareholders’ Funds
Share capital (Par value Rs.10)
Reserves and surplus
Non-current Liabilities
Long-term borrowings
Long-term provisions
Current Liabilities
Short-term borrowings
Trade payables
Short-term provisions
External funds requirement
ASSETS
Non-current Assets
Fixed assets
Non-current investments
Long-term loans and advances
Current Assets
Current investments
Inventories
Trade receivables
Cash and cash equivalents
Short-term loans and advances
Pro forma
balance sheet
for year 3
800
890
100
1020
150
150
150
118
129
No change
Proforma
statement
of P & L
167
144
13
175
19
18.83
No change
192
19
150
126
40
180
167
45
19.49
17.26
5.03
199
176
51
5
959
300
20
15
380
20
14
40.10
No change
1.72
409
20
18
21
173
180
12
20
741
20
192
200
14
25
865
No change
21.60
22.49
1.54
2.65
20
220
229
16
27
959
The external financing needed is 5
4.
The additional l funds requirement of Jaihind is:
AFN =A*/S0 (∆S) – L*/S (∆S) – mS1 (r)
=0.8 × 20 – 0.4 × 20 - .06 × 100 × 0.6=Rs.4.4 million
5.
Sustainable growth rate = 0.06 x 0.9 x 1.2 x (1-0.4) = 3.89 percent
Minicase
Solution:
We have sustainable growth rate = ROE x Retention ratio = (150/240) x (40/150) = 16.66 %
As no outside finance would be sought we have:
Increase in assets – increase in spontaneous liabilities
= net profit margin x next year sales x retention ratio
= (150/1200)x (1200x1.1667) x (40/150)
=Rs. 46.67 lakhs
Increase in assets = Rs. 46.67 lakhs as no increase is possible in spontaneous liabilities.
As there will not be increase in building value or cash holding,
increase in in inventory = Rs. 46.67 lakhs
So her advice would be to increase the inventory level by Rs. 46.67 lakhs
Chapter 8
Time Value of Money
1.
2.
Value five years hence of a deposit of Rs.1,000 at various interest rates is as follows:
r
=
8%
FV5
=
=
1000 x FVIF (8%, 5 years)
1000 x 1.469 =
Rs.1469
r
=
10%
FV5
=
=
1000 x FVIF (10%, 5 years)
1000 x 1.611 =
Rs.1611
r
=
12%
FV5
=
=
1000 x FVIF (12%, 5 years)
1000 x 1.762 =
Rs.1762
r
=
15%
FV5
=
=
1000 x FVIF (15%, 5 years)
1000 x 2.011 =
Rs.2011
Rs.160,000 / Rs. 5,000 = 32 = 25
According to the Rule of 72 at 12 percent interest rate doubling takes place
approximately in 72 / 12 = 6 years
So Rs.5000 will grow to Rs.160,000 in approximately 5 x 6 years = 30 years
3.
In 12 years Rs.1000 grows to Rs.8000 or 8 times. This is 23 times the initial deposit. Hence
doubling takes place in 12 / 3 = 4 years.
i) if we use the rule of 69 , doubling period = 0.35 + 69 / Interest rate
Equating this to 4 and solving for interest rate, we get
Interest rate = 18.9%.
ii) According to the Rule of 72, the doubling period is: 72/4 =18 years
4.
Saving Rs.2000 a year for 5 years and Rs.3000 a year for 10 years thereafter is equivalent to
saving Rs.2000 a year for 15 years and Rs.1000 a year for the years 6 through 15.
Hence the savings will cumulate to:
2000 x FVIFA (10%, 15 years) + 1000 x FVIFA (10%, 10 years)
=
2000 x 31.772 + 1000 x 15.937
=
Rs.79481.
5.
Let A be the annual savings.
6.
A x FVIFA (12%, 10 years) =
A x 17.549
=
1,000,000
1,000,000
So, A = 1,000,000 / 17.549 =
Rs.56,983.
1,000 x FVIFA (r, 6 years)
=
10,000
FVIFA (r, 6 years)
=
10,000 / 1000 = 10
=
=
9.930
10.980
From the tables we find that
FVIFA (20%, 6 years)
FVIFA (24%, 6 years)
Using linear interpolation in the interval, we get:
20% + (10.000 – 9.930)
r=
x 4% = 20.3%
(10.980 – 9.930)
7.
1,000 x FVIF (r, 10 years)
FVIF (r,10 years)
From the tables we find that
=
=
5,000
5,000 / 1000 = 5
FVIF (16%, 10 years) =
FVIF (18%, 10 years) =
4.411
5.234
Using linear interpolation in the interval, we get:
(5.000 – 4.411) x 2%
r = 16% +
= 17.4%
(5.234 – 4.411)
8.
The present value of Rs.10,000 receivable after 8 years for various discount rates (r ) are:
r = 10%
PV
= 10,000 x PVIF(r = 10%, 8 years)
= 10,000 x 0.467 = Rs.4,670
r = 12%
PV
= 10,000 x PVIF (r = 12%, 8 years)
= 10,000 x 0.404 = Rs.4,040
r = 15%
PV
= 10,000 x PVIF (r = 15%, 8 years)
= 10,000 x 0.327 = Rs.3,270
9.
Assuming that it is an ordinary annuity, the present value is:
2,000 x PVIFA (10%, 5years)
= 2,000 x 3.791 = Rs.7,582
10
The present value of the income stream is:
1,000 x PVIF (12%, 1 year) + 2,500 x PVIF (12%, 2 years)
+ 5,000 x PVIFA (12%, 8 years) x PVIF(12%, 2 years)
= 1,000 x 0.893 + 2,500 x 0.797 + 5,000 x 4.968 x 0.797 = Rs.22,683.
11
The present value of the income stream is:
2,000 x PVIFA (10%, 5 years) + 3000/0.10 x PVIF (10%, 5 years)
= 2,000 x 3.791 + 3000/0.10 x 0.621
= Rs.26,212
12.
To earn an annual income of Rs.5,000 beginning from the end of 15 years from now, if the
deposit earns 10% per year a sum of
Rs.5,000 / 0.10 = Rs.50,000
is required at the end of 14 years. The amount that must be deposited to get this sum is:
Rs.50,000 / FVIF (10%, 14 years) = Rs.50,000 / 3.797 = Rs.13,165
13.
Rs.20,000 =- Rs.4,000 x PVIFA (r, 10 years)
PVIFA (r,10 years) = Rs.20,000 / Rs.4,000 = 5.00
From the tables we find that:
PVIFA (15%, 10 years)
PVIFA (18%, 10 years)
Using linear interpolation we get:
5.019 – 5.00
r = 15% +
---------------5.019 – 4.494
=
=
5.019
4.494
x 3%
= 15.1%
14.
PV (Stream A) = Rs.100 x PVIF (12%, 1 year) + Rs.200 x
PVIF (12%, 2 years) + Rs.300 x PVIF(12%, 3 years) + Rs.400 x
PVIF (12%, 4 years) + Rs.500 x PVIF (12%, 5 years) +
Rs.600 x PVIF (12%, 6 years) + Rs.700 x PVIF (12%, 7 years) +
Rs.800 x PVIF (12%, 8 years) + Rs.900 x PVIF (12%, 9 years) +
Rs.1,000 x PVIF (12%, 10 years)
= Rs.100 x 0.893 + Rs.200 x 0.797 + Rs.300 x 0.712
+ Rs.400 x 0.636 + Rs.500 x 0.567 + Rs.600 x 0.507
+ Rs.700 x 0.452 + Rs.800 x 0.404 + Rs.900 x 0.361
+ Rs.1,000 x 0.322
= Rs.2590.9
Similarly,
PV (Stream B) = Rs.3,625.2
PV (Stream C) = Rs.2,825
15.
It will grow to 10,000(1+0.16/4)4x5 = Rs. 21,911
16.
It will be equal to 5,000(1+0.12/4)5x4 = Rs. 9,031
17
A
B
C
D
Stated rate (%)
12
12
24
24
Frequency of compounding
2times
6 times
4 times
12 times
Effective rate (%)(1 + 0.12/2)2- 1 ( 1 + 0.12/6)6- 1 (1+0.24/4)4 –1 (1 + 0.24/12)12-1
= 12.36
Difference between the
effective rate and stated
= 12.6
= 26.2
= 26.8
rate (%)
18.
0.36
0.6
2.2
2.8
Investment required at the end of 8th year to yield an income of Rs.12,000 per year from
the end of 9th year (beginning of 10th year) for ever:
Rs.12,000 x PVIFA(12%, ∞ )
= Rs.12,000 / 0.12 = Rs.100,000
To have a sum of Rs.100,000 at the end of 8th year , the amount to be deposited
Rs.100,000
Rs.100,000
=
= Rs.40,388
PVIF(12%, 8 years)
2.476
now is:
19. The interest rate implicit in the offer of Rs.20,000 after 10 years in lieu of Rs.5,000 now is:
Rs.5,000 x FVIF (r,10 years) = Rs.20,000
Rs.20,000
FVIF (r,10 years) =
= 4.000
Rs.5,000
From the tables we find that
FVIF (15%, 10 years) = 4.046
This means that the implied interest rate is nearly 15%.
I would choose Rs.20,000 after 10 years from now because I find
quite acceptable.
20.
FV10
a return of 15%
= Rs.10,000 [1 + (0.10 / 2)]10x2
= Rs.10,000 (1.05)20
= Rs.10,000 x 2.653
= Rs.26,530
If the inflation rate is 8% per year, the value of Rs.26,530 10 years from now, in terms of
the current rupees is:
Rs.26,530 x PVIF (8%,10 years)
= Rs.26,530 x 0.463 = Rs.12,283
21.
A constant deposit at the beginning of each year represents an annuity due.
PVIFA of an annuity due is equal to : PVIFA of an ordinary annuity x (1 + r)
To provide a sum of Rs.50,000 at the end of 10 years the annual deposit should
be
A
=
Rs.50,000
FVIFA(12%, 10 years) x (1.12)
Rs.50,000
=
= Rs.2544
17.549 x 1.12
22. The discounted value of the annuity of Rs.2000 receivable for 30 years, evaluated as at the end
of 9th year is:
Rs.2,000 x PVIFA (10%, 30 years) = Rs.2,000 x 9.427 = Rs.18,854
23
The present value of Rs.18,854 is:
Rs.18,854 x PVIF (10%, 9 years)
=
Rs.18,854 x 0.424
=
Rs.7,994
30 per cent of the pension amount is
0.30 x Rs.6000 = Rs.1800
Assuming that the monthly interest rate corresponding to an annual interest rate of 12% is
1%, the discounted value of an annuity of Rs.1800 receivable at the end of each month for 180
months (15 years) is:
Rs.1800 x PVIFA (1%, 180)
Rs.1800 x
(1.01)180 - 1
---------------- = Rs.149,980
.01 (1.01)180
If Mr. Ramesh borrows Rs.P today on which the monthly interest rate is 1%
P x (1.01)60 =
P x 1.817
=
P
24
=
Rs.149,980
Rs.149,980
Rs.149,980
------------ = Rs.82,540
1.817
Rs.3000 x PVIFA(r, 24 months) = Rs.60,000
PVIFA (r,24) =
Rs.60000 / Rs.3000 = 20
From the tables we find that:
PVIFA(1%,24)
=
PVIFA (2%, 24)
=
21.244
18.914
Using a linear interpolation
21.244 – 20.000
r = 1% +
---------------------21.244 – 18,914
= 1.53%
x 1%
Thus, the bank charges an interest rate of 1.53% per month.
The corresponding effective rate of interest per annum is
[ (1.0153)12 – 1 ] x 100 = 20%
25
The discounted value of the debentures to be redeemed between 8 to 10 years evaluated at
the end of the 5th year is:
Rs.1000 million x PVIF (8%, 3 years)
+ Rs.1000 million x PVIF (8%, 4 years)
+ Rs.1000 million x PVIF (8%, 5 years)
= Rs.1000 million (0.794 + 0.735 + 0.681)
= Rs. 2210 million
If A is the annual deposit to be made in the sinking fund for the years 1 to 5,
then
A x FVIFA (8%, 5 years) = Rs.2210 million
A x 5.867 = Rs.2210 million
A = Rs.2210 million / 5.867 = Rs.376.68 million
26
Let `n’ be the number of years for which a sum of Rs.200,000 can be withdrawn annually.
Rs.200,000 x PVIFA (10%, n) = Rs.1,000,000
PVIFA (10 %, n) = Rs.1,000,000 / Rs.200,000 = 5.000
From the tables we find that
PVIFA (10%, 7 years) =
PVIFA (10%, 8 years) =
4.868
5.335
Thus n is between 7 and 8. Using a linear interpolation we get
n=7+
27
5.000 – 4.868
----------------- x 1 = 7.3 years
5.335 – 4.868
Equated annual installment
= 500000 / PVIFA(14%,4)
= 500000 / 2.914
= Rs.171,585
Loan Amortisation Schedule
Year
-----1
2
3
4
Beginning
amount
------------500000
398415
282608
150588
(*) rounding off error
Annual
installment
--------------171585
171585
171585
171585
Interest
----------70000
55778
39565
21082
Principal
repaid
------------101585
115807
132020
150503
Remaining
balance
------------398415
282608
150588
85*
28
Define n as the maturity period of the loan. The value of n can be obtained from the
equation.
200,000 x PVIFA(13%, n)
PVIFA (13%, n)
29
=
=
1,500,000
7.500
From the tables or otherwise it can be verified that PVIFA(13,30) = 7.500
Hence the maturity period of the loan is 30 years.
(a) PV = Rs.500,000
(b) PV = 1,000,000PVIF10%,6yrs = 1,000,000 x 0.564 = Rs.564,000
(c ) PV = 60,000/r = 60,000/0.10 = Rs.600,000
(d) PV = 100,000 PVIFA10%,10yrs = 100,000 x 6.145 = Rs.614,500
Option d has the highest present value viz. Rs.614,500
30
Assuming 52 weeks in an year, the effective interest rate is
0.08
1 +
52
- 1 = 1.0832 - 1 = 8.32 percent
52
31
We have
( 1+ r/365)365x7 = 2
( 1+ r/365)2555 = 2
r = (21/2555- 1)x365 = 0.099 or 9.9 percent
32
If A is the equated annual instalment, we have A x PVIFA(9.5%,5 yrs) = 100,000
A x[ (1- 1/1.0955)/0.095] = 100,000
A x 3.8397 = 100,000 or A = Rs.26,044
Loan amortisation schedule
Beginning Annual
Year amount
instalment Interest
1
100,000
26,044
9500
2
83,456
26,044
7928
3
65,340
26,044
6207
4
45,504
26,044
4323
5
23,782
26,044
2259
Amounts in Rs.
Principal
Remaining
repayment balance
16,544
83,456
18,116
65,340
19,837
45,504
21,721
23,782
23,785
-2
Minicase
a ) At 15 % down payment the housing loan would be for 94 x 0.85 = Rs.80 lakhs.
The monthly interest rate r on the housing loan would be such that;
b)
c)
(1+r)12- 1 = 0.09
r = (1.09)1/12 -1 = 0.00720 or 0.72 %.
EMI = 80,00,000/PVIFA0.72%, 240
PVIFA0.72%, 240 = ( 1 – 1/1.0072240) / 0.0072 = 114.0635
EMI = 80,00,000 /114.0635 = Rs.70,136
Loan amount /114.0635 = Rs.50,000
Loan amount = 50,000 x 114.0635 = 57,03,175 or say Rs.57 lakhs.
The down payment required for a loan of Rs.57 lakhs would be 94 – 57 = Rs.37 lakhs
He has on hand Rs.14 lakhs which if kept for 3 years deposit would mature to
14,00,000 x (1.02)12 =Rs.17,75,538
To get the balance Rs. 19,24,462 he has to deposit A @ 0.7% for 36 months
A x (1.007^36 -1)/0.007 = Rs.19,24,462
A = 19,24,462 /40.781 = Rs.47,190
Chapter 9
Valuation of Securities
1.
P =
5

t=1
11
100
+
(1.15)t
(1.15)5
= Rs.11 x PVIFA(15%, 5 years) + Rs.100 x PVIF (15%, 5 years)
= Rs.11 x 3.352 + Rs.100 x 0.497
= Rs.86.7
2.(i)
When the discount rate is 14%
7
12
100
P = 
+
t=1
(1.14) t (1.14)7
= Rs.12 x PVIFA (14%, 7 years) + Rs.100 x PVIF (14%, 7 years)
= Rs.12 x 4.288 + Rs.100 x 0.4
= Rs.91.46
(ii)
When the discount rate is 12%
7
12
100
P = 
+
= Rs.100
t=1
(1.12) t (1.12)7
Note that when the discount rate and the coupon rate are the same the value is equal to par value.
3.
The yield to maturity is the value of r that satisfies the following equality.
7 120
1,000
Rs.750 = 
+
t
t=1 (1+r)
(1+r)7
Try r = 18%. The right hand side (RHS) of the above equation is:
Rs.120 x PVIFA (18%, 7 years) + Rs.1,000 x PVIF (18%, 7 years)
=
Rs.120 x 3.812 + Rs.1,000 x 0.314
=
Rs.771.44
Try r = 20%. The right hand side (RHS) of the above equation is:
Rs.120 x PVIFA (20%, 7 years) + Rs.1,000 x PVIF (20%, 7 years)
= Rs.120 x 3.605 + Rs.1,000 x 0.279
= Rs.711.60
Thus the value of r at which the RHS becomes equal to Rs.750 lies between 18% and 20%.
Using linear interpolation in this range, we get
771.44 – 750.00
Yield to maturity = 18% + 771.44 – 711.60
x 2%
= 18.7%
4.
80 =
10 14
100

+
t=1 (1+r) t
(1+r)10
Try r = 18%. The RHS of the above equation is
Rs.14 x PVIFA (18%, 10 years) + Rs.100 x PVIF (18%, 10 years)
=
Rs.14 x 4.494 + Rs.100 x 0.191 = Rs.82
Try r = 20%. The RHS of the above equation is
Rs.14 x PVIFA(20%, 10 years) + Rs.100 x PVIF (20%, 10 years)
= Rs.14 x 4.193 + Rs.100 x 0.162
= Rs.74.9
Using interpolation in the range 18% and 20% we get:
Yield to maturity
82 - 80
= 18% + ----------- x 2%
82 – 74.9
= 18.56%
5.
P =
12

t=1
6
100
+
(1.08) t (1.08)12
= Rs.6 x PVIFA (8%, 12 years) + Rs.100 x PVIF (8%, 12 years)
= Rs.6 x 7.536 + Rs.100 x 0.397
= Rs.84.92
6.
The post-tax interest and maturity value are calculated below:
Bond A
Bond B
12(1 – 0.5)
=Rs.6
10 (1 – 0.5)
=Rs.5
*
Post-tax interest (C )
*
Post-tax maturity value (M) 100 [ (100-70)x 0.3]
=Rs.91
100 [ (100 – 60)x 0.3]
=Rs.88
The post-tax YTM, using the approximate YTM formula is calculated below
Bond A :
Post-tax YTM =
=
Bond B :
Post-tax YTM =
6 + (91-70)/10
-------------------0.6 x 70 + 0.4 x 91
10.33%
5 + (88 – 60)/6
---------------------0.6x 60 + 0.4 x 88
=
13.58%
( Note: In the list of solutions given in App.B in the book, the answers had inadvertently been
worked out at some other tax rates)
7.
P =
14

t=1
6
100
+
(1.08) t (1.08)14
= Rs.6 x PVIFA(8%, 14) + Rs.100 x PVIF (8%, 14)
= Rs.6 x 8.244 + Rs.100 x 0.341
= Rs.83.56
8.
Do = Rs.2.00, g = 0.06, r = 0.12
Po = D1 / (r – g) = Do (1 + g) / (r – g)
=
=
Rs.2.00 (1.06) / (0.12 - 0.06)
Rs.35.33
Since the growth rate of 6% applies to dividends as well as market price, the market price at the end
of the 2nd year will be:
P2
9.
10.
11.
12
Po
Po
=
=
Po x (1 + g)2 = Rs.35.33 (1.06)2
Rs.39.70
=
=
D1 / (r – g)
=
Do (1 + g) / (r – g)
Rs.12.00 (1.10) / (0.15 – 0.10)
=
=
D1 / (r – g)
Rs.32 =
g
=
Rs.2 / (0.12 – g)
0.0575 or 5.75%
Po
Do
So
8
D1/ (r – g) = Do(1+g) / (r – g)
Rs.1.50, g = -0.04, Po = Rs.8
=
=
Rs.264
= 1.50 (1- .04) / (r-(-.04)) = 1.44 / (r + .04)
Hence r = 0.14 or 14 per cent
The market price per share of Commonwealth Corporation will be the sum of three
components:
A:
B:
C:
Present value of the dividend stream for the first 4 years
Present value of the dividend stream for the next 4 years
Present value of the market price expected at the end of 8 years.
A=
1.50 (1.12) / (1.14) + 1.50 (1.12)2 / (1.14)2 + 1.50(1.12)3 / (1.14)3 +
+ 1.50 (1.12)4 / (1.14)4
=
=
B=
1.68/(1.14) + 1.88 / (1.14)2 + 2.11 / (1.14)3 + 2.36 / (1.14)4
Rs.5.74
2.36(1.08) / (1.14)5 + 2.36 (1.08)2 / (1.14)6 + 2.36 (1.08)3 / (1.14)7 +
+ 2.36 (1.08)4 / (1.14)8
=
2.55 / (1.14)5 + 2.75 / (1.14)6 + 2.97 / (1.14)7 + 3.21 / (1.14)8
C
=
Rs.4.89
=
P8 / (1.14)8
P8 = D9 / (r – g) =
3.21 (1.05)/ (0.14 – 0.05) = Rs.37.45
So
C
=
Thus,
Po
=
=
13
Rs.37.45 / (1.14)8 = Rs.13.14
A + B + C = 5.74 + 4.89 + 13.14
Rs.23.77
Let us assume a required rate of return of 12 percent. Using the two stage formula, the
intrinsic value of the equity share will be :
Intrinsic value of the equity share (using the 2-stage growth model)
(1.15)5
2.30 x
1 - ----------2.30 x (1.15)4 x (1.10)
5
(1.12)
= --------------------------------- + ----------------------------------0.12 – 0.15
(0.12 – 0.10) x (1.12)5
- 0.1413
----------- + 125.54
- 0.03
=
2.30 x
=
Rs.136.37
14
Post-tax interest (C ) =
100(1 – 0.3) = Rs.70
Post-tax maturity value (M) 1000 - (1000-880)x 0.09]
=Rs. 989.2
The post-tax YTM, using the approximate YTM formula is calculated below
Post-tax YTM =
=
70 + (989.2 -880)/8
-------------------0.6 x 880 + 0.4 x 989.2
9.06 %
15
Dividend next expected = 200 x1.30x 0.12 x0.10 = Rs.3.12 crore
DPS next year = 3.12/0.8 = Rs.3.9
Intrinsic value of the equity share (using the 2-stage growth model)
(1.30)3
1 - ----------3.9 x (1.30)2 x (1.10)
(1.16)3
= --------------------------------- + ----------------------------------0.16 – 0.30
(0.16 – 0.10) x (1.16)3
= 11.35 +77.41
3.9 x
=
Rs.88.76
16
Do = Rs.6.00, g = 0.05, r = 0.20
Po = D1 / (r – g) = Do (1 + g) / (r – g)
=
=
Rs.6.00 (1.05) / (0.20 - 0.05)
Rs.42
The market price at the end of the 2nd year will be:
P2
17
=
=
Po x (1 + g)2 = Rs.42 (1.05)2
Rs.46.3
Let the YTD be r%.
We have:
100 PVIFA(r ,12) + 1000 PVIF(r,12) = 1050
Trying r =10%, LHS = 100 x 6.814 + 1000 x 0.319 = Rs. 1000.4
Trying r =9%, LHS = 100 x 7.161 +1000 x 0.356 = Rs.1072.1
By linear interpolation:
YT D = 9% + (1072.1 – 1050) /(1072.1 -1000.4) %
= 9.31 %
.
18
100 + (-50/12)
= 9.30 percent
0.4 x 1000 + 0.6 x 1050
19.
Given that investors require a return of 14 percent and the constant dividend growth rate
is 8 percent, the dividend yield is 6%. On the current price of Rs. 90, the dividend expected
a year from now will be Rs. 90 x 0.06 = Rs 5.4. This means that the dividend paid per share
recently was = Rs 5.4 /1.08=
Rs 5.00
Note: In the list of solutions given in Appendix B of the book, the answer was
inadvertantly given as Rs. 5.4 )
20. Current price = 3(1.08) / (0.15 – 0.08) = Rs.46.29
Price after 3 years = 46.29(1.08)3 = Rs. 58.31
21.
Po
Do
So
10
=
=
D1/ (r – g) = Do(1+g) / (r – g)
Rs.2.00, g = -0.05, Po = Rs.10
= 2.00 (1- .05) / (r-(-.05)) = 1.9 / (r + .05)
Hence r = 0.14 or 14 per cent
Note: In the list of solutions given in Appendix B of the book, the answer was
inadvertantly given as 0.15 )
Minicase
Dividends paid and to be paid in the first 4 years of the new share issue
= 6/1.12 + 6 + 6x 1.12 + 6 x 1.12x1.08 = 25.33
Price of the share at the end of the first 4 years = 89
If k is the required rate of return at the time of the share issue:
(89 + 25.33)/(1+k)4 = 65
k = (114.33/65)1/4 - 1 = 0.1516
The required return on bond = 15.16 % - 4 % = 11.16 % p.a or 5.58 % per half year
and there are three more years for maturity.
Fair value per bond , P = 50 x PVIFA5.58%,6 + 1000/(1.0558)6
PVIFA 5.58%, 6= (1 – 1/1.05586)/0.0558 = 4.9829
P = 50 x 4.9829+ 1000/(1.0558)6
=Rs.971.1
He should quote a selling price of Rs.971 per bond.
.
Chapter 10
Risk and Return
1 (a)
Expected price per share a year hence will be:
= 0.4 x Rs.10 + 0.4 x Rs.11 + 0.2 x Rs.12 = Rs.10.80
(b)
Probability distribution of the rate of return is
Rate of return (Ri)
10%
20%
30%
Probability (pi)
0.4
0.4
0.2
Note that the rate of return is defined as:
Dividend + Terminal price
-------------------------------- - 1
Initial price
2 (a) For Rs.1,000, 20 shares of Alpha’s stock can be acquired. The probability distribution of
the return on 20 shares is
Economic Condition
High Growth
Low Growth
Stagnation
Recession
Expected return
Return (Rs)
20 x 55 = 1,100
20 x 50 = 1,000
20 x 60 = 1,200
20 x 70 = 1,400
Probability
0.3
0.3
0.2
0.2
=
(1,100 x 0.3) + (1,000 x 0.3) + (1,200 x 0.2) + (1,400 x 0.2)
=
=
330 + 300 + 240 + 280
Rs.1,150
Standard deviation of the return = [(1,100 – 1,150)2 x 0.3 + (1,000 – 1,150)2 x
0.3 + (1,200 – 1,150)2 x 0.2 + (1,400 – 1,150)2 x 0.2]1/2
=
Rs.143.18
(b)
For Rs.1, 000, 20 shares of Beta’s stock can be acquired. The probability distribution of the
return on 20 shares is:
Economic condition
Return (Rs)
Probability
High growth
Low growth
Stagnation
Recession
20 x 75 = 1,500
20 x 65 = 1,300
20 x 50 = 1,000
20 x 40 = 800
0.3
0.3
0.2
0.2
Expected return =
(1,500 x 0.3) + (1,300 x 0.3) + (1,000 x 0.2) + (800 x 0.2)
= Rs.1,200
Standard deviation of the return = [(1,500 – 1,200)2 x .3 + (1,300 – 1,200)2 x .3
+ (1,000 – 1,200)2 x .2 + (800 – 1,200)2 x .2]1/2 = Rs.264.58
(c )
For Rs.500, 10 shares of Alpha’s stock can be acquired; likewise for Rs.500, 10
shares of Beta’s stock can be acquired. The probability distribution of this option is:
Return (Rs)
Probability
(10 x 55) + (10 x 75) =
1,300
0.3
(10 x 50) + (10 x 65) =
1,150
0.3
(10 x 60) + (10 x 50) =
1,100
0.2
(10 x 70) + (10 x 40) =
1,100
0.2
Expected return
=
(1,300 x 0.3) + (1,150 x 0.3) + (1,100 x 0.2) +
(1,100 x 0.2)
=
Rs.1,175
Standard deviation =
[(1,300 –1,175)2 x 0.3 + (1,150 – 1,175)2 x 0.3 +
d.
(1,100 – 1,175)2 x 0.2 + (1,100 – 1,175)2 x 0.2 ]1/2
=
Rs.84.41
For Rs.700, 14 shares of Alpha’s stock can be acquired; likewise for Rs.300, 6
shares of Beta’s stock can be acquired. The probability distribution of this
option is:
Return (Rs)
Probability
(14 x 55) + (6 x 75)
(14 x 50) + (6 x 65)
(14 x 60) + (6 x 50)
(14 x 70) + (6 x 40)
=
=
=
=
1,220
1,090
1,140
1,220
Expected return
=
=
(1,220 x 0.3) + (1,090 x 0.3) + (1,140 x 0.2) + (1,220 x 0.2)
Rs.1,165
Standard deviation
=
0.3
0.3
0.2
0.2
[(1,220 – 1,165)2 x 0.3 + (1,090 – 1,165)2 x 0.3 +
(1,140 – 1,165)2 x 0.2 + (1,220 – 1,165)2 x 0.2]1/2
=
Rs.57.66
The expected return to standard deviation of various options are as follows :
Expected return
Standard deviation Expected / Standard
Option
(Rs)
(Rs)
return
deviation
a
1,150
143
8.04
b
1,200
265
4.53
c
d
1,175
1,165
84
58
13.99
20.09
Option `d’ is the most preferred option because it has the highest return to risk
3.
The returns on 4 stocks, A, B, C and D over a period of 6 years have been as follows:
1
2
3
4
5
6
A
B
10%
8%
12%
4%
–8%
15%
15%
12%
– 2%
10%
20%
6%
C
7%
8%
12%
9%
6%
12%
D
9%
9%
11%
4%
8%
16%
Calculate the return on:
(a) portfolio of one stock at a time
(b) portfolios of two stocks at a time
(c) portfolios of three stocks at a time
(d) a portfolio of all the four stocks.
Assume equiproportional investment.
4
The required rate of return on stock A is:
RA
=
=
=
RF + βA (RM – RF)
0.10 + 1.5 (0.15 – 0.10)
0.175
Intrinsic value of share = D1 / (r- g) = Do (1+g) / ( r – g)
Given Do = Rs.2.00, g = 0.08, r = 0.175
2.00 (1.08)
Intrinsic value per share of stock A =
0.175 – 0.08
=
5.
ratio.
Rs.22.74
The SML equation is RA = RF + βA (RM – RF)
Given RA = 15%.
RF = 8%,
RM = 12%, we have
0.15 = .08 + βA (0.12 – 0.08)
0.07
i.e.βA =
= 1.75
0.04
Beta of stock A = 1.75
6.
The SML equation is: RX = RF + βX (RM – RF)
We are given 0.15 = 0.09 + 1.5 (RM – 0.09) i.e., 1.5 RM = 0.195
or RM = 0.13%
Therefore return on market portfolio = 13%
Minicase
State of
nature
Recession
Normal
Mildly
buoyant
Boom
26.01
82.81
1.00
25.00
Square of the
Return on Deviation of the return
Jeet (%)
on Bright from its
(2)
expected value
[(1)– 12.90]2
Probability
Return on
Bright (%)
(1)
0.2
0.3
-5
15
10
12
18
14
22
18
0.4
0.1
320.41
4.41
Square of
the
Deviation of
the return on
Jeet from its
expected
value
[(2)– 13.0]2
9.00
1.00
Expected value of the return on Bright = 0.2(-5) + 0.3x15 + 0.4x18+0.1x22 =
Expected value of the return on Jeet = 0.2(10) + 0.3x12 + 0.4x14+0.1x18 =
Standard deviation of the return on
Bright=(0.2x320.41+0.3x4.41+0.4x26.01+0.1x82.81=
12.90
13.00
9.17
Standard deviation of the return on Jeet =(0.2x9 + 0.3x1 + 0.4x1 + 0.1x25 =
2.24
Expected Portfolio return = 0.2 x[(2/3)x(-5) + (1/3)x10] + 0.3 x[(2/3)x 15 + (1/3)x12]
+ 0.4 x[(2/3)x18 + (1/3)x14] + 0.1 x[(2/3)x 22 + (1/3)x18]
= 0.2 x(0) + .3(14) + 0.4(16.67) + 0.1(20.67) = 12.9
Standard deviation of the portfolio =( 0.2 x (0-12.9)2 + 0.3(14-12.9) 2 +0.4(16.67-12.9) 2
+0.1(20.67-12.9)2)1/2 = 6.74
If the coefficient of correlation is r:
[ (2/3)2x (9.17)2 + (1/3)2x (2.24)2 + 2 x 2/3 x 1/3 x r x 9.17 x 2.24]1/2 = 6.74
0r 37.93 + 9.13r = 6.742 = 45.43
So, r = 0.82 .
As the coefficient of correlation is near 1, Jeet is not a good stock for diversification.
Chapter 11
Techniques Of Capital Budgeting
1.(a)
(b)
NPV of the project at a discount rate of 14%.
=
- 1,000,000 + 100,000 + 200,000
---------- -----------(1.14)
(1.14)2
+ 300,000 + 600,000 + 300,000
----------- ------------------3
4
(1.14)
(1.14)
(1.14)5
=
- 44837
NPV of the project at time varying discount rates
=
- 1,000,000
+ 100,000
(1.12)
+ 200,000
(1.12) (1.13)
+ 300,000
(1.12) (1.13) (1.14)
+ 600,000
(1.12) (1.13) (1.14) (1.15)
+ 300,000
(1.12) (1.13) (1.14)(1.15)(1.16)
=
=
- 1,000,000 + 89286 + 158028 + 207931 + 361620 + 155871
- 27264
2.
IRR (r) can be calculated by solving the following equations for the value of r.
60000 x PVIFA (r,7) =
i.e., PVIFA (r,7)
=
300,000
5.000
Through a process of trial and error it can be verified that r = 9.20% pa.
The IRR (r) for the given cashflow stream can be obtained by solving the following
equation for the value of r.
-3000 + 9000 / (1+r) – 3000 / (1+r) = 0
Simplifying the above equation we get
r = 1.61, -0.61; (or) 161%, (-)61%
NOTE: Given two changes in the signs of cash flow, we get two values for the
IRR of the cash flow stream. In such cases, the IRR rule breaks down.
3.
Define NCF as the minimum constant annual net cash flow that justifies the purchase
of the given equipment. The value of NCF can be obtained from the equation
NCF x PVIFA (10,8)
NCF
4.
=
=
=
500000
500000 / 5.335
93271
Define I as the initial investment that is justified in relation to a net annual cash
inflow of 25000 for 10 years at a discount rate of 12% per annum. The value
of I can be obtained from the following equation
25000 x PVIFA (12,10)
i.e., I
=
=
I
141256
5.
Let us assume a discount rate of 15 %.
PV of benefits (PVB) =
+
+
+
+
=
25000 x PVIF (15,1)
40000 x PVIF (15,2)
50000 x PVIF (15,3)
40000 x PVIF (15,4)
30000 x PVIF (15,5)
122646
(A)
6.
Investment
=
100,000
(B)
Benefit cost ratio
=
1.23 [= (A) / (B)]
The NPV’s of the three projects are as follows:
P
Project
Q
0%
5%
400
223
500
251
600
312
10%
15%
69
- 66
40
- 142
70
- 135
R
Discount rate
25%
- 291
- 435
- 461
30%
- 386
- 555
- 591
For detailed working out please see the excel solution manual)
7.
NPV profiles for Projects P and Q for selected discount rates are as follows:
(a)
Project
P
Q
Discount rate (%)
0
2950
500
5
1876
208
10
1075
- 28
15
471
- 222
20
11
- 382
(Detailed calculations are as shown in the companion excel file)
b)
(i)
The IRR (r ) of project P can be obtained by solving the following
equation for `r’.
-1000 -1200 x PVIF (r,1) – 600 x PVIF (r,2) – 250 x PVIF (r,3)
+ 2000 x PVIF (r,4) + 4000 x PVIF (r,5) =
0
Through a process of trial and error we find that r = 20.13%
(ii)
The IRR (r') of project Q can be obtained by solving the following equation for
r'
-1600 + 200 x PVIF (r',1) + 400 x PVIF (r',2) + 600 x PVIF (r',3)
+ 800 x PVIF (r',4) + 100 x PVIF (r',5)
=
0
Through a process of trial and error we find that r' = 9.34%.
c)
From (a) we find that at a cost of capital of 10%
NPV (P)
NPV (Q)
=
=
1075
- 28
Given that NPV (P) . NPV (Q); and NPV (P) > 0, I would choose project P.
From (a) we find that at a cost of capital of 20%
NPV (P)
=
11
NPV (Q)
=
- 382
Again NPV (P) > NPV (Q); and NPV (P) > 0. I would choose project P.
7.( Problem no. repeated)
(a)
Project A
NPV at a cost of capital of 12%
=
- 100 + 25 x PVIFA (12,6)
=
Rs.2.79 million
IRR (r ) can be obtained by solving the following equation for r.
25 x PVIFA (r,6)
=
100
i.e., r = 12,98%
Project B
NPV at a cost of capital of 12%
=
- 50 + 13 x PVIFA (12,6)
=
Rs.3.45 million
IRR (r') can be obtained by solving the equation
13 x PVIFA (r',6)
=
50
i.e.,
r' = 14.40% [determined through a process of trial and error]
(b)
Difference in capital outlays between projects A and B is Rs.50 million
Difference in net annual cash flow between projects A and B is Rs.12 million.
NPV of the differential project at 12%
=
-50 + 12 x PVIFA (12,6) ==-50 +12 x4.111
=
- Rs.0.67 million
IRR (r'') of the differential project can be obtained from the equation
12 x PVIFA (r'', 6) =
50
i.e.,
r''
=
11.53%
8.
(a)
Project M
The pay back period of the project lies between 2 and 3 years. Interpolating in
this range we get an approximate pay back period of 2.63 years/
Project N
The pay back period lies between 1 and 2 years. Interpolating in this range we
get an approximate pay back period of 1.55 years.
(b)
Project M
Cost of capital
=
12% p.a
Year Cash flow Discounted cash flow Cumulative discounted
Cash flow
1
11
9.82
9.82
2
19
15.15
24.97
3
32
22.78
47.75
4
37
23.51
71.26
Discounted pay back period (DPB) lies between 3 and 4 years. Interpolating in this
range we get an approximate DPB of 3.1 years.
Project N
Cost of capital
=
12% per annum
Year Cash flow Discounted cash flow Cumulative discounted
cash flow
1
38
33.93
33.93
2
22
17.54
51.47
DPB lies between 1 and 2 years. Interpolating in this range we get an approximate
DPB of 1.92 years.
(c )
Project M
Cost of capital
NPV
=
=
Project N
Cost of capital
NPV
=
12% per annum
- 50 + 11 x PVIFA (12,1)
+ 19 x PVIF (12,2) + 32 x PVIF (12,3)
+ 37 x PVIF (12,4)
Rs.21.26 million
= 12% per annum
= Rs.20.63 million
Since the two projects are independent and the NPV of each project is (+) ve,
both the projects can be accepted. This assumes that there is no capital constraint.
(d)
Project M
Cost of capital
NPV
Project N
Cost of capital
NPV
= 10% per annum
= Rs.25.02 million
= 10% per annum
= Rs.23.08 million
Since the two projects are mutually exclusive, we need to choose the project with the
higher NPV i.e., choose project M.
NOTE: The MIRR can also be used as a criterion of merit for choosing between the
two projects because their initial outlays are equal.
(e)
Project M
Cost of capital
=
15% per annum
NPV
=
16.13 million
Project N
Cost of capital:
15% per annum
NPV
=
Rs.17.23 million
Again the two projects are mutually exclusive. So we choose the project with the
higher NPV, i.e., choose project N.
9. The discounted payback period for A is calculated as follows:
Year
Cash flow
0
1
2
3
4
-100,000
30,000
40,000
50,000
30,000
Discounting
factor at 14
%
1.000
0.877
0.769
0.675
0.592
Present
Value
100,000
26,316
30,779
33,749
17,762
Cumulative
net cash
flow after
discounting
-100,000
-73,684
-42,906
-9,157
8,605
Discounted payback period = 3 + 9,157 / (9,157 + 8,605) = 3.52 years.
The discounted payback period for B is calculated as follows:
Year
Cash flow
0
1
2
3
4
5
-150,000
50,000
50,000
50,000
50,000
50,000
Discounting
factor at 14
%
1.000
0.877
0.769
0.675
0.592
0.519
Present
Value
150,000
43,860
38,473
33,749
29,604
25,968
Cumulative
net cash
flow after
discounting
-150,000
-106,140
-67,667
-33,918
-4,314
21,654
Discounted payback period = 4 + 4,314 / (4,314 + 21,654) = 4.17 years.
10. The equivalent annual cost (EAC) associated with the durable paint is:
= 100,000 / PVIFA5 yrs, 16%
= 100,000 / 3.274 = 30,544
The equivalent annual cost (EAC) associated with the not so durable paint is:
= 75,000 / PVIFA3yrs, 16%
= 75,000 / 2.246 = 33,393
As the EAC associated with the durable paint is lower I will choose that option.
11. The present value of costs associated with the bulldozer is:
500,000 + 50,000 x PVIFA15 yrs, 15% -200,000 xPVIF15 yrs, 15%
= 500,000 + 50,000 x 5.847 -200,000 x 0.123 = 767,750
The equivalent annual cost (EAC) is:: 767,750/ 5.847 = Rs. 131,307
Minicase
(a) Project A
Cumulative Discounting
Cash
net cash
factor
Year flow
inflow
@12%
0 (15,000)
(15,000)
1.000
1
11,000
(4,000)
0.893
2
7,000
3,000
0.797
3
4,800
0.712
Cumulative net
Present cash flow after
value
discounting
(15,000)
(15,000)
9,823
(5,177)
5,579
402
3,418
Payback period is between 1 and 2 years. By linear interpolation we get the
payback period = 1 + 4,000 /(4,000 + 3,000) = 1.57 years.
Discounted payback period = 1 + 5,177 / ( 5,177 + 402) = 1.93 years
Project B
Cumulative Discounting
Cumulative net
Cash
net cash
factor
Present cash flow after
Year flow
inflow
@12%
value
discounting
0 (15,000)
(15,000)
1.000
(15,000)
(15,000)
1
3,500
(11,500)
0.893
3,126
(11,875)
2
8,000
(3,500)
0.797
6,376
(5,499)
3
13,000
9,500
0.712
9,256 3,757
Payback period is between 2 and 3 years. By linear interpolation we get the payback period =
2 + 3,500 /(3,500 + 9,500) = 2.27 years.
Discounted payback period = 2 + 5,499 / ( 5,499 + 3,757) = 2.59 years
(b)Project A
Year
0
1
2
3
Discounting
Cash
factor
flow
@12%
(15,000)
1.000
11,000
0.893
7,000
0.797
4,800
0.712
Net present value=
Present
value
(15,000)
9,823
5,579
3,418
3,820
Project B
Year
0
1
2
3
Year
0
1
2
3
Discounting
Cash
factor
flow
@12%
(15,000)
1.000
3,500
0.893
8,000
0.797
13,000
0.712
Net present value=
Project C
Discounting
Cash
factor
flow
@12%
(15,000)
1.000
42,000
0.893
(4,000)
0.797
Net present value=
Present
value
(15,000)
3,126
6,376
9,256
3,758
Present
value
(15,000)
37,506
(3,188)
19,318
(c)
Project A
IRR is the value of r in the following equation.
11,000 / (1+r) + 7,000 / (1+r)2 + 4,800 / (1+r)3 = 15,000
Trying r = 28 %, the LHS = 11,000 / (1.28) + 7,000 / (1.28)2 + 4,800 / (1.28)3
= 15,155
As this value is slightly higher than 15,000, we try a higher discount rate of
29% for r to get 11,000 / (1.29) + 7,000 / (1.29)2 + 4,800 / (1.29)3
= 14,970
By linear interpolation we get r = 28 + (15,155 – 15,000) / (15,155 – 14,970) =
28.84 %
Project B
IRR is the value of r in the following equation.
3,500 / (1+r) + 8,000 / (1+r)2 + 13,000 / (1+r)3 = 15,000
Trying r = 23 %, the LHS = 3,500 / (1.23) + 8,000 / (1.23)2 + 13,000 / (1.23)3
= 15,119
As this value is slightly higher than 15,000, we try a higher discount rate of
24% for r to get 3,500 / (1.24) + 8,000 / (1.24)2 + 13,000 / (1.24)3
= 14,844
By linear interpolation we get r = 23 + (15,119 – 15,000) / (15,119 – 14,844) =
23. 43 %
Project C
IRR rule breaks down as the cash flows are non conventional.
Chapter 12
Project Cash Flows
1. The incremental post-tax cash flows associated with the replacement project are worked out as
follows:
(Rs. in thousands)
Cash Flows of the Replacement Project
0
1
2
I Investment Outlay
1. Cost of new asset
2. Salvage value of old asset
(2000)
640
3. Total net investment (1-2+3)
(1360)
II. Operating Inflows
7.
Aftertax
savings
in
manufacturing costs
5. Depreciation on new machine
6. Depreciation on old machine
7. Incremental depreciation (5-6)
8. Tax savings on Incremental
depreciation ( 0.5 x 7)
9. Net operating cash flow (4+8)
III. Terminal Cash Flow
10. Net terminal value
machine
IV. Net Cash Flow
(3+ 9+10)
of
3
300
300
300
660
128
532
266
442.2
102.4
339.8
169.9
296.3
81.9
214.4
107.2
566
469.9
407.2
new
1200
(1360)
566
469.9
1607.2
2
The incremental post-tax cash flows associated with the replacement project are worked out
as follows:
(Rupees in thousands)
Cash Flows of the Replacement Project
0
1
2
3
4
5
A. Net investment in the
new hammer
(800)
B. Increase in revenues
100
100
100
100
100
C. Savings in operating costs
D. Depreciation on new
hammer
120
120
120
120
120
528
353.8
237
158.8
106.4
59
53.1
47.8
43
38.7
469
300.7
189.2
115.8
67.7
(249)
(80.7)
30.8
104.2
152.3
(124.5)
40.4
15.4
52.1
76.2
(124.5)
(40.3)
15.4
52.1
76.1
E. Depreciation on old hammer
F. Incremental depreciation
on new hammer (D – E)
G. Incremental taxable
profit (B + C – F)
H. Incremental tax
I. Incremental profit after tax
J. Net incremental salvage
value
K. Initial flow (A)
L. Operating flow (I + F)
M. Terminal flow (J)
800
(800)
344.5
(260.4)
204.6
167.9
143.8
800
N. Net cash flow
(K + L +M)
(800)
344.5 (260.4)
204.6
167.9
943.8
Note: There was an error in the NCF figure for year 2 in the list of solutions given in the book.
3
The cash flows associated with the new product are calculated as under:
Year ending
Cost of Plant &
Equipment
Working capital margin
Sales
Manufacturing cost
Selling & distribution
cost
Contribution loss
Depreciation
Profit before tax
Tax
Profit ater tax
Net salvage value of
Plant & Equipment
Net salvage value of
working capital
Initial cash flow
Operational cash flow
Terminal cash flow
Net cash flow
0
1
(Rs. in thousands)
2
3
4
5
3,000
1,100
-2,000
-800
3,000
1,100
3,000
1,100
3,000
1,100
3,000
1,100
600
100
500.0
700.0
210.0
490.0
600
100
375.0
825.0
247.5
577.5
600
100
281.3
918.8
275.6
643.1
600
600
100
100
210.9
158.2
989.1 1,041.8
296.7
312.5
692.3
729.3
300.0
800.0
2,800.0
2,800.0
990.0
952.5
924.4
903.3
887.5
1,100.0
990.0
952.5
924.4
903.3 1,987.5
Assumptions
The project life will be 5 years. Net salvage value of Plant & machinery at the end of
the project will be Rs.500 million and that of the working capital will be the original
invested amount. Income tax will be at 30 percent and depreciation will be at 25
percent under WDV method.
4.
The present value of the depreciation tax shields is as follows:
Year
1
2
3
4
Depreciation@33% Tax shield@60% Present value@12%
33,000
19,800
17,679
22,110
13,266
10,575
14,814
8,888
6,326
9,925
5955
3,784
Total= Rs 38,364
We have:
P x PVIFA(12%, 4yrs) + 38,364 + 50,000 x PVIF(12%, 4yrs)= 160,000
P. x 3.037 + 38,364 + 50,000 x 0.636 = 160,000
P = 29581
5.
Cash Flows for the Replacement Project
Year
I Investment Outlay
Cost of new machine
Salvage value of old machine
Net investment
II. Operating Inflows
After- tax savings in
operating
costs
Depreciation on new machine
8. Depreciation on old machine
9. Incremental depreciation
10. Tax
savings
on
Incremental
depreciation
11. Net operating cash flow
III. Terminal Cash Flow
12. Net terminal value of new machine
13.
14.
15.
0
(Rs. In ‘000)
4
5
1
2
3
30
30
30
30
30
26.4
6.6
19.8
11.9
17.7
4.4
13.3
8.0
11.9
2.9
9.0
5.4
8.0
1.9
6.1
3.7
5.4
1.3
4.1
2.5
41.9
38.0
35.4
33.7
32.5
(80)
30
(50)
50
(50)
IV. Net Cash Flow
41.9
38.0
35.4
33.7
82.5
By trial and error method it can be found out that the IRR is 77.6 percent.
6.
Cash Flows for the Replacement Project
Year
I Investment Outlay
Cost of new machine
Salvage value of
machine
0
old
Net investment
II. Operating Inflows
After- tax savings in
incremental revenue
After- tax savings in
operating costs
Depreciation on new
machine
16. Depreciation on old machine
17. Incremental depreciation
18. Tax savings on Incremental
depreciation
19. Net operating cash flow
III. Terminal Cash Flow
20. Net terminal value of new
machine
1
2
(Rs. In ‘000)
4
5
3
(1,500)
600
(900)
60
60
40
40
495
331.6
169.0
326
195.6
295.6
60
40
60
60
20
20
222.2
148.9
99.8
113.2
218.4
131.0
75.8
146.4
87.8
50.8
98.1
58.9
34.0
65.8
39.5
231.0
187.8
138.9
119.5
900
21.
22. Net terminal value of old
machine
23.
IV. Net Cash Flow
150
(900)
295.6
231.0
187.8
138.9
869.5
3
4
5
700
700
700
300.0 300.0
875.0 437.5
-475.0 -37.5
-285.0 -22.5
-190.0 -15.0
685.0 422.5
300.0
218.8
181.3
108.8
72.5
291.3
300.0
109.4
290.6
174.4
116.3
225.6
7.
Year ending
Computer cost
Savings in clerical cost &
space
Operation & maintenance
costs
Depreciation
Profit before tax
Tax
Proft after tax
Net cash flow
0
-3,500
( Rs. In thousands)
1
2
700
-3,500
300.0
1,750.0
-1,350.0
-810.0
-540.0
1,210.0
700
NPV = -3,500 + 1,210 / (1.12)1 + 685 / (1.12)2 + 422.5 / (1.12)3 +291.3 / (1.12)4
+225.6/ (1.12)5
= - 1,26 million
Minicase
(Rs.in lakhs)
Year
0
Investment on machinery, repairs and
40.00
renovation
-3.00
Working capital margin
1
2
3
4
5
Revenues
Rent loss
Salary loss
Costs (Other than D&I)
Depreciation
Profit before Tax
Tax
Profit after tax
Sale of machinery
Net recovery of WC margin
Initial Flow
Operating Flow
Terminal Flow
Net Cash Flow
62.00
0.48
6.00
51.00
6.00
-1.48
0.00
-1.48
68.20
0.48
6.00
53.55
5.10
3.07
0.77
2.30
75.02
0.48
6.00
56.23
4.34
7.97
1.99
5.98
82.52
0.48
6.00
59.04
3.68
13.32
3.33
9.99
90.77
0.48
6.00
61.99
3.13
19.17
4.79
14.38
3.00
3.00
4.52
7.40
10.32
13.67
4.52
7.40
10.32
13.67
17.51
6.00
23.51
-43.00
-43.00
Solution:
Let the IRR be r %. Trying r = 9 %, we have:
4.52/1.09 + 7.40/1.09 2 + 10.32/1.093 + 13.67/1.094 + 23.51/1.095 = 43.31
Trying r = 10 %,
4.52/1.10 + 7.40/1.102 + 10.32/1.103 + 13.67/1.104 + 23.51/1.105 = 41.91
So, r = 9 % +[ (43.31 – 43)/(43.31 – 41.91)]x 1% = 9.22 %
As the IRR is less than the loan interest rate the project is not worthwhile.
Chapter 13
Risk Analysis in Capital Budgeting
1.
NPV of the project
=
=
-250 + 50 x PVIFA (13,10)
Rs.21.31 million
NPVs under alternative scenarios:
Pessimistic
(Rs. in million)
Expected
Optimistic
Investment
Sales
Variable costs
Fixed costs
Depreciation
Pretax profit
Tax @ 28.57%
Profit after tax
Net cash flow
Cost of capital
300
150
97.5
30
30
- 7.5
- 2.14
- 5.36
24.64
14%
250
200
120
20
25
35
10
25
50
13%
200
275
154
15
20
86
24.57
61.43
81.43
12%
NPV
- 171.47
21.31
260.10
Assumptions: (1)
The useful life is assumed to be 10 years under all three
scenarios. It is also assumed that the salvage value of the
investment after ten years is zero.
2.
(2)
The investment is assumed to be depreciated at 10% per annum; and
it is also assumed that this method and rate of depreciation are
acceptable to the IT (income tax) authorities.
(3)
The tax rate has been calculated from the given table i.e. 10 / 35 x
100 = 28.57%.
(4)
It is assumed that only loss on this project can be offset against the
taxable profit on other projects of the company; and thus the company
can claim a tax shield on the loss in the same year.
Accounting break even point (under ‘expected’ scenario)
Fixed costs + depreciation
Contribution margin ratio
Break even level of sales
= Rs. 45 million
= 80 / 200 = 0.4
= 45 / 0.4 = Rs.112.5 million
Financial break even point (under ‘expected’ scenario)
i.
Annual net cash flow
= 0.7143 [ 0.4 x sales – 45 ] + 25
= 0.2857 sales – 7.14
ii.
PV (net cash flows)
= [0.2857 sales – 7.14 ] x PVIFA (13,10)
= 1.5502 sales – 38.74
5.426
iii.
Initial investment
= 250
iv.
Financial break even level
of sales
= 288.74 / 1.5502
= Rs.186.25 million
Note: In the list of solutions given in Appendix B of the book, the answer given is
incorrect , by oversight.
3.
Cash
Year Flow
0 (30,000)
1
7,000
2
8,000
3
9,000
4
10,000
5
8,000
Certainty
Equivalent Certainty
Discount
Factor: αt Equivalent Factor at Present
=1 - 0.06t value
8%
Value
1
(30,000)
1 (30,000.00)
0.94
6,580
0.9259
6,092.59
0.88
7,040
0.8573
6,035.67
0.82
7,380
0.7938
5,858.48
0.76
7,600
0.7350
5,586.23
0.7
5,600
0.6806
3,811.27
NPV
=
(2,615.77)
4.
C21:Strong demand
Annual
cash flow: 7Mn
Probability: 1/3
C2
D21: Invest Rs.20 Mn.
Probability:1/3
Moderate demand
Annual cash flow5Mn
Probability:1/3
C11: Success
Probability: 0.6
Weak demand
C22
D2
D11
Annual cash flow : 3mn
Carry out
Market survey
D22
Stop
C1
Rs,3 million
D1
C12: Failure
Stop
D3
Probability:
D31
D12: Do nothing
1).Starting at the right-hand end of the tree the expected monetary value (EMV)
at chance point C2 that comes first as we proceed leftward.
EMV(C2) = 1/3 x PVIFA (10, 12%) [ 7+5+3]
= 1/3 x 5.650 x 15 = Rs. 28.25 million
2). Evaluate the EMV of the decision alternatives at D2 the last stage decision point.
Alternative
EMV
D21 (Invest Rs 20 million)
D22 (Stop)
Rs 8.25 million
0
3). Select D21 and truncate D22 as EMV(D21) > EMV(D22).
4). Calculate the EMV at chance point C1 that comes next as we roll backwards.
EMV (C1)= 0.6 [8.25] + 0.4 [0]
= Rs 4.95 million
5). Evaluate the EMV of the decision alternatives at D1 the first stage decision point:
Alternative
EMV
D11 (Carry out
market survey at a cost of
Rs 3 million)
Dl2 (Do nothing)
Rs 1.95 million
0
Based on the above evaluation, we find that the optimal decision strategy is as follows: Choose D1 (carryout
market survey) at the decision point D1 and wait for the outcome at the chance point C1. If the outcome at
C1 is C11 (success), invest Rs 20 million; if the outcome at C1 is C12 (failure) stop.
5.
NPV of the project
=
-220 + 62 x PVIFA (12,10)
=
Rs.-220 + 62 x 5.650 = 130.3 million
NPVs under alternative scenarios:
Pessimistic
Investment
Sales
Variable costs
Fixed costs
Depreciation
Pretax profit
Tax @ 31%
Profit after tax
Net cash flow
Cost of capital
PVIFA
NPV
300
300
225
50
30
-5
- 1.55
- 3.45
26.55
13%
5.426
-155.94
(Rs. in million)
Expected
Optimistic
220
400
280
40
22
58
18
40
62
12%
180
500
325
30
18
127
39.37
87.63
105.63
11%
5.650
130.3
5.889
442.06
C21 High
demand
Minicase
0.6
Annual
cash flow
30 million
D21 Invest
C2
Rs. 150 million
C11 Success
D11 Carry out
pilot production
and market C1
test – Rs.20
million
D1
C22 Low
demand
D2
0.4
Annual
cash flow
20 million
Probability : 0.7
D22 Stop
C12 Failure
D31 Stop
D3
Probability: 03
D10 Do thing
The
alternatives are evaluated as follows:
1. Start at the right-hand end of the tree and calculate the expected monetary value
(EMV) at chance point C2 that comes first as we proceed leftward.
EMV (C2) = 0.6 [30 x PVIFA (20, 12%)] + 0.4 [20 x PVIFA (20, 12 %)]
= Rs.194.2 million
2. Evaluate the EMV of the decision alternatives at D2 the last stage decision point.
Alternative
EMV
D21 (Invest Rs.150 million)
Rs.44.2 million
D22 (Stop)
0
3.
Select D21 and truncate D22 as EMV (D21) > EMV (D22)
4.
Calculate the EMV at chance point C1 that comes next as we roll backwards.
EMV (C1) = 0.7 [44.2] + 0.3 [0]
= Rs.30.9 million
5.
Evaluate the EMV of the decision alternatives at D1 the first stage decision point
Alternative
EMV
D11 (Carryout pilot production
and market test at a cost
of Rs.20 million )
Rs.10.9 million
D12 (Do nothing )
0
Based on the above evaluation, we find that the optimal decision strategy is as follows: Choose D 11 (carry
out pilot production and market test) at the decision point D 1 and wait for the outcome at the chance point
C1. If the outcome at C1 is C11 (success), invest Rs.150 million, if the outcome at C1 is C 12 (failure) stop.
Chapter 14
The Cost of Capital
1 (a) Define rD as the pre-tax cost of debt. Using the approximate yield formula, rD can be
calculated as follows:
rD
=
(b) After tax cost =
2.
14 + (100 – 108)/10
------------------------ x 100 = 12.60%
0.4 x 100 + 0.6x108
12.60 x (1 – 0.35) = 8.19%
Define rp as the cost of preference capital. Using the approximate yield formula rp can be
calculated as follows:
rp
3.
WACC
=
9 + (100 – 92)/6
-------------------0.4 x100 + 0.6x92
=
0.1085 (or) 10.85%
=
0.4 x 13% x (1 – 0.35)
+ 0.6 x 18%
14.18%
=
4.
5.
Cost of equity
=
(using SML equation)
10% + 1.2 x 7% = 18.4%
Pre-tax cost of debt
14%
=
After-tax cost of debt =
14% x (1 – 0.35) = 9.1%
Debt equity ratio
=
2:3
WACC
=
2/5 x 9.1% + 3/5 x 18.4%
=
14.68%
Given
0.5 x 14% x (1 – 0.35) + 0.5 x rE = 12%
where rE is the cost of equity capital.
Therefore rE – 14.9%
Using the SML equation we get
11% + 8% x β = 14.9%
where β denotes the beta of Azeez’s equity.
Solving this equation we get β = 0.4875.
6.
The cost of equity capital = 1 / 17 + 0.08 = 13.88 percent
7.
The required rate of return on A = 8 + 0.8(12 – 8) = 11.2 percent
The required rate of return on B = 8 + 1.2(12 – 8) = 12.8 percent
The required rate of return on C = 8 + 1.7(12 – 8) = 14.8 percent
8.
Source of Capital Proportion under
BV
MV
Cost
Weighted Cost of capital under
BV method
MV method
Equity
Preference
0.36
0.07
0.54
0.05
17.0%
14.0%
6.12%
0.98%
9.18
0.70
Debt
0.57
0.41
9.0 %
5.13%
3.69
WACC = 12.23 %
9.
13.57
Cost of equity =
D1/P0 + g
=
3.00 / 30.00 + 0.05
=
15%
(a) The first chunk of financing will comprise of Rs.5 million of retained earnings costing
15 percent and Rs.2.5 million of debt costing 14 (1-.6) = 5.6 per cent
The second chunk of financing will comprise of Rs.5 million of additional equity costing
15 per cent and Rs.2.5 million of debt costing 15 (1-.6) = 6 per cent
(b) The marginal cost of capital in the first chunk will be :
5/7.5 x 15% + 2.5/7.5 x 5.6% = 11.87%
The marginal cost of capital in the second chunk will be :
5/7.5 x 15% + 2.5/7.5 x 6% = 12%
Note : We have assumed that
(i) The net realisation per share will be Rs.25, after floatation costs, and
(ii) The planned investment of Rs.15 million is inclusive of floatation costs
Note: The answer listed in Appendix B in the book is inadvertently incorrect.
2.50
10.
ke =
+0.12 =0.1562 or 15.62 percent
75 (1-.08)
2
11.
ke =
+ 0.14 =0.177
60 (1-f)
So, f = 8.55 percent
Note: The answer listed in Appendix B in the book is inadvertently incorrect
Minicase
Market value proportions of the outstanding securities:
Equity shares : 8,000,000 x 250
Debentures : 3,000,000 x 1020
Total
Market value(Rs.) Market value proportion
2,000,000,000
0.4
3,060,000,000
0.6
5,060,000,000
As the commercial paper has to be paid back in full the next day, the same is not taken into account
in the above calculation.
Pre-tax cost of debenture = (100 + (1000 – 1020)/3) / (0.4 x 1000 + 0.6 x 1020) = 9.22 %
If the cost of equity be r:
0.4 x r + 0.6 x 9.22 x (1- 0.3) = 15
0.4r = 15 – 3.87
or r = 27.82 %.
Using CAPM: 8 + beta x (15 – 8) = 27.82
Beta = 19.82 / 7 = 2.83
Chapter 15
Capital Structure and Cost of Capital
1.
Net operating income (O)
Interest on debt (I)
Equity earnings (P)
Cost of equity (rE)
:
:
:
:
Rs.30 million
Rs.10 million
Rs.20 million
15%
Cost of debt (rD)
Market value of equity (E)
:
:
10%
Rs.20 million/0.15 =Rs.13 million
Market value of debt (D)
:
Market value of the firm (V) :
2.
(a)
Market value of equity
Market value of debt
Market value of the firm
Rs.10 million/0.10 =Rs.100 million
Rs.233 million
Box
Cox
2,000,000/0.15
= Rs.13.33 million
0
1,500,000/0.15
= Rs.10 million
500,000/0.10
=Rs.5 million
=15 million
Rs.13.33million
(b) Average cost of capital for Box Corporation
13.33.
0
x 15% +
x 10%
13.33
13.33
= 15%
Average cost of capital for Cox Corporation
10
5.00
x 15% +
x 10% = 13.33%
15
15
(c) If Box Corporation employs Rs.30 million of debt to finance a project that yields
Rs.4 million net operating income, its financials will be as follows.
Net operating income
Interest on debt
Equity earnings
Cost of equity
Cost of debt
Market value of equity
Market value of debt
Market value of the firm
Rs.6,000,000
Rs.3,000,000
Rs.3,000,000
15%
10%
Rs.20 million
Rs.30 million
Rs.50 million
Average cost of capital
20
15% x
30
+ 10%
50
= 12%
50
(d) If Cox Corporation sells Rs.10 million of additional equity to retire
Rs.10 million of debt , it will become an all-equity company. So its
average cost of capital will simply be equal to its cost of equity,
which is 15%.
3.
4.
rE
=
20
=
So D/E = 2
E
D+E
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
rA + (rA-rD)D/E
12 + (12-8) D/E
D
D+E
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
E
rE
(%)
rD
(%)
11.0
11.0
11.5
12.5
13.0
14.0
15.0
16.0
18.0
20.0
6.0
6.5
7.0
7.5
8.5
9.5
11.0
12.0
13.0
14.0
rA =
D
rE +
D+E
rD
D+E
11.00
10.55
10.60
11.00
11.20
11.75
12.60
13.20
14.00
14.20
The optimal debt ratio is 0.10 as it minimises the weighted average
cost of capital.
5. (a) If you own Rs.10,000 worth of Bharat Company, the levered company
which is valued more, you would sell shares of Bharat Company, resort
to personal leverage, and buy the shares of Charat Company.
(b) The arbitrage will cease when Charat Company and Bharat Company
are valued alike
6. The value of Ashwini Limited according to Modigliani and Miller
hypothesis is
Expected operating income
15
=
= Rs.125 million
Discount rate applicable to the
0.12
risk class to which Aswini belongs
7
Debt/Total
Assets
0
0.1
0.2
0.3
0.4
Interest on
debt(%)
0
10
10
10.5
11
Cost of equity
without
bankruptcy
and agency
costs(%)
Cost of equity
with
bankruptcy and
agency
costs(%)
Average
cost of
capital
without
bankruptcy
and agency
costs(%)
12
12
12.5
13.5
13.5
12
12
13
14
15
12.00
11.20
10.80
10.71
9.86
Average cost of
capital with
bankruptcy and
agency costs(%)
12.00
11.20
11.20
11.06
10.76
0.5
11.5
14
16
0.6
12
14.5
17
0.7
13
15
18
0.8
15
15.5
19
0.9
17
16
20
Tax rate
60%
a. Minimum average cost of capital without bankruptcy and
agency costs
Optimal capital structure without bankruptcy and agency
costs is when the debt/total assets is
b. Minimum average cost of capital with bankruptcy and
agency costs
Optimal capital structure with bankruptcy and agency
costs is when debt/total assets is
8.
9.30
8.68
8.14
7.90
7.72
10.30
9.68
9.04
8.60
8.12
=
7.72
=
0.9
=
8.12
=
0.9
The tax advantage of one rupee of debt is :
1-(1-tc) (1-tpe)
(1-0.55) (1-0.05)
=
1 (1-tpd)
(1-0.25)
= 0.43 rupee
( tc in the book is corrected to 55 percent here)
9.
Average cost of interest = 0.09 x 0. 8 + 0.10 x 0. 2 = 9.2 %
Interest on debt
= 0.092 x 100 =Rs.9.2 million
Net operating income (O) :
Rs.20 million
Interest on debt (I)
:
Rs. 9.2 million
Equity earnings (P)
:
Rs.10.8 million
Cost of equity (rE)
:
16%
Cost of debt (rD)
Market value of equity (E)
Market value of debt (D)
Market value of the firm (V)
:
:
:
:
9.2 %
Rs.10.8 million/0.16 =Rs.67.5 million
Rs. 100 million
Rs.167.5 million
10.
.
rE
=
rA + (rA-rD)D/E
18
=
12 + (12-9) D/E
So D/E = 6/3 = 2
11.
Expected operating income
12
=
Discount rate applicable to the
= Rs.120 million
0.10
12.
Let the cost of equity be r.
We have: r x 1/3 + 12 x(1-0.33) x 2/3 = 14
i.e. r/3 = 14 – 5.36 = 8.64 so r = 25.92%
using CAPM:
25.92 = 8 + beta x 6
so, beta = (25.92-8)/6 = 2.99
Minicase
Calculation of the EBIT indifference level:
(EBIT* - 100 x 0.12)(1 – tax rate)/(8+1)
= (EBIT* - (100 x 0.12+ 80 x 0.10))(1 – tax rate)/8
(EBIT* - 12)/9 = (EBIT*-20)/8
8 EBIT* - 96 = 9 EBIT* - 180
EBIT* = Rs.84 crores
Even a 5 percent growth would take the EBIT above the indifference level and this could very well
happen in the very next year. So after the first year, the growth in EPS would very likely be more
under the debt option than the equity option for the machinery purchase. Other things, in particular
the PE ratio, remaining unchanged, the market price of the company’s equity share would be
higher, higher the EPS. So, based solely on the given data, I would recommend going in for the
additional bank loan offer.
Chapter 16
Planning the Capital Structure
1.(a) Currently
No. of shares = 1,500,000
EBIT
= Rs 7.2 million
Interest
= 0
Preference dividend = Rs.12 x 50,000 = Rs.0.6 million
EPS
= Rs.2
(EBIT – Interest) (1-t) – Preference dividend
EPS =
No. of shares
(7,200,000 – 0 ) (1-t) – 600,000
Rs.2 =
1,500,000
Hence t = 0.5 or 50 per cent
The EPS under the two financing plans is :
Financing Plan A : Issue of 1,000,000 shares
(EBIT - 0 ) ( 1 – 0.5) - 600,000
EPSA
=
2,500,000
Financing Plan B : Issue of Rs.10 million debentures carrying 15 per cent
interest
(EBIT – 1,500,000) (1-0.5) – 600,000
EPSB =
1,500,000
The EPS – EBIT indifference point can be obtained by equating EPSA and EPSB
(EBIT – 0 ) (1 – 0.5) – 600,000
(EBIT – 1,500,000) (1 – 0.5) – 600,000
=
2,500,000
1,500,000
Solving the above we get EBIT = Rs.4,950,000 and at that EBIT, EPS is Rs.0.75
under both the plans
(b)
As long as EBIT is less than Rs.4,950,000 equity financing maximixes EPS.
When EBIT exceeds Rs.4,950,000 debt financing maximises EPS.
2.
(a)
EPS – EBIT equation for alternative A
EBIT ( 1 – 0.5)
EPSA =
2,000,000
(b) EPS – EBIT equation for alternative B
EBIT ( 1 – 0.5 ) – 440,000
EPSB =
1,600,000
(c)
EPS – EBIT equation for alternative C
(EBIT – 1,200,000) (1- 0.5)
EPSC =
1,200,000
(d) The three alternative plans of financing ranked in terms of EPS over varying
Levels of EBIT are given the following table
Ranking of Alternatives
EBIT
(Rs.)
EPSA
(Rs.)
2,000,000
2,160,000
3,000,000
4,000,000
4,400,000
More than 4,400,000
0.50(I)
0.54(I)
0.75(I)
1.00(II)
1.10(II)
(III)
EBIT
3. a.
Interest coverage ratio
=
Interest on debt
15
=
4
= 3.75
EPSB
(Rs.)
0.35(II)
0.40(II)
0.66(II)
0.98(III)
1.10(II)
(II)
EPSC
(Rs.)
0.33(III)
0.40(II)
0.75(I)
1.17(I)
1.33(I)
(I)
EBIT + Depreciation
b.
Cash flow coverage ratio =
Loan repayment instalment
Int.on debt +
(1 – Tax rate)
= 15 + 3
4+5
= 2
4. The debt service coverage ratio for Pioneer Automobiles Limited is given by:
DSCR
5
 PAT i + Depi + Inti)
i=1
5
Inti + LRIi)
i=1
=
=
133.00 + 49.14 +95.80
95.80 + 72.00
=
277.94
167.80
1.66
=
Chapter 17
Dividend Policy and Share Valuation
1.
Payout ratio
Price per share
3(0.5)+3(0.5)
0.15
0.5
0.12
= Rs. 28.13
0.12
3(0.7 5)+3(0.25) 0.15
0.12
0.75
= Rs. 26.56
0.12
3(1.00)
1.00
= Rs. 25.00
0.12
2.
Po =
Dividend
payout ratio
30 %
50%
60 %
100% =
Yo(1  b)
k  br
Price as per Gordon model P0
=E1(1-b)/(k-br)
= 8 x 0.30 / (0.12 - 0.70x 0.16)
= 8 x 0.50/(0.12 - 0.50x 0.16)
= 8 x 0.60/(0.12 - 0.40x 0.16)
8 x 1,00/(0.12 - 0x 0.16)
=Rs. 300
=Rs. 100
=Rs. 85.71
=Rs. 66.67
Chapter 18
Dividend Policy: Practical Aspects
1
Dt = cr EPSt + (1 – c)Dt–1
Dt = 0.7 x 0.5 x 4 + (1 – 0.7)1.80 = Rs.1.94
2. Dt = cr EPSt + (1 - C) Dt – 1
Dt = 0.5 X 0.6 X 6 + 0.5 X 2.5 = 1.8 + 1.25 = 3.05
Chapter 20
Raising Long-Term Finance
1. Po = Rs. 220, N = 4, S = Rs. 150
(a) Rs. 220
(b) NPo + S
4 X 220 + 150
=
= Rs. 206
N+1
5
(c) N(Po – S) 4(220 – 150)
=
= Rs. 56
N+1
5
Note: Inadvertently an error has crept in in the answer given in Appendix B of the book
2.
a.
Po = Rs.180
N=5
The theoretical value of a right if the subscription price is Rs.150
Po – S
5( 180 – 150)
=
= Rs.25
N+1
5+1
Note: Inadvertently an error has crept in in the answer given in Appendix B of the
book
b. The ex-rights value per share if the subscription price is Rs.160
NPo + S
5 x 180 + 160
=
= Rs.176.7
N+1
5+1
c.
The theoretical value per share, ex-rights, if the subscription price is
Rs.180? 100?
5 x 180 + 180
= Rs.180
5+1
5 x 180 + 100
= Rs.166.7
5+1
Chapter 21
Securities Market
1.
Share
M
N
O
P
Q
Price in
base year
(Rs.)
Price in
year t
(Rs.)
Price
Relative
1
12
18
35
20
15
2
16
15
60
30
6
3
133
83
171
150
40
577
The equal weighted index
For year t is
:
577
The value weighted index
For year t is
:
1975
No. of
outstanding
shares
(in million)
4
10
5
6
40
30
Market
Market
capitalisation capitalisation
in the base
in year t
year (1 x 4)
(2 x 4)
5
6
120
160
90
75
210
360
800
1200
450
180
1670
1975
= 115.4
5 (since there are 5 scrip’s)
x 100 = 118.3
1670
2.
Share
Price in
base year
Price in
year t
Price
Relative
No .of
outstanding
Market
Market
capitalisation capitalisation
X
Y
Z
(Rs.)
(Rs.)
1
80
40
30
2
100
30
shares
3
125
75
4
15
20
50
in the base
year (1 x 4)
5
1200
800
1500
3500
in year t
(2 x 4)
6
1500
600
The value weighted index for year t is: Market capitalisation in year t
x 100
3500
Market capitalisation in year t
115 =
115 x 3500 =
x 100
3500
Market capitalisation in year t x 100
115 x 3500
Market capitalisation in year t
Market capitalisation of z
=
100
= 4025
= 4025 – (500 + 600)
= 1925
1925
Price of share z in year t
=
50
= 38.5
Chapter 22
Working Capital Policy
Average inventory
1
Inventory period =
Annual cost of goods sold/365
(60+64)/2
=
= 62.9 days
360/365
Average accounts receivable
Accounts receivable =
period
Annual sales/365
(80+88)/2
=
= 61.3 days
500/365
Average accounts payable
Accounts payable
period
=
Annual cost of goods sold/365
(40+46)/2
=
= 43.43 days
360/365
Operating cycle
=
62.9 + 61.3
= 124.2 days
Cash cycle
=
124.2 – 43.43 = 80.77 days
(110+120)/2
2.
Inventory period
=
=
56.0 days
=
52.9 days
=
30.7 days
750/365
(140+150)/2
Accounts receivable =
period
1000/365
(60+66)/2
Accounts payable
period
=
750/365
Operating cycle = 56.0 + 52.9 = 108.9 days
Cash cycle
= 108.9 – 30.7 = 78.2 days
3.
A : Current Assets
Rs.in milllion
Total cash cost
Debtors
100
x 1
=
x
1=
8.33
x
2 =
8.00
1=
7.50
=
2.00
A : Current Assets
=
25.83
B : Current Liabilites
Rs.in million
12
12
Material cost
Raw material
stock
48
x 2
=
12
12
Cash manufacturing cost
Finished goods
stock
Cash balance
90
x1=
12
12
A predetermined amount
Material cost
Sundry creditors
x
48
x 2=
x
2
= 8.00
12
12
Manufacturing
expenses outstanding
One month’s cash
manufacturing expenses
=
2.00
Wages outstanding
One month’s wages
=
1.50
B : Current liabilities
11.50
Working capital (A – B)
Add 15 % safety margin
14.33
2.15
Working capital required
16.48
Working Notes 1. Manufacturing expenses
Rs in million
120
24
96
1. Sales
Less: Gross profit (20%)
Total manufacturing cost
Less: Materials
48
Wages
18
66
30
24
Manufacturing expenses
2. Cash manufacturing expenses
(Rs 2 million x 12)
3. Depreciation: (1) – (2)
4. Total cash cost
Total manufacturing cost
Less: Depreciation
Cash manufacturing cost
Add: Administration and selling expenses
Total cash cost
6
96
6
90
10
100
4.
Solution:
A. Current Assets
Calculation
Item
Debtors
Amount
Total cash cost
x2=
12
2,520,000 x 2
420,000
12
Raw material stock
Material cost
800,000
x 3 =
x3
200,000
12
12
Finished good stock
Cash manufacturing cost
2,220,000
x3=
x3
555,000
12
12
Pre-paid sales promotional
Quarterly sales promotional expense
30,000
expenses
Cash balance
A predetermined amount
100,000
A : Current Assets
1,305,000
B. Current Liabilities
Item
Calculation
Sundry creditors
Material cost
Amount
800,000 x 2
x2=
Manufacturing expenses
outstanding
Wages outstanding
Total administrative
expenses outstanding
133,333
12
12
One month’s cash manufacturing expenses
60,000
One month’s wages
One month’s total administrative
expenses
15,000
B : Current Liabilities
266,666
58,333
Working capital (A – B)
Add 20 percent (assumed) safety margin
1,038,334
207,667
Working capital required
1,246,001
Working Notes
1. Manufacturing expenses
Sales
Less : Gross profit (25%)
Total manufacturing cost
Less: Materials
800,000
Wages
700,000
Manufacturing expenses
2. Cash manufacturing expenses
(Rs.60,000 x 12)
3. Depreciation: (1) –(2)
4. Total cash cost
Total manufacturing cost
Less : Depreciation
Cash manufacturing cost
Add Total administrative expenses
4,000,000
1,000,000
3,000,000
1,500,000
1,500,000
720,000
780,000
3,000,000
780,000
2,220,000
180,000
Sales promotion expenses
Total cash cost
120,000
2,520,000
Minicase
Annual figures:
Sales
Profit @ 25 %
Rent
Salaries
Electricity, water etc
Franchisee fee
Total of profit and
expenses
Purchases
30,000 x 12
33,000 x 12
16,000 x 12
8000000 x 0.1
Rs.
8,000,000
2,000,000
360,000
396,000
192,000
800000
3748000
4252000
Calculation of working capital loan amount
Rs.
Current Assets
2 months'
Stocks
purchases
708,667
Debtors
1 month's sales
666,667
Cash balance
50,000
Franchisee fee
0.1 month's sales
66,667
Total
1,492,001
Current Liabilities
1 month's
Creditors
purchase
354,333
Salaries and wages
1 month in arrears
33,000
Rent
1month in arrears
30,000
Other expenses
1month in arrears
16,000
Total
433,333
Working capital needed
Margin
Amount of loan
1,058,668
264,667
794,001
@25 %
Amount of loan Rs.7.94 lakhs.
Chapter 23
1
Forecast of Cash Receipts
(Rs)
JanuaryFebruary March
April
May
June
1. Sales
150,000 150,000
150,000 200,000
200,000 200,000
2. Credit Sales
105,000 105,000
105,000 140,000
140,000 140,000
3. Collection of Accounts Receivable 1m.after
33,600
42,000
42,000 42,000
56,000
56,000
4. Collection of Accounts Receivable 2m.after
50,400
50,400
42,000
42,000
42,000
56,000
45,000
45,000
45,000
60,000
60,000
60,000
4. Cash Sales
5. Receipt from Sale of machine
70,000
6. Interest
3,000
Total Cash Receipts
129,000 137,400
129,000 214,000
158,000 175,000
Forecast of Cash Payments
JanuaryFebruary March
April
May
(Rs)
June
1. Material Purchases on credit
60,000 60,000
60,000 80,000 80,000
80,000
3. Payment of Accounts Payable
60,000 60,000
60,000 60,000 80,000
80,000
4. Miscellaneous Cash Purchases
3,000
5. Wages
3,000
3,000
3,000
3,000
3,000
25,000 25,000
25,000 25,000 25,000
25,000
6. Manufacturing Expenses
32,000 32,000
32,000 32,000 32,000
32,000
7. General Administrative and
Selling Expenses
15,000 15,000
15,000 15,000 15,000
15,000
8. Dividend
–
–
–
–
–
30,000
9. Tax
–
–
–
–
–
35,000
–
–
80,000
–
–
–
10. Machine Purchase
Total Payments
135,000 135,000 215,000 135,000 155,000 220,000
Summary Cash Forecast
JanuaryFebruary March
April
May
(Rs)
June
1. Opening Cash Balance
28,000
2. Receipts
129,000
3. Payments
135,000 135,000 215,000 135,000 155,000 220,000
4. Net Cash Flow (2–3)
(6,000)
5. Cumulative Net Cash Flow
6. Opening Cash
Balance + Cumulative
Net Cash Flow (1 + 5)
(6,000) (3,600) (89,600) (10,600) (7,600) (52,600)
22,000
137,400 129,000
214,000 158,000
2,400 (86,000) 79,000
175,000
3,000 (45,000)
24,400 (61,600) 17,400 20,400 (24,600)
7. Minimum Cash Balance Required30,000 30,000 30,000 30,000 30,000 30,000
8. Surplus or Deficit in Relation to the
Minimum Cash Balance
Required (6–7)
(8,000) (5,600) (91,600) (12,600) (9,600) (54,600)
2
The projected cash inflows and outflows for the quarter, January through March, is shown
below.
Month
December
(Rs.)
Inflows :
Sales collection
Outflows :
Purchases
Payment to sundry creditors
Rent
Drawings
Salaries & other expenses
Purchase of furniture
Total outflows (2to6)
22,000
January
(Rs.)
February
(Rs.)
March
(Rs.)
50,000
55,000
60,000
20,000
22,000
5,000
5,000
15,000
-
22,000
20,000
5,000
5,000
18,000
25,000
25,000
22,000
5,000
5,000
20,000
-
47,000
73,000
52,000
Given an opening cash balance of Rs.5000 and a target cash balance of Rs.8000, the surplus/deficit
in relation to the target cash balance is worked out below :
January
(Rs.)
1. Opening balance
2. Inflows
3. Outflows
4. Net cash flow (2 - 3)
5. Cumulative net cash flow
6. Opening balance + Cumulative
net cash flow
7. Minimum cash balance required
8. Surplus/(Deficit)
February
(Rs.)
March
(Rs.)
5,000
50,000
47,000
3,000
3,000
55,000
73,000
(18,000)
(15,000)
60,000
52,000
8,000
(7,000)
8,000
8,000
-
(10,000)
8,000
(18,000)
(2,000)
8,000
(10,000)
3 The balances in the books of Datta co and the books of the bank are shown below:
(Rs.)
1
2
3
4
5
6
7
8
9
10
Books of
Datta
Co:
Opening
Balance
Add:
Cheque
received
Less:
Cheque
issued
30,000 46,000 62,000 78,000
94,000 1,10,000 1,26,000 1,42,000 1,58,000 1,74,000
20,000 20,000 20,000 20,000
20,000
20,000
20,000
20,000
20,000
20,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
46,000 62,000 78,000 94,000 1,10,000 1,26,000 1,42,000 1,58,000 1,74,000 1,90,000
Closing
Balance
Books of
the
Bank:
30,000 30,000 30,000 30,000 30,000
Opening
Balance
Add:
Cheques
realised
Less:
Cheques
debited
-
-
-
-
-
-
-
-
-
-
30,000 30,000 30,000 30,000 30,000
30,000
50,000
70,000
90,000
1,06,000
20,000
20,000
20,000
20,000
20,000
4,000
4,000
-
50,000
-
70,000
-
90,000
1,06,000 1,22,000
Closing
Balance
From day 9 we find that the balance as per the bank’s books is less than the balance as per Datta
Company’s books by a constant sum of Rs.68,000. Hence in the steady situation Datta Company
has a negative net float of Rs.68,000.
Chapter 24
Credit Management
1
Contribution on additional sales = 10,000,000 x 0.15 = 1,500,000
Less: Bad debt loss on additional sales = 10,000,000 x 0.08 = 800,000
Pretax income on additional sales
= 700,000
Investment on receivables on additional sales:
= 10,000,000x60x0.85/360
= 1,416,667
Cost of funds on additional sales = 1,416,667 x 0.25 = 354,167
Increase in profit
= 700,000 - 354,167 =Rs.345,833
2. The effect of extending the credit periods by 45 days and 60 days is shown below:
Existing
Credit Period
Option
45 days
Rs (million)
60 days
Rs (million)
A. Expected sales
15.000
16.500
B. Contribution (20%)
3.000
3.300
1.875
0.075
2.750
1.500
2.200
0.300
0.440
2.700
2.785
C. Bad debts increase
D. Average receivables
Sales x Credit period
360
E. Investment in
receivables (80% of D)
F. Required return on
investment in
receivables (20% of E)
G. Residual Profit
(B – C – F)
Lengthening the credit period increases the profit by Rs.85,000
3.
Old policy
New policy
A Annual sales
12,000,000
13,200,000
B Cash discount availed on sales
0.3 x 12,000,000 x0.01= 0.7 x 13,200,000 x0.02 =
36,000
184,800
C Investment in receivables
12,000,000x24/360x0.8
640,000
Reduction in
receivables
investment
= 13,200,000x16/360x0.8
469,333
in
=
170,667
Savings in capial charge on
account of the above reduction
170,667 x 0.20 = 34,133
Increase in discount allowed
=184,800-36,000 = 148,800
The effect of relaxing the discount policy is a reduction in profit by Rs.114,667
4
Current
policy
New
policy
A. Sales
50,000,000
56,000,000
B. Contribution
12,500,000
14,000,000
C. Bad debts
2,000,000
D. Investment in receivables
2,604,167
Sales
X ACP X Proportion of variable costs
360
3,360,00
4,666,667
E. Required return on
investment in receivables (15% of D)
F. Residual profit
390625
700000
10,109,375
9,940,000
G. Overall effect on residual profit
The effect of relaxing the collection effort on the profit of the firm is a reduction in the residual profit by
Rs.169,375.
5
30% of sales will be collected on the 10th day
70% of sales will be collected on the 50th day
ACP = 0.3 x 10 + 0.7 x 50 = 38 days
Rs.40, 000,000
Value of receivables =
x 38
360
= Rs.4, 222,222
Assuming that V is the proportion of variable costs to sales, the investment in
receivables is :
Rs.4, 222,222 x V
6
30% of sales are collected on the 5th day and 70% of sales are collected on the
25th day. So,
(a) ACP = 0.3 x 5 + 0.7 x 25 = 19 days
Rs.10, 000,000
Value of receivables =
x 19
360
= Rs.527,778
(b) Investment in receivables = 0.7 x 527,778
= Rs.395,833
7
Increase in contribution = 10,000,000 x0.15 = 1,500,000 ---(A)
Increase in discount = 0.03 x 60,000,000x0.6 - 0.02 x 50,000,000x0.7=Rs.380, 000—(B)
Increase in investment in receivables of the existing sales on account of the increase in average
collection period = 50,000,000 x (24-20) / 360 = Rs.555,556
Investment in the receivables of the additional sales =10,000,000 x 0.85 x 24/360
=Rs.566,667
Cost of the increased investment in receivables = 0.12 x (555,556+566,667)
= Rs.134, 667---(C)
The expected change in residual profit = A-B-C =1,500,000 – 380,000 – 134,667 =
= Rs.985, 333
8
Profit when the customer pays = Rs.10,000 - Rs.8,000 = Rs.2000
Loss when the customer does not pay = Rs.8000
Expected profit = p1 x 2000 –(1-p1)8000
Setting expected profit equal to zero and solving for p1 gives :
p1 x 2000 – (1- p1)8000 = 0
p1 = 0.80
Hence the minimum probability that the customer must pay is 0.80
9
The effect of extending the credit periods by 45 days and 60 days is shown below:
(Rs.in million)
16%
Required return on investment
2
Increase in sales expected
Bad debts proportion on current sales
4%
Bad debt proportion on additional sales
5%
Ratio of variable costs to sales
0.7
Existing Proposed
Credit period (in days)
30
40
Sales
20.00
22.00
Contribution
6.000
6.600
Bad debts(sales x proportion of bad debts)
Investment in receivables (sales/360 x ACP x0.7) say A
Required return on investment in receivables (A x 0.16)
Residual profit
Increase in the residual income before tax
0.800
1.167
0.187
5.013
0.900
1.711
0.274
5.426
0.413
10
(Rs. )
25%
10%
Existing
Proposed
30
20
40,000,000
30,000,000
35
30
Required return on investment
Cost of capital
Credit period allowed- in days
Sales(S)
Average collection period in days (ACP)
Variable costs to sales ratio(V)
0.90
Investment in receivables (sales/360 x ACP x0.9) say A
Required return on investment in receivables (A
x0.25)
Incentives offered
Residual profit
0.90
2250000
3500000
562,500
875,000
100,000
2,437,500
3,025,000
587,500
Increase in residual profit expected
.
11
Discount sales
Accounts receivable = [ACP on discount sales]
360
Non – discount sales
+ [ACP on non-discount sales]
360
80,000,000
120,000,000
15,000,000 = [10]
+ ACP
360
360
Solving the above we get ACP = 38.3 days
12.
Existing
30 days
Rs. in million
New
40 days
Rs. in. million
200.00
220.00
B. Contribution (0.3)
60.00
66.0
C. Bad debts
10.00
13.20
16.67
24.44
11.67
17.11
2.10
3.08
A. Expected Sales
D. Average receivables
Sales
-------- x Credit Period
360
E. Investment in receivables
( 0.7 of D)
F. Required return on investment in
receivables
(18% of E)
H Overall effect on residual Income ( B – C –
F)
Increase in the residual income before tax =1.82
mn.
47.9
49.72
The relaxation in credit efforts will increase the pre-tax residual income by Rs.1.82 million
13.
Existing
50 days
Rs. in million
Option
80 days
Rs. in. million
A. Expected Sales
600.00
680.00
B. Contribution (1/3)
200.00
226.67
12.00
27.20
83.33
151.11
55.55
100.74
12.22
22.16
175.78
177.31
C. Bad debts
D. Average receivables
Sales
-------- x Credit Period
360
E. Investment in receivables
( 2/3 of D)
F. Required return on investment in
receivables
(22% of E)
G. Overall effect on residual Income ( B – C –
Residual Income in creases by Rs.1.53 million
14.
(Amounts in Rs.millon)
Credit sales
At
presen
t
Propose
d
800
800
60%
Proportion of the customers taking discount
Percentage of discount
1%
Discount allowed
Average collection period (in days)
Ratio of variable costs to sales
Investment in receivables
Reduction in investment in receivables
Required return from investment
Savings in capital charge
0
5
40
20
0.8
0.8
71
36
36
30%
11
As the savings in capital charge is more than the discount allowed, it is worthwhile to
introduce the discount scheme. Increase in income Rs.6 million
15
0.02
360
x
1 – 0.02
= 29.39 %
45– 20
16
(Amounts in Rs.million)
Receivables
Daily sales( 30 days averaging)
30%
End of quarter 1
100.00
2.33
End of
quarter 2
83.00
2.33
End of
quarter
3
97.00
2.50
42.86
2.17
46.15
DSO((30 days averaging)
Daily sales(60 days averaging)
DSO( 60 days averaging)
Age bracket
Quarter I
35.57
2.42
34.34
31-60
61-90
Quarter
III
Quarter II
60.0%
35.0%
5.0%
0-30
38.80
2.42
40.14
54.2%
36.1%
9.6%
55.7%
37.1%
7.2%
Minicase
End of quarter
Receivables
Daily sales(60/61 days
averaging)
DSO( 60/61 days
averaging)
Age
bracket
60/61 – 90
days
1
85
2
87
3
78
4
80
1.92
2.10
1.79
2.10
44.32
41.46
43.65
38.10
Quarter 1
Quarter 2
Quarter 3
Quarter 4
11.8%
12.6%
11.5%
12.50%
Shyam was indeed successful in achieving the targets set.
Chapter 25
Inventory Management
1.
a.
No. of
Orders Per
Year
(U/Q)
Order
Quantity
(Q)
Ordering Cost
(U/Q x F)
Units
Rs.
Carrying Cost Total Cost
Q/2xPxC
of Ordering
(where
and Carrying
PxC=Rs.30)
Rs.
Rs.
1
2
5
10
250
125
50
25
200
400
1,000
2,000
3,750
1,875
750
375
2 UF
2x250x200
b. Economic Order Quantity (EOQ) =
=
PC
2UF
3,950
2,275
1,750
2,375
30
= 58 units (approx)
2. a EOQ =
PC
U=10,000 , F=Rs.300, PC= Rs.25 x 0.25 =Rs.6.25
2 x 10,000 x 300
EOQ =
= 980
6.25
10000
b. Number of orders that will be placed is
= 10.20
980
Note that though fractional orders cannot be placed, the number of orders relevant for the year will
be 10.2 . In practice 11 orders will be placed during the year. However, the 11th order will serve
partly(to the extent of 20 percent) the present year and partly(to the extent of 80 per cent) the
following year. So only 20 per cent of the ordering cost of the 11th order relates to the present year.
Hence the ordering cost for the present year will be 10.2 x Rs.300
c. Total cost of carrying and ordering inventories
980
= [ 10.2 x 300 +
x 6.25 ] = Rs.6122.5
2
3. U=6,000, F=Rs.400 , PC =Rs.100 x 0.2 =Rs.20
2 x 6,000 x 400
EOQ =
= 490 units
20
U
Δπ = UD +
Q*
Q’(P-D)C
U
FQ’
Q* PC
-
2
2
6,000
6,000
= 6000 x .5 +
490
x 400
1,000
1,000 (95)0.2
490 x 100 x 0.2
-
2
2
= 30,000 + 2498 – 4600 = Rs.27898
4. U=5000 , F= Rs.300 , PC= Rs.30 x 0.2 = Rs.6
2 x 5000 x 300
EOQ =
= 707 units
6
If 1000 units are ordered the discount is : .05 x Rs.30 = Rs.1.5 Change in
profit when 1,000 units are ordered is :
5,000
Δπ = 5000 x 1.5 +
5,000
-
707
1000 x 28.5 x 0.2
-
x 300
1,000
707 x 30 x 0.2
-
= 7500 + 622-729 =Rs.7393
2
2
If 2000 units are ordered the discount is : .10 x Rs.30 = Rs.3 Change in profit
when 2,000 units are ordered is :
5000
Δπ = 5000 x 3.0 +
5000
-
707
= 15,000 +1372 – 3279
2000x27x0.2
x 300-
2000
707x30x0.2
-
2
2
= Rs.13,093
5. The quantities required for different combinations of daily usage rate(DUR) and lead times(LT)
along with their probabilities are given in the following table
LT
(Days)
*
DUR
(Units)
5(0.6)
10(0.2)
15(0.2)
4(0.3)
6(0.5)
8(0.2)
20*(0.18)
30 (0.30)
40 (0.12)
40(0.06)
60(0.10)
80(0.04)
60(0.06)
90(0.10)
120(0.04)
Note that if the DUR is 4 units with a probability of 0.3 and the LT is 5 days with
a probability of 0.6, the requirement for the combination DUR = 4 units and LT =
5 days is 20 units with a probability of 0.3x0.6 = 0.18. We have assumed that the
probability distributions of DUR and LT are independent. All other entries in the
table are derived similarly.
The normal (expected) consumption during the lead time is :
20x0.18 + 30x0.30 + 40x0.12 + 40x0.06 + 60x0.10 + 80x0.04 + 60x0.06 + 90x0.10 +
120x0.04 = 46.4 tonnes
6.
a. Costs associated with various levels of safety stock are given below :
Safety
Stock*
Stock
outs(in
tonnes)
Stock out
Cost
Probability
1
2
3
4
Tonnes
73.6
43.6
0
30
0
120,000
0
0.04
10
40
40,000
160,000
0.10
0.04
20
30
60
80,000
120,000
240,000
0.04
0.10
0.04
13.6
33.6
54,400
134,400
0.16
0.04
33.6
13.6
0
Expected
Stock out
5
[3x4]
Carrying
Cost
Total Cost
6
[(1)x1,000]
7
[5+6]
Rs.
0
4,800
Rs.
73,600
43,600
Rs.
73,600
48,400
10,400
33,600
44,000
24,800
13,600
38,400
43,296
0
43,296
43.6
73.6
174,400
294,400
0.10
0.04
Safety stock = Maximum consumption during lead time – Normal
consumption during lead time
So the optimal safety stock= 13.6 tonnes
Reorder level = Normal consumption during lead time + safety stock
K= 46.4 + 13.6 = 60 tonnes
*
b. Probability of stock out at the optimal level of safety stock = Probability
(consumption being 80 or 90 or 120 tonnes)
Probability (consumption = 80 tonnes) + Probability (consumption = 90 tonnes) +
Probability (consumption = 120 tonnes)
= 0.04 +0.10+0.04 = 0.18
7
Item
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Annual Usage
(in Units)
400
15
6,000
750
1,200
25
300
450
1,500
1,300
900
1,600
600
30
Price per
Unit
Rs.
20.00
150.00
2.00
18.00
25.00
160.00
2.00
1.00
4.00
20.00
2.00
15.00
7.50
40.00
Annual
Usage Value
Rs.
8,000
2,250
12,000
13,500
30,000
4,000
600
450
6,000
26,000
1,800
24,000
4,500
1,200
Ranking
6
10
5
4
1
9
14
15
7
2
11
3
8
12
15
45
20.00
900
13
1,35,200
Cumulative Value of Items & Usage
Item
No.
Rank
5
10
12
4
3
1
9
13
6
2
11
14
15
7
8
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Annual
UsageValue
(Rs.)
30,000
26,000
24,000
13,500
12,000
8,000
6,000
4,500
4,000
2,250
1,800
1,200
900
600
450
Cumulative
Annual Usage
Value (Rs.)
30,000
56,000
80,000
93,500
105,500
113,500
119,500
124,000
128,000
130,250
132,050
133,250
134,150
134,750
135,200
Cumulative Cumulative
% of Usage % of Items
Value
22.2
41.4
59.2
69.2
78.0
83.9
88.4
91.7
94.7
96.3
97.7
98.6
99.2
99.7
100.0
6.7
13.3
20.0
26.7
33.3
40.0
46.7
53.3
60.0
66.7
73.3
80.0
86.7
93.3
100.0
Class
No. of Items
A
B
C
% to the Total
4
3
18
Annual Usage
Value Rs.
26.7
20.0
53.3
% to Total Value
93,500
26,000
15,700
15
69.2
19.2
11.6
135,200
Minicase
Normal usage = ( 4 x 0.4 + 5 x 0.6)x(20 x 0.3 + 30 x 0.5 + 40 x 0.2) = 133 tons
Daily usage
rate(tons)
4
4
4
5
5
5
Safety
stock
(tons)
67
27
17
Lead time in
days
20
30
40
20
30
40
Possible
levels of
usage(tons)
80
120
160
100
150
200
Safety stock(tons)
27
17
67
Expected
stockout
Carrying
Total
Probability
cost(Rs.)
cost(Rs.) cost(Rs.)
0.00
0
166,500 166,500
0.12
28,800
66,500
95,300
0.12
36,000
41,500
82,300
0.08
4,800
40,800
0
66.6
399,600
0.12
47,952
16.6
99,600
0.30
29,880
26.6
159,600
0.12
0
96,984
19,152
96,984
The optimal level of safety stock is 17 tons because at that level the cost is
minimised.
Stockout
(tons)
0
40
50
10.0
Stockout
cost(Rs.)
0
240,000
300,000
60,000
The probability of stockout when the safety stock is 17 tons is: (0.08 + 0.12) = 0.20
As the stockout probability is less than 30 percent it can be
implemented.
Chapter 26
Working Capital Financing
1. Annual interest cost is given by,
Discount %
360
x
Credit period – Discount period
1- Discount %
Therefore, the annual per cent interest cost for the given credit terms will be as
follows:
a.
0.01
360
x
0.99
b.
0.02
= 0.367
= 36.7%
= 0.318
= 31.8%
= 0.364
= 36.4%
= 0.104
= 10.4%
=
=
360
0.98
20
0.03
360
x
d.
= 18.2%
20
x
c.
= 0.182
0.97
35
0.01
360
x
0.99
10
0.01
360
2.
a.
x
0.99
b.
35
0.02
360
x
0.98
c.
0.03
360
= 0.223
0.97
50
0.01
360
x
0.99
21%
35
x
d.
0.21
= 0.145
25
= 22.3%
= 14.5%
3. The maximum permissible bank finance under the three methods suggested by
The Tandon Committee are :
Method 1 : 0.75(CA-CL) = 0.75(36-12) = Rs.18 million
Method 2 : 0.75(CA)-CL = 0.75(36-12 = Rs.15 million
Method 3 : 0.75(CA-CCA)-CL = 0.75(36-18)-12 = Rs.1.5 million
Minicase
(Rupees in lakhs)
a) Projected sales = 800 x 1.4 = 1120
Less: Gross profit(25%)
= 280
Cost of goods sold
= 840
Current assets:
Raw materials 840 x 0.6x 2/12
= 84
Stock in process 840 x 1/24
= 35
Finished Goods 840 x 1/12
= 70
Receivables 1120 x 2/12
= 187
Cash
=
8
Total Current assets
= 384
Current Liabilities:
Trade creditors 840 x 0.6x 1/12
= 42
Wages and other overheads 840x0.20/12 =14
Total Current Liabilities
= 56
MPBF
=0.75x 384- 56 = 232
b) Prime security: Hypothecation of inventory and assignment (a form of creating charge) of
receivables.
Collateral security: Mortgage of factory land and building.
Chapter 27
Leasing, Hire Purchase and Project Finance
1.
Assume that the lease rental is payble at the end of the year.
Present Value of Post-tax Rentals
End of
Year
Lease
Rental
(1)
Post-tax
Present Value
Lease Rental of Post-tax rental
(9.6 % discount)
(2)
(3)
1
270,000
162,000
147,810
2
270,000
162,000
134,863
3
270,000
162,000
123,050
4
5
270,000
270,000
162,000
162,000
112,272
102,438
620,433
Present Value of Buying (with Borrowed Fund) Option
End of Principal Interest Depreciation Tax Shield
Post-tax
Present Value of
Year RepaymentPayment
on Interest
Cash
Post-tax cash flow
& Depreciation Outflow
at 9.6% discount
[(2) + (3)] x T (1) + (2) – (4)
(1)
(2)
(3)
(4)
(5)
(6)
1
200,000
160,000
200,000
144,000
216,000
197,080
2
200,000
128,000
200,000
131,200
196,800
163,834
3
200,000
96,000
200,000
118,400
177,600
134,904
4
5
200,000
200,000
64,000
32,000
200,000
200,000
105,600
92,800
158,400
139,200
109,777
88,021
693,616
PV of the net cash flow of the borrowal option = -693,616 + 150,000 / (1.096)5 = -598,766
Sigma should choose the borrowal option as the net cash outflow is lower.
2.
Present Value of Post-tax Lease Rentals
1,080,000 x 0.70 x PVIFA( 11.2% ,8 yrs) = 1,080,000 x 0.70 x [1-1/1.1128] / 0.112
= Rs. 3,862,876
Present Value of the purchase option:
As the loan will be amortised over an eight year period the annual instalment will be:
5,000,000
5,000,000
=
PVIFA (8 yrs, 16%)
= 1,151,013
4.344
The split-up of this instalment between interest payment and principal repayment is as shown in the
following table.
Year
ending
1
2
3
4
5
6
7
8
Loan at
the
beginning
of the year
5,000,000
4,648,987
4,241,812
3,769,489
3,221,594
2,586,036
1,848,789
993,582
Instalment
1,151,013
1,151,013
1,151,013
1,151,013
1,151,013
1,151,013
1,151,013
1,151,013
Interest
800,000
743,838
678,690
603,118
515,455
413,766
295,806
158,973
Principal
repayment
351,013
407,175
472,323
547,895
635,558
737,247
855,207
992,040
Loan
outstanding at
the year end
4,648,987
4,241,812
3,769,489
3,221,594
2,586,036
1,848,789
993,582
1,542
*Because of rounding off error some loan is still shown as outstanding. For practical purposes this
may be approximated to zero.
Given the break-up of instalment payments between interest and principal, the present value of
the post-tax cash flows associated with the purchase option is calculated:.
Year
ending Instalment Interest
1 1,151,013 800,000
2 1,151,013 743,838
3 1,151,013 678,690
4 1,151,013 603,118
5 1,151,013 515,455
6 1,151,013 413,766
7 1,151,013 295,806
8 1,151,013 158,973
Tax savings
on interest
Present value
and
Post-tax cash
of post-tax cash
Depreciation depreciation outflow
outflow@11.2%
625,000
427,500
723,513
650,641
625,000
410,651
740,362
598,735
625,000
391,107
759,906
552,644
625,000
368,435
782,578
511,809
625,000
342,137
808,876
475,728
625,000
311,630
839,383
443,947
625,000
276,242
874,771
416,065
625,000
235,192
915,821
391,717
Net salvage value
1,500,000
-641,583
Total
3,399,703
Since the present value of the post-tax cash flows associated with the leasing option is more
than that of the purchase option, Southern Electronics is advised to choose the purchase option.
Minicase
Equated annual instalment of bank loan = 50,00,000/PVIFA12%,4yrs
= 50,00,000/3.037 = Rs.16,46,362
Loan amortization schedule:
Loan
outstanding at
Principal
Year year beginning Instalment interest'@12% repayment
1
5,000,000
1646362
600,000
1,046,362
2
3,953,638
1646362
474,437
1,171,925
3
2,781,713
1646362
333,806
1,312,556
4
1,469,156
1646362
176,299
1,470,063
PV of post-tax cash outflow if loan is availed
(Rs.)
Yea
r
Instalmen
t
1
1,646,362
2
1,646,362
3
1,646,362
4
1,646,362
Net sale
value
Interest
600,00
0
474,43
7
333,80
6
176,29
9
Depreciatio
n
Tax
Savings
(Rs.)
Loan
outstanding at
year end
3,953,638
2,781,713
1,469,156
(907)
of:
Post-tax
Cash
Outflow
PVIF at
14%
PV of
Post-tax
Cash
Outflow
1,250,000
555,000
1,091,362
0.877
957,124
937,500
423,581
1,222,781
0.769
940,319
703,125
311,079
1,335,283
0.675
901,316
527,344
211,093
1,435,269
0.592
553,679
3,352,43
8
(500,000)
935,269
Total
Let MF be the indifference value of lease management fee. Then PV
of post-tax lease cash outflow
=0.877(MF+1500000)x0.7+1500000x0.7(0.769+0.675+0.592)
=0.614MF+30,58,650
On solving: 0.614MF+ 30,58,650 = 3,352,438, we get MF =
293,788/0.614 = Rs.478,482
So, a discount of Rs.4 lakhs can be offered on the Management fee.
Chapter 28
Mergers, Acquisitions, and Takeovers
1. Post-merger EPS of International Corporation will be
2 x 100,000 + 2 x100,000
100,000 + ER x 100,000
Setting this equal to Rs.2.5 and solving for ER gives
ER = 0.6
2. PVA = Rs.25 million, PVB = Rs.10 million
Benefit = Rs.4 million, Cash compensation = Rs.11 million
Cost = Cash compensation – PVB = Rs.1 million
NPV to Alpha = Benefit – Cost = Rs.3 million
NPV to Beta = Cash Compensation – PVB = Rs.1 million
3. Let A stand for Ajeet and J for Jeet
PVA = Rs.60 x 300,000 = Rs.18 million
PVJ = Rs.25 x 200,000 = Rs.5 million
Benefit = Rs.4 million
PVAJ = 18 + 5 + 4 = Rs.23 million
Exchange ratio = 0.5
The share of Jeet in the combined entity will be :
100,000
=
= 0.25
300,000 + 100,000
a) True cost to Ajeet Company for acquiring Jeet Company
Cost = PVAB - PVB
= 0.25 x 27 - 5
= Rs.1.75 million
b) NPV to Ajeet
= Benefit - Cost
=
4 - 1.75 = Rs.2.25 million
c) NPV to Jeet = Cost = Rs.1.75 million
4.
a) PVB = Rs.12 x 2,000,000 = Rs.24 million
The required return on the equity of Unibex Company is the value of k in the
equation.
Rs.1.20 (1.05)
Rs.12
=
k - .05
k = 0.155 or 15.5 per cent.
If the growth rate of Unibex rises to 7 per cent as a sequel to merger, the intrinsic value per share
would become :
1.20 (1.07)
=
Rs.15.11
0.155 - .07
Thus the value per share increases by Rs.3.11 Hence the benefit of the
acquisition is
2 million x Rs.3.11 = Rs.6.22 million
(b)
(i)
If Multibex pays Rs.15 per share cash compensation, the cost of the
merger is 2 million x (Rs.15 – Rs.12) = Rs.6 million.
(ii)
If Multibex offers 1 share for every 3 shares it has to issue 2/3 million
shares to shareholders of Unibex.
So shareholders of Unibex will end up with
0.667

= 0.1177 or 11.77 per cent
5+0.667
Shareholding of the combined entity,
The present value of the combined entity will be
PVAB = PVA + PVB + Benefit
= Rs.225 million + Rs.24 million + Rs.6.2 million
= Rs.255.2 million
So the cost of the merger is :
Cost
=  PVAB
- PVB
= .1177 x 255.2 - 24 = Rs.6.04 million
5
The present value of FCF for first seven years is
16.00
PV(FCF)
=
-
14.30
-
(1.15)2
(1.15)
0
+
9.7
(1.15)5
= - Rs.20.4 million
+
(1.15)3
10.2
+
16.7
+
(1.15)6
0
(1.15)7
(1.15)4
The horizon value at the end of seven years, applying the constant growth model is
FCF8
V4
=
18
=
= Rs.257.1 million
0.15 – 0.08
0.15-0.08
1
PV (VH) = 257.1 x
=
Rs.96.7 million
(1.15)7
The value of the division is :
- 20.4 + 96.7 = Rs.76.3 million
Minicase
a. Free cash flow projections for KPTL:
Year
1
2
3
4
5
6
7
Invested Capital (Year beginning) 93.00
105.09 118.75 134.19 151.63 171.35 193.62
NOPAT
13.95
15.76
17.81
20.13
22.75
25.70
29.04
Net investment
12.09
13.66
15.44
17.44
19.71
22.28
19.36
Free cash flow
1.86
2.10
2.38
2.68
3.03
3.43
9.68
Growth rate (%)
13.00
13.00
13.00
13.00
13.00
13.00
10.00
PV of free cash flows during the steady growth rate period of 13 %
= 1.86/1.13 + 2.10/1.132 + 2.38/1.133 + 2.68/1.134 + 3.03/1.135 + 3.43/1.136 = 9.88 million
Horizon value at the end of the 6th year = 9.68/(0.13 – 0.10) = 322.7 million
PV of the horizon value = 322.7/1.136 = 155 million
Possible purchase price = 155 + 9.88 = 164.88 million or say 165 million
b. Assuming that the minimum number of shares that needs to be given to the shareholders of
KPTL is s:
After merger the share of ACL owned by the shareholders of KPTL = s/(4000000 + s )
PV of ACL after the merger = 500 x 4 +100 x 3 + 20 = Rs.2320 million
Cost of the merger to ACL shareholders = Rs.2320 x (s/(4000000 + s ))– 100 x 3 million
Equating the above cost to the possible purchase value of KPTL’s operations:
2320 x (s/(4000000 + s ))– 100 x 3 = 165
s/(4000000 + s )= 465/2320 = 0.2
s = 800,000 + 0.2s or 0.8s = 800,000 or s = 1,000,000
ACL may have to give at least 1 millionshares in exchange to the shareholders of KPTL.
Chapter 29
International Finance Management
1.
S0 = Rs.70, rh = 7 per cent , rf = 3 per cent
Hence the forecasted spot rates are :
Year
1
2
3
4
5
Forecasted spot exchange rate
Rs.70 (1.07 / 1.03)1 = Rs.72.72
Rs.70 (1.07 / 1.03)2 = Rs.75.54
Rs.70 (1.07 / 1.03)3 = Rs.78.48
Rs.70 (1.07 / 1.03)4 = Rs.81.52
Rs.70 (1.07 / 1.03)5 = Rs.84.69
The expected rupee cash flows for the project
Year
0
1
2
3
4
5
Cash flow in dollars Expected exchange
(million)
rate
-200
70
50
72.72
70
75.54
90
78.48
105
81.52
80
84.69
Cash flow in rupees
(million)
-14,000.0
3,636.0
5,287.8
7,063.2
8,559.6
6,775.2
Given a rupee discount rate of 15 per cent, the NPV in rupees is :
3,636.0
NPV
=
-14,000.0 +
+
(1.15)
8,559.6
+
6,775.2
+
(1.15)4
= Rs.6,066.7 million
5,287.8
(1.15)5
7,063.2
+
(1.15)2
(1.15)3
( Note: In the list of answers in Appendix B of the book, inadvertently the answer mentioned is
incorrect)
Chapter 30
Risk Management: Basics of Financial Engineering
30.1
LIBOR -25BP
5.25%
EXCEL
EXCEL
CORP
N.
LIBOR+ 50BP
SWAP
BANK
LIBOR - 25BP
5%
APPLE
LTD.
5%
Total savings = (6.25% – 5%) – [(LIBOR +0.5%) –(LIBOR)] = 0.75% or 75BP
Each saves 0.25 as seen below:
EXCEL: ( LIBOR -25BP) - ( LIBOR+ 50BP) – 525BP = -600BP
APPLE : 500BP – 500BP – (LIBOR-25BP) = LIBOR +25BP