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EQUITY & CORPORATE VALUATION

CW Solutions

Sanjay Saraf Educational Institute Pvt. Ltd. | 1

1. The intrinsic value of EC Limited’s share according to Mr. R. Ramamurthy is calculated as follows: 0

0

D 1 g 11 1.075 11.825VKe g 0.14 0.075 0.065

= Rs.181.92b. The intrinsic value of EC Limited’s share according to Mr. S.Prabhu is calculated as follows:

Year Dividends PV @ 14% PV of dividends123

13.7517.1821.48

0.8770.7690.674

12.0613.2114.48

39.75

Price at the end of year 3, 3

3

D 1 g 21.48 1.05P 250.60

0.14 0.05 0.09

PV of P3 = 250.6 x 0.674 = 168.90V0 = 168.90 + 39.75 = Rs.208.65c. If we assume that the stock is currently correctly priced, the implied perpetual growth rate is

calculated as follows: 11 1 g

1600.14 g

=160 (0.14 -- g) = 11 + 11g= 22.4 -- 160g = 11 + 11g

Or + 171g = +11.4

Or11.4g 6.67%171

2. To calculate the present value of the share we employ the formula given. According to the formulawe calculate the present value of the dividends we would obtain during years 1, 2 and 3 after whichthere will be a constant growth. That is,

331 2

2 3 3

11 1 1 1

o

D gDD DPk k k k k g

Substituting the respective values, we have= 4(1 + 0.14) + 7 (1 + 0.14)2 + 11/(1 + 0.14)2 + 11.44 / ( + 0.14)3 (0.14 - 0.04)= 3.509 + 5.39 + 7.425 + 77.22 = Rs. 93.54Therefore, the price of the share is Rs. 93.54 through the dividend discount model.

3. Required rate of return for Aksh optima= f i m fR R R

= 9.86 + 0.86 (15.26-9.86

DIVIDEND DISCOUNT MODEL


CW Solutions


= 9.86 + 4.64 = 14.5%

a. 00

1

e

D gV

K g

g = RoE (1 - d)= 0.1 (1 - 0.60)(Where d is the dividend pay-out ratio)= 0.1 (0.4) = 0.04 4%D0 = 6.75 × 0.6 = 4.05

0

4 05 1 04 4 2120 145 0 04 0 105

. . .V. . .

= Rs. 40.11b. D0 = 4.05

Year Div [email protected]% PV (Div)123

3.05 × 1.2 = 4.864.86 × 1.2 = 5.835.83 × 1.2 = 7.00

0.8730.7630.666

4.244.454.66

13.35

3

7 00 1 04 7 28 69 330 145 0 04 0 105

. . .P .. . .

Present value of P3 = 69.33 × PVIF(145.3)

= 69.33 × 0.666= 46.17

Intrinsic Value = 46.17 + 13.35= Rs. 59.52

4. Calculation of present value of dividend stream:(i) @ 12% p.a. in the first 2 years.

= [1.50(1.12) 0.86] [1.50(1.12)2 0.74]

= 1.45 1.39 2.84

(ii)@ 10% in the next 2 years= [1.88(1.1) 0.64] [1.88(1.1)2 0.55] = 1.33 + 1.25= 2.58

(iii) Market value of equity share at the end of 4th year applying the constant dividend growthmodel:

54

e g

DPK

Where

4P = Market price of Equity Share at the end of 4thyear.


CW Solutions


5D = Dividend in 5th year

g = Growth rate

eK = Required rate of return

Now 5 4D D (1 g)

5D `2.28 (1+ 0.08) = `2.46

`30.750.16 0.08

4Rs.2.46P Rs.30.75

0.16 0.08

Present market value of P4= `30.75 ×0.55 = `16.91The intrinsic value of Equity Share of Z Ltd. would be (i) + (ii)(iii)=`2.84 +`2.58+ `16.91 =`22.33

5. Expected rate of return on Equity Share of Target Ltd.

P f i m fE(R ) R [E(R ) R ] = 10 + 1.4(15% - 10%) = 17%

Computation of share price based on dividend growth model.

Dividend growth model = 1

0

D gP

Where D1 = Dividend per share in year 1g = Growth rate of dividends

0P =Market price/share in year o.

0

4(1.08)0.17 0.08P

0

4(1.08)0.09P

04(1.08)P

0.9 `48

The target Ltd’s equity share is valued at an equilibrium price of `48 and its present market value isat `36. Hence it is recommended to purchase at market price.


CW Solutions


6. (i) Firm’s expected or required return on equity(Using a dividend discount model approach)According to Dividend discount model approachthe firm’sexpected or required return on equityis computed as follows :

1e

0

DK gP

Where,

eK = Cost of equity share capital or (Firm’s expected or required return on equity share capital)

1D = Expected dividend at the end of year 1

0P = Current market price of the share.

g = Expected growth rate of dividend.Now, 1 0D D (1 g) or £1(1 0.12) or £1.12,P0 £20 and g = 12% per annum

Therefore, e1.12K 12%20

or eK 17.6%(ii) Firm’s expected or required return on equity

(If dividends were expected to grow at a rate of 20% per annum for 5 years and 10% per yearthereafter)Since in this situation if dividends are expected to grow at a super normal growth rate gs, for nyears and thereafter, at a normal, perpetual growth rate of gn beginning in the year n + 1, thenthe cost of equity can be determined by using the following formula:

0P n

t 1

t0 s n 1

t ne e n e

Div (1 g ) Div 1(1 K ) K g (1 k )

Where,

sg = Rate of growth in earlier years.

ng = Rate of constant growth in later years.

0P = Discounted value of dividend stream.

eK = Firm’s expected, required return on equity (cost of equity capital).

Now,

sg = 20% for 5 years, ng 10%


CW Solutions


Therefore,

0P t

0 s 1t n

e e e

sD (1 0.20) Div 1

(1 K ) K 0.10 (1 k )t 1

= 1 2 3 4 5 5e e e e e e e

1.20 1.44 1.73 2.07 2.49 2.49(1 0.10) 1(1 K ) (1 K ) (1 K ) (1 K ) (1 k ) K 0.10 (1 K )

or o 1 e 2 e 3 eP £1.20(PVF ,K ) £1.44(PVF ,K ) £1.73(PVF ,K ) £2.07

5 e4 e 5 e

e

2.74(PVF ,K )(PVF ,K ) £2.49(PVF ,K )K 0.10

By trial error we are required to find out eK

Now, assume eK 18% then we will have

0P £1.20(0.8475) £1.44(0.7182) £1.73(0.6086) £2.07(0.51589) £2.49

1(0.43710) £2.74(0.4371)0.18 0.10

= £1.071 +£1.034 + £1.052 + £1.067 + £1.09 + £14.97= £20.23

Since the present value of dividend stream is more than required it indicates that eK is greater

than 18%.Now, assume eK 19% will be have

0P £1.20(0.8403) £1.44(0.7061) £1.73(0.5934) £2.07(0.4986) £2.49

1(0.4190) £2.74(0.4190)0.19 0.10

= £ 1.008 +£1.016 + £1.026 +£1.032 + £1.043 + £12.76= £17.89

Since the market price of share (expected value of dividend stream) is £20. Therefore, thediscount rate is closer to 18% than it is to 19%, we can get the exact rate by interpolation by usingthe following formula:

s De

r (PV PV )K rPV

Where,R = Eitherof two interest rates sPV = Present value of share

DPV = Present value of dividend stream

r = Difference in value of dividend streamPV = Difference in calculated present value of dividend stream.


CW Solutions


e18% (£ 20 £ 20.23)K 0.01

£ 20.23 £ 17.89

=18% ( Rs.0.23) 0.01

£2.34

=18% (£0.23) 0.01

2.34

= 18% + 0.10%= 18.10%

Therefore, the firm’s expected, or required, return on equity is 17.10%. At this rate the presentdiscounted value of dividend stream is equal to the market price of the share.

7. e f m fK R (K R ) = 0.09 + 1.50(0.13 – 0.09) = 0.15

10

DP 2.50 / (0.15 0.07) 2.050 / 0.80Ke g

`31.25

Present Value of Share = `31.25Where, 1D = Dividend at the end of Year 1

Ke = Cost of Equityg = growth rateNow with the development, Beta value will go up to 1.75

e f m fK R (K R ) = 0.09 + 1.75 (0.13 – 0.09) = 0.16

10

DPKe g

= 2.50/(0.16 – 0.07) = 2.50/0.90 = `27.78

Value of Share due to likely development = `27.78

8. (a) Expected EPS for next yearsEPS 1 = €10 (1 + 0.20) = € 12EPS2 = € 12 (1 + 0.20) = €14.40EPS3 = € 14.40 (1 + 0.20) = € 17.28EPS4 = € 17.28 + (1 + 0.20) = €20.736EPS5 = € 20,736 (1 + 0.20) = € 24.88EPS 6=€24.88(1 + 0.15) = € 28.61Thus D6 = 0.40(€ 28.61) = € 11.44Hence, value of DESC’s share 5 years from now =

6D 11.44P5Ke g 15% 9%

€ 191 [Note: g = 0.60 × 0.15 = 9%]


CW Solutions


So the value of DESC’s share today is 5

191(1 0.15)

€ 94.96

Note :There is no dividend payment from year 1 to year 5 as given in questionNote :Growth rate from year 1 to year 5 : g = b × r = 100% ×0.20= 20%

(b) The price should rise by 15% per year until year 6.(c) The value of DESC’s shares 5 years from now.

[Note :g = 0.80 × 0.15 = 12%]Note :g = b ×r = 0.80× 0.15= 0.12and D6 = 28.61×20% = 5.722

9. 97d 2.115

02d 3No. of years lapsed = 6 years

6MV PV(1 g) 3 = 2.115(1 + g)6g = 6%

od 3

1 0d d (1 g)

1d 3 1.06 3.18

s e f m fr k r (r r ) 10 (5 1.6) 18%

10

2

DPK g

=3.18

0.18 0.06= `26.5

11. The required rate of Return : Rt + (Rm - Rf) = 8 + 16 (13 - 8) = 16%Expected rate of Return : [Do (1 + g ) /po] + g = [2.60 (1 + 0.08)/30]0.08 = 17.36%At equilibrium, the required rate of return is equal to the expected rate of return. 0.16 =[2.60(1.08)/Po] + 0.08Or, 0.08 Po = 2.808Or, Po = 2.808/0.08 = `35.10Hence the price should be increased by `5.10(35.10 - 30.00) or 17.00%So that it is at equilibrium

10. NO SOLUTIONS


CW Solutions


ALTERNATIVEusing CAPM, Re = Rf + (Rm - Rf)Betaor, Re = 8+(13-8)1.6

= 16%IVo = D1/(Re-g)

= 2.6(1.08)/(.16-.08)= 35.1

Po = 30To reach at equilibrium level, Po = IVo.so the stock should go from ₹30 to ₹35.1i.e. (35.1-30)/30*100

=17%

12. IVo = PV of D1 and P1 discounted at Re = 16%D1 = 18, P1 = 800so, IVo = (D1+P1)PVIF(16%,1)

= 818*0.8621=705.20

Po = 700(given)AsPo<IVo, the stock is underpriced and should be purchased.

13. Computation of intrinsic value of the stockyears CF df @18% PV1 25 .8475 21.192 30 .7182 21.553 39 .6086 23.674 45 .5158 23.215 55+700 .4371 330.01Total 419.63

Po = ₹640(given)Since,Po>IVo, the stock is overpriced and should not be purchased.

16. stage 1: explicit forecast period (for first 5 years)D1=D2=D3=D4=D5=0.So, pv of all dividend = 0.stage 2: horizon period(beyond 5 years)D6 = 20,

14. NO SOLUTIONS

15. NO SOLUTIONS


CW Solutions


P5 = D6/(Re-g)= 20/(.18-.07)= 181.82

pv of P5 = 181.82 × pvif(18%,5)=181.82 × .4371= 79.48

IVo = stage 1+ stage 2= 0+79.48=79.48

17. Po = D1/(Re-g)= 50/(.15-.05)= 500

If g = 6%, new Po = D1/(Re- new g)= 50/(.15-.06)= 555.56

18. IVo = D1/(Re-g)= 20/(.20-.07)= 153.85

19. (1) share price today i.e. Po = D1/(Re-g)= 50(1.05)/(.18-.05)= ₹403.85

share price at the end of 1st year i.e. P1=D2/(Re-g)=50*1.05*1.05/(.18-.05)=₹424.04

share price at the end of 2nd year i.e. P2=D3/(Re-g)=50*1.05*1.05*1.05/(.18-.05)=₹₹445.24

20. CAGR = (14.9/13)to the power 1/4 -1 = 3.47%.IVo = D1/(Re-g)

= 13/(.18-.0347)= ₹89.47

21. Stage 1: explicit forecast period (for first 2 years)years CF df @15% PV1 60 .8696 52.182 90 .7561 68.05total 120.23


CW Solutions


Stage 2: horizon period (beyond 2 years)D3 = 90*1.08

= 97.20P2 = D3/(Re-g)

= 97.2/(.15-.08)= 1388.57

PV of P2 =1388.57*.7561= 1049.90

IVo = stage1 + stage2= 120.23+1049.90=₹1170.13

22. Stage 1: explicit forecast period (for first 2 years)years CF df @20% PV1 42 .8333 352 58.8 .6944 40.83total 75.83

Stage 2: horizon period (2 to 6 years)YEARS g(%) DPS df@20% pv3 32.5 77.91 .5787 45.094 25 97.39 .4823 46.975 17.5 114.43 .4019 45.996 10 125.87 .3349 42.15total 180.20

Stage 3: horizon period (beyond 6 years)D7 = 125.87*1.10=138.46P6 = D7/(Re-g)

= 138.46/(.20-.10)=1384.60

PV of P6 = 1384.60*.3349= 463.70

IVo = stage1 + stage2 + stage3= 75.83+180.20+463.70= ₹719.73

23. when the market changes by 7.5%, the stock return changes by 15%,so the beta of the stock = 15/7.5

=2%.As per CAPM, Re = Rf+(Rm-Rf)beta

=7+6*2=19%.


CW Solutions


25. 0 0P IV 80 given

10

e

DPR g

e

12 1.0780

R 0.07

Or, e12.84R 0.07

80

Or, Re = 23.05%Also, as per CAPM - Re = Rf + (Rm - Rf) βOr, 23.05 = 5 + 7 β β = 2.5786 2.58If β increases by 50%, new β = 2.8 × 1.50

= 3.87New Re = 5 + 7 × 3.87

= 32.09%

New P0 = 1

e

DR g

12 1.070.3209 0.07

= 51.30

If systematic risk increases by 50%, investors would require a higher return and thus share pricewill decrease.

26. E0 = 4.5D0 = 1.65

Payout Ratio 1.65 1004.5

= 36.67% e f m fR R R R β

= 5.75 + 6 × 2= 17.75%

Stage I - Explicit forecast period (first 5 years)Years EPS DPS DF@ 17.75% PV2006 6.75 2.48 0.8493 2.112007 10.135 3.71 0.7212 2.682008 15.19 5.57 0.6125 3.41

24. NO SOLUTIONS


CW Solutions


2009 22.78 8.36 0.5202 4.352010 34.17 12.53 0.4418 5.54

18.09

Stage II - Horizon Period (beyond 5 years)New Re = 5.75 + 6 × 1.5

= 14.75%Earnings in 2011 = 34.17 × 1.08

= 36.90 DPS = 36.90 × 85% = 31.37

20112010

e

D 31.37PR g 0.1475 0.08

= 464.74Present value of 2010P 464.75 0.4419 205.32

a. Thus, the expected share price of the sock at the end of 2010 = ` 464.74b. Value of the stock using the two stage DDM -

= Stage I + Stage II= 18.09 + 205.32= ` 223.41

28.a. E0 = 7.24

D0 = 55% of 7.24= 3.982

Payout ratio = 55% Retention ratio = 45%g = b × r

= 45% of 12= 5.4%

As per CAPM, e f m fR R R R β

Or, eR 6.71 11.40 6.71 1.15

= 12.1035%

10

e

DIVR g

3.982 1.0540.121035 0.054

= 62.61

27. NO SOLUTIONS


CW Solutions


b. Stage I - Explicit forecast period (first 3 year) -Years Dividend Df @12.1035% PV

1 4.58 0.8920 4.092 5.27 0.7957 4.193 6.06 0.7098 4.30

12.58

Stage II - Horizon period (beyond 3 year) - 4 3D D 1 g

= 6.06 × 1.054= 6.39

43

e

DPR g

6.390.121035 0.054

= 95.32

PV of 3P 95.32 0.7058

= 67.66

0IV Stage I Stage II

= 12.58 + 67.66= ` 80.24

32. As per CAPM, e f m fR R R R β

= 7 + (11 - 7) 1.2= 11.8%

10

e

DPR g

30.118 0.08

= ` 78.95New eR 7 4 1.5

= 13%

29. NO SOLUTIONS

30. NO SOLUTIONS

31. NO SOLUTIONS


CW Solutions


10

e

DPR g

30.13 0.08

35.a. Calculation of IV0 -

Years DPS DF @ 14% PV1 14.58 0.8772 12.792 15.75 0.7695 12.123 17.01 0.6750 11.484 18 - 37 + 500 0.5921 306.93

343.32 IV0

Thus, Mr. A should pay ` 343.32 if he requires a rate of return of 14%.

b. 10

e

DIVR g

14.580.14 0.08

= ` 243

c. Price at the end of 4th year i.e. 4P 243 PVAF 14%,4

= 243 × 2.9137= ` 708.03

37. Working Notes:a. Determination of Weighted Average Cost of Capital

Sources of funds Cost (%) Proportions Weights WeightedCost

Equity Stock 16 12/20 0.60 9.6012% Bonds 12%(1-0.30)

=8.408/20 0.40 3.36

12.96 say 13

FCFF

= ` 6033. NO SOLUTIONS

34. NO SOLUTIONS

36. NO SOLUTIONS


CW Solutions


b. Schedule of Depreciation$ Million

Year Opening Balance ofFixed Assets

Addition duringthe year

Total Depreciation@ 15%

1 17.00 0.50 17.50 2.632 14.87 0.80 15.67 2.353 13.32 2.00 15.32 2.304 13.02 2.50 15.52 2.335 13.19 3.50 16.69 2.506 14.19 2.50 16.69 2.507 14.19 1.50 15.69 2.358 13.34 1.00 14.34 2.15

c. Determination of Investment$ Million

Year Investment Required ExistingInvestment in

CA

AdditionalInvestment

requiredFor CapitalExpenditure

CA (20% ofRevenue)

Total

12345678

0.500.802.002.503.502.501.501.00

1.602.003.004.406.005.204.604.00

2.102.805.006.909.507.706.105.00

3.002.50*

2.00**3.004.406.005.204.60

0.000.303.003.905.101.700.900.40

* Balance of CA in Year 1 ($3 Million) – Capital Expenditure in Year 1($ 0.50 Million)** Similarly balance of CA in Year 2 ($2.80) – Capital Expenditure in Year 2($ 0.80 Million)

d. Determination of Present Value of Cash Inflow

Particulars Years1 2 3 4 5 6 7 8

Revenue (A)ExpensesVariable CostsFixed cash operatingcostAdvertisement Cost

8.00 10.00 15.00 22.00 30.00 26.00 23.00 20.00

3.201.600.502.63

4.001.601.502.35

6.001.601.502.30

8.801.603.002.33

12.002.003.002.50

10.402.003.002.50

9.202.001.002.35

8.002.001.002.15

7.93 9.45 11.40 15.73 19.50 17.90 14.55 13.15


CW Solutions


DepreciationTotal Expenses (B)EBIT (C) = (A) - (B)Less: Taxes@30% (D)NOPAT (E) = (C) - (D)Gross Cash Flow(F) = (E) + DepreciationLess:Investment in CapitalAssets plus CurrentAssets (G)Free Cash Flow (H) =(F) - (G)PVF@13%(I) PV (H)(I)

0.070.02

0.550.16

3.601.08

6.271.88

10.503.15

8.102.43

8.452.53

6.852.06

0.05 0.39 2.52 4.39 7.35 5.67 5.92 4.79

2.68

0

2.74

0.30

4.82

3.00

6.72

3.90

9.85

5.10

8.17

1.70

8.27

0.90

6.94

0.40

2.680.8852.371

2.440.7831.911

1.820.6931.261

2.820.6131.729

4.750.5432.579

6.470.4803.106

7.370.4253.132

6.540.3762.46

Total present value = $ 18.549 million

e. Determination of Present Value of Terminal Value 9 $6.54 million 1.05 $6.867 millionFCFCV $85.8375 million

k g 0.13 0.05 0.08

Present Value of Continuing Value (CV) = $85.8376 million X PVF13%,8 = $85.96875 million X0.376 = $32.2749 million(i) Value of Firm from total point of view

$ MillionPresent Value of cash flow during explicitperiod

18.5490Present Value of Continuing Value 32.2749Total Value 50.8239

(ii) Value of Firm from equity point of view of or value of equity$ Million

Total Value of Firm 50.8239Less: Value of Debt 8.0000Value of Equity 42.82

39

38. Present Value of Cash Flows during the forecast Periodt

0 t1 t t

[FCFE (1 g ) ]PV(1 WACC)

52 3 4

1 5 2 3 4 5

4 (1.35)(4 1.35) {4 (1.35) } {4 (1.35) } {4 (1.35) }PV1.18 (1.18) (1.18) (1.18) (1.18)


CW Solutions


= 2 3 4 5

5.4 7.29 9.84 13.28 17.931.18 (1.18) (1.18) (1.18) (1.18)

= 4.58 + 5.24 + 5.99 +6.85+7.84= `30.50 lakh

Calculate the terminal valueWhere,

nn

e

FCFE (1 g) (17.93 1.05) 18.83P(k g) 0.12 0.05 0.07

`269 lakh

PV of terminal price

5

269 117.58(1.18)

0,FCFE 1 5 TP PV PV 30.50 117.58 `148.08 lakh

Alternative Solution

Stage I - Explilit forecast period (first 5 years) -Years FCF DF @ 18% PV

1 99.9 0.8475 84.672 134.87 0.7182 96.863 182.07 0.6086 110.814 245.79 0.5158 126.785 333.82 0.4371 145.91

565.03

Stage II - Horizon period (beyond 5 years) - 6 5FCF FCF 1 g

= 333.82 (1.05)= 350.51

65

c

FCFFVK g

350.510.12 0.05

= 5007.3

PV of V5 = 5007.3 × 0.4371= 2188.69

firmV Stage I Stage II

= 565.03 + 2188.69= 2753.72


CW Solutions


39. The free cash flow formula temporary supernormal growth followed by zero growth is given as

0 0 sV X (1 T)(1 b )(1 h) t n 1

s 0 st n

n(1 g ) X (1 T)(1 g )(1 k) k(1 k)

t 1

0 0 sV X (1 T)(1 b )(1 h) t 1 n0s

nX (1 T)(1 h) (1 h) (1 g )

kt 1

g = r × b = 0.30×0.60 = 18%

Where, r = Probability rate and b = Retention ratio1 g) (1 0.18) 1.181 h 1.0727

(1 k) (1 0.10) 1.10

h = 1.0727– 1= 0.0727Valuation

1st term10[1.0727(1.0727 1)]1,000(1 0.4)(1 0.6) 240 15.0178

0.0727

`3,604

2nd term101000(1 0.4) 1 0.18{ } (1.18) 600 2,017 1.18

0.1 1 0.10

`1,428

Total value of the firm = `5,032

Alternative SolutionNOPAT = 30% of 60% of 80,000 = 14,400CS - Dep = 20,000WC = 3,000FCFF = NOPAT - Net Inv.

= NOPAT - [CS - Dep + WC]= 14,400 - [20,000 + 3000]= - 8,600

40. NO SOLUTIONS41. NO SOLUTIONS42. NO SOLUTIONS


CW Solutions


43. Determination of forecasted Free Cash Flow of the Firm (FCFF)(` in crores)

Yr. 1 Yr. 2 Yr 3 Terminal YearRevenueCOGSOperating ExpensesDepreciationEBITTax @30%EATCapital Exp. – Dep.∆ Working CapitalFree Cash Flow (FCF)

9000.003600.001980.00

720.002700.00

810.001890.00

172.50375.00

1342.50

10800.004320.002376.00

864.003240.00

972.002268.00

198.38450.00

1619.62

12960.005184.002851.001036.003888.001166.402721.60

228.13540.00

1953.47

13996.805598.723079.301119.744199.041259.712939.33

-259.20

2680.13

Present Value (PV) of FCFF during the explicit forecast period is:FCFF (` in crores) PVF @ 15% PV (` in crores)

1342.501619.621953.47

0.86960.75610.6575

1167.441224.591284.413676.44

PV of the terminal, value is:

32680.13 1 38287.57 Crore 0.6575 25174.08 Crore

0.15 0.08 1.15

` `

The value of the firm is :` 3676.44 Crores + ` 25174.08 Crores = ` 28,850.52 Crores

44.1200. 30

40

croreNo of Shares Crores``

.

PATEPSNo of shares

300 10.0030

croreEPScrore

``

FCFE = Net income – [(1-b) (capex – dep) + (1-b) ( ΔWC )]FCFE = 10.00 – [(1- 0.25) (48 - 40) + (1 - 0.25) (4)]

= 10.00 – [6.00 + 3.00] = 1.00

FCFE


CW Solutions


Cost of Equity = Rf + β (Rm – Rf)= 8.7 + 0.1 (10.3 – 8.7) = 8.86%

0

1 1.00 1.08 1.08 125.580.0886 0.08 0.0086

e

FCFE gP

K g`

45.

Cost Equity : e f m fk R (R R ) Cost of equity in high growth period = 7.5 +1.45(5.5) = 15.48%Cost of equity in stable growth period = 7.5 + 1.1(5.5) = 13.55%Expected growth rate during high growth period

=Db ROA {ROA i(1 t) 0.667[12.5 1{12.5 8.5(1 0.36)}] 13.04%E

Pay-out ratio during stable growth period

= g 0.061 1 69.33%D [12.5 1{12.5 8.5(1 0.36)}][ROA {ROA i(1 t)}]E

Estimationof Presentvalue of DividendsYear EPS DPS(33.33% on EPS) Present Value12345

30.5234.53944.149.85

10.1711.541314.716.61

8.88.68.48.38.1

Private value = 2 3 4 5

10.17 11.5 13 14.7 16.61(1.1548) (1.548) (1.1548) (1.1548) (1.1548)

Cumulative present value of dividends @ 15.48%= 8.8 8.6 8.4 8.3 8.1 `42.2

Estimation of terminal price

Terminal Price = s

e

D(k g)

Expected earnings per share =49.85 ×(1.06) = `52.82Expected dividend per share = 52.82× 0.6933 =`36.62

Terminal Price =36.62 36.62

(0.1355 0.06) 0.075

`485.16

Present value of terminal price = 5

485.16(1.1548)

=`236.25


CW Solutions


Cumulative present value of dividends and terminal price

0P 42.2 236.25 =`278.45

Therefore, value of equity = `278.45

49.

Projected Balance Sheet Year 1 Year 2 Year 3 Year 4Fixed Assets (40%) of SalesCurrent Assets (20%) of SalesTotal AssetsEquity

96,00048,000

1,44,0001,44,000

1,15,20057,600

1,72,8001,72,800

1,49,76074,880

2,24,6402,24,640

1,94,68897,344

2,92,0322,92,032

Projected Cash Flows:-Year 1 Year 2 Year 3 Year 4

SalesPBT (10%) of salePAT (70%)DepreciationAddition to Fixed AssetsIncrease in Current AssetsOperating cash flow

2,40,00024,00016,800

8,00024,000

8,000(7,200)

2,88,00028,80020,160

9,60028,800

9,600(8,640)

3,74,40037,44026,20811,52046,08017,280

(25,632)

4,86,72048,67234,07014,97659,90422,464

(33,322)

PV of Projected Cash Flows:-

Present value of Projected Cash Flows:-Cash Flows PV at 15% PV

-7,200-8,640

-25,632

0.8700.7560.658

-6,264.00-6,531.84

-16,865.86-29,661.70

Residual Value - 33,322/0.15 = -2,22,147

ALCAR MODEL

46. NO SOLUTIONS

47. NO SOLUTIONS

48. NO SOLUTIONS


CW Solutions


Present value of Residual value = -2,22,147/(1.15)3

= -2,22,147/1.521 = -1,46,065.00Total shareholders’ value = -29,661.70 - 1,46,065 = -1,75,726.70Pre strategy value = 14,000 / 0.15 = 93,333.33∴ Value of strategy = -1,75,726.70 - 93,333.33 = – 2,69,060.03

Conclusion: The strategy is not financially viable

50. Given that g4 = 9%, ga = 3%, 2H = 4 years, D0 = Rs. 8 and P0 = Rs. 150,00.Student may recall that in the h model, the period during which the growth declines to a constantlong run growth is 2H.The present value of the stock while applying the H model is given by

00

0

1 a a nDP g H g g

r g

Substituting the respective values we have

8 00 1 0 03 2 0 09 0 030 15 0 13

. . . .. .

= Rs. 76.67

52.(i) Working for calculation of WACC

Orange Grape AppleTotal debtPost tax Cost of debtEquity Fund

80,00010.4%20,000

50,0008.45%50,000

20,0009.75%80,000

WACCOrange: (10.4 x 0.8) + (26 x 0.2) = 13.52%Grape: (8.45 x 0.5) + (22 x 0.5) = 15.225%Apple: (9.75 x 0.2) + (20 x 0.8) = 17.95%

H MODEL

EVA AND NVA

51. NO SOLUTIONS


CW Solutions


(ii)Orange Grape Apple

WACCEVA [EBIT (1-T)-(WACC x Invested Capital)]

13.522,730

15.2251,025

17.95-1,700

(iii) Orange would be considered as the best investment since the EVA of the company ishighest and its weighted average cost of capital is the lowest.

(iv) Estimated Price of each company sharesOrange Grape Apple

EBIT (`)Interest (`)Taxable Income (`)Tax 35% (`)Net Income (`)SharesEPS (`)Stock Price (EPS x PE Ratio) (`)

25,00012,80012,200

4,2707,9306,100

1.314.30

25,0006,500

18,5006,475

12,0258,300

1.44879515.94

25,0003,000

22,0007,700

14,30010,000

1.4315.73

Since the three entities have different capital structures they would be exposed todifferent degrees of financial risk. The PE ratio should therefore be adjusted for the risk factor.Alternative Answer

Orange Grape AppleNet Income (Given) (`)SharesEPS (`)Stock Price (EPS x PE Ratio) (`)

8,9706,100

1.470516.18

12,3508,3001.48816.37

14,95010,000

1.49516.45

(v) Market CapitalisationEstimated Stock Price (`) 14.30 15.94 15.73No. of shares 6,100 8,300 10,000Estimated Market Cap (`) 87,230 1,32,302 1,57,300Alternative AnswerEstimated Stock Price (`) 16.18 16.37 16.45No. of shares 6,100 8,300 10,000Estimated Market Cap (`) 98,698 1,35,871 1,64,500


CW Solutions


53.a. Determination of Economic value added (EVA)

$ MillionEBITLess: Taxes @ 35%Net Operating Profit after TaxLess : Cost of Capital Employed [W. No.1]Economic Value Added

180.0063.00

117.0072.6044.40

b.$ Million

Market value of Equity Stock [W. No. 2]Equity Fund [W. No. 3]Market Value Added

500425

75

Working Notes:(1) Total Capital Employed

Equity Stock $ 100 MillionReserve and Surplus $ 325 MillionLoan $ 180 Million

$ 605 MillionWACC 12%Cost of Capital employed $ 605 Million х 12% $ 72.60 Million

(2) Market Price per equity share (A) $ 50No. of equity share outstanding (B) 10 MillionMarket value of equity stock (A) х (B) $ 500 Million

(3) Equity FundEquity Stock $ 100 MillionReserve & Surplus $ 325 Million

$ 425 Million54. NO SOLUTIONS

55. NO SOLUTIONS

56. NO SOLUTIONS

57. NO SOLUTIONS

58. NO SOLUTIONS


CW Solutions


60. a. Value of per unit for Mehta Investment Trust (MIT) as per the dividend discount model:b. The book value and residual incomes for the next four years are:

Year 1 2 3 4Beginning book value 100.00 110.00 125.00 150.00Retained earnings (Net income – Dividends) 10.00 15.00 25.00 (150.00)Ending book value 110.00 125.00 150.00 0.00Net income 20.00 35.00 50.00 62.50Less equity charge (r ??? book value) 10.00 11.00 12.50 15.00Residual income 10.00 24.00 37.50 47.50Present value @ 10% 9.09 19.83 28.17 32.44

Therefore Value per unit as per residual income= 100 + 9.09 + 19.83 + 28.17 + 32.44 = 189.53.

c.Year 1 2 3 4Net income 20.00 35.00 50.00 62.50Beginning book value 100.00 110.00 125.00 150.00Return on equity 20.00% 31.82% 40.00% 41.67%ROE – r 10.00% 21.82% 30.00% 31.67%Residual income = (ROE – r) ??? Book value 10.00 24.00 37.50 47.50Present value @ 10% 9.09 19.83 28.17 32.44

Therefore Value per unit as per residual income= 100 + 9.09 + 19.83 + 28.17 + 32.44 = 189.53.

61.

(i) Workings:Asset turnover ratio = 1.1Total Assets = ` 600Turnover ` 600 lakhs × 1.1 = ` 660 lakhs

Effective market rate Interest 8% GivenLiabilities

Liabilities = ` 125 lakhs + ` 50 lakhs = ` 175 lakhInterest = ` 175 lakhs × 0.08 = ` 14 lakhOperating Margin = 10%

RESIDUAL VALUATION

ACCOUNTING VALUATION

59. NO SOLUTIONS


CW Solutions


Hence operating cost = (1 - 0.10) ` 660 lakhs = ` 594 lakhDividend Payout = 16.67%Tax rate = 40%Income statement

(` Lakhs)Sale 660Operating Exp 594EBIT 66Interest 14EBT 52Tax @ 40% 20.80EAT 31.20Dividend @ 16.67% 5.20Retained Earnings 26.00

(ii) SGR = G = ROE (1-b)PATROE and NW 100 lakh 300lakh 400 lakhNW ` ` `

31.2 lakhsROE 100 7.8%400 lakhs

``

SGR = 0.078(1 - 0.1667) = 6.5%(iii) Calculation of fair price of share using dividend discount model

oo

e

D 1 gP

k g

5.2 lakhsDividends 0.5210 lakhs

`

`

Growth Rate = 6.5%

o0.52 1 0.065 0.5538Hence P 6.510.15 0.065 0.085

` `

`

Since the current market price of share is ` 14, the share is overvalued. Hence the investor shouldnot invest in the company.

62.a. Calculation of Profit after tax (PAT)

`

Profit before interest and tax (PBIT)Less: Debenture interest (` 64,00,000 × 12/100)Profit before tax (PBT)Less: Tax @ 35%Profit after tax (PAT)

32,00,0007,68,000

24,32,0008,51,200

15,80,800


CW Solutions


Less: Preference Dividend(` 40,00,000 × 8/100) 3,20,000Equity Dividend (` 80,00,000 × 8/100) 6,40,000Retained earnings (Undistributed profit)

9,60,0006,20,800

Calculation of Interest and Fixed Dividend CoveragePAT Debenture int erest

Debenture int erest Preference dividend

15,80,800 7,68,000 23,48,800 2.16 times7,68,000 3,20,000 10,88,000

b. Calculation of Capital Gearing RatioFixed int erest bearing fundsCapital Gearing RatioEquity shareholders' funds

Preference Share Capital Debentures 40,00,000 64,00,000 1,04,00,000 0.93Equity Share Capital Reserves 80,00,000 32,00,000 1,12,00,000

c. Calculation of Yield on Equity Shares:Yield on equity shares is calculated at 50% of profits distributed and 5% on undistributedprofits:

(`)50% on distributed profits (` 6,40,000 × 50/100) 3,20,0005% on undistributed profits (` 6,20,800 × 5/100) 31,040Yield on equity shares 3,51,040

Yield on equity shares % = Yield on shares 100Equity share capital

3,51,040 100 4.39% or 4.388%80,00,000

Calculation of Expected Yield on Equity sharesNote: There is a scope for assumptions regarding the rates (in terms of percentage for every onetime of difference between Sun Ltd. and Industry Average) of risk premium involved withrespect to Interest and Fixed Dividend Coverage and Capital Gearing Ratio. The belowsolution has been worked out by assuming the risk premium as:(i) 1% for every one time of difference for Interest and Fixed Dividend Coverage.(ii) 2% for every one time of difference for Capital Gearing Ratio.a. Interest and fixed dividend coverage of Sun Ltd. is 2.16 times but the industry average

is 3 times. Therefore, risk premium is added to Sun Ltd. Shares @ 1% for every 1 time ofdifference.Risk Premium = 3.00 – 2.16 (1%) = 0.84 (1%) = 0.84%


CW Solutions


b. Capital Gearing ratio of Sun Ltd. is 0.93 but the industry average is 0.75 times.Therefore, risk premium is added to Sun Ltd. shares @ 2% for every 1 time ofdifference.Risk Premium = (0.75 – 0.93) (2%)

= 0.18 (2%) = 0.36%Calculation of Rate of Return (%)Normal return expected 9.60Add: Risk premium for low interest and fixed dividend coverage 0.84Add: Risk premium for high interest gearing ratio 0.36Rate of Return 10.80

Value of Equity ShareActual yield 4.39Paid up value of share 100 40.65

Expected yield 10.80 `

63.a. Net Assets Method

To compute the value of shares as per this method we shall compute the Net Assets.(i) Value of Land & Building of XYZ Ltd. = ` 1,500 lac (1.25)4 = ` 3,662.11 lac.

Thus, net asset value will be:`

Land & Building 3,662.11 lacPlant & Machinery 2,800.00 lacAccount Receivable 2,400.00 lacStock 2,100.00 lacBank/Cash 400.00 lac

11,362.11 lacLess: Bank Overdraft 100.00 lacSundry Creditors 1,100.00 lacTax Payable 400.00 lacDividend Payable 400.00 lacLong Term Loan 1,000.00 lac

8362.11 lac(ii) Estimated profit for next 5 years

= ` 1,510 lac (1.12) + ` 1,510 lac (1.12)2 + ` 1,510 lac (1.12)3 + ` 1,510 lac (1.12)4 + ` 1,510 lac(1.12)5

= ` 1,691.20 lac + ` 1,894.14 lac + ` 2,121.44 lac + ` 2,376.01 lac + ` 2,661.14 lac = `10,743.93 lac.The total yield value= ` 8,362.11 lac + ` 10,743.93 lac = ` 19,106.04 lacXYZ Ltd.s share’s current market value = ` 470 x 40 lacs shares = ` 1,88,00,00,000 =` 18,800 lac


CW Solutions


The premium is thus ` 306.04 lac (` 19,106.04 lac – ` 18,800 lac) i.e. ` 7.65 per share or1.63% [7.65/470].This is not a sound basis for valuation as it ignores the time value of money. Thepremium of 1.63% above the current market price is very small compared to thoseachieved in many real bids.

b. Dividend Valuation Model 01

0e e

D 1 gDPK g K g

0760 lacD 19 per share40 lac

`

`

Thus D1 = ` 19(1+0.12) = ` 21.28Ke using CAPMKe = Rf +βj (Rm - Rf) =10% + 1.05(16% - 10%) = 16.3%

021.28 21.28P 494.88 per share

16.3% 12% 4.3%

` `

`

The premium is ` 24.88 (` 494.88 – ` 470) i.e. 5.29% above the current market price.Thus, this method should be used for bidding shares of XYZ Ltd.’s shareAssumptions Valuation is based on a constant growth rate and unchanged dividend policy. It will be more rational to assess the value of XYZ Ltd. incorporating post merger

synergies.

66. The historical and expected dividend payout ratios are equal for both the companiesFor Company AAccording to Dividend discount modelPO = ???? Where the symbols are in standard use.Dividing both sides by E1

???? where ????ke = 5.25+1.35 (11.50 – 5.25)

= 5.25 + 11.2= 13.6875

COMPARABLE FIRMS APPROACH

64. NO SOLUTIONS

65. NO SOLUTIONS


CW Solutions


Growth = ROE retention ratioTherefore,P/E ratio = ???? = ??? = 9.786For Company BDividing both sides by E1

???? where ?????ke = 5.25 + 1.05 (11.5-5.25)

= 11.8125g = 0.11 0.50 = 0.055P/E ratio = ?????

= 7.92Alternative method:The P/E ratio estimated above uses the forecasted EPS for the next period, which is called leadingP/E ratio. Alternatively, P/E ratio can be estimated using the current (latest available) EPS. This iscalled trailing P/E ratio:

For company ATrailing P/E ratio :Dividing both sides by Eo

??? where ????ke = 5.25+1.35 (11.50 – 5.25)

= 5.25 + 11.2= 13.6875

Growth = ROE retention ratio= 0.16 0.60= 0.096

Trailing ???? = ????= ????= 10.725

For company BTrailing P/E ratio :???? where ????ke = 5.25 + 1.05 (11.5-5.25)

= 11.8125g = 0.11 0.50 = 0.055Trailing P/E ratio : ????= 8.3556b. The possible reasons for the difference in the PE ratios of the two companies are

(i) Difference in the payout ratios(ii) Difference in the ROE


CW Solutions


(iii) Difference in the Beta values(iv) Difference in growth rates

c. Calculation of long-term growth rate when the company B’s stock is trading at sixteen times itsnext expected earnings.12 = ?????12 = ????? 1.4175 – 12g = 0.5 12g = 0.9175 g = 7.65%

67. a. Required rate of return ?????Here, ?????

b. ?????????????

Retention ratio = 1-0.1527 = 0.84731. ????2. ????3. ????c.1. The calculated P/E is more than the current P/E, Therefore as per P/E stock is undervalued.2. The calculated P/B is less than the current P/B, Therefore as per P/B stock is slightly

overvalued.3. The calculated P/S is greater than the current P/S, Therefore as per P/S stock is undervalued.

68. Given,Current market price = Rs. 80Current EPS = Rs. 7Growth rate in earnings = 3%Retention ratio = 40%Holding period = 4 yearsRequired rate of return = 13%The price of the share, P0 is equal to the PV of the dividend stream for four years and the PV of themarket price at the end of the fourth year. The market price at the end of the fourth year

404 4

1EPS P /E E g P /E

Mathematically we express it as shown below.

44

00 40 4

1

11

1 1

t

tt

E g P /EE g Payout ratioP

k k


CW Solutions


Substituting te respective value we have

2

2

7 1 0 03 0 60 7 1 0 03 0 0680

1 0 13 1 0 13

. . . .. .

3 4

3 4

7 1 0 03 0 60 7 1 0 03 0 06

1 0 13 1 0 13

. . . .. .

4

44

7 1 0 03

1 0 13

. P /E

.

480 3 828 3 489 3 180 2 899 4 832. . . . . P /E

480 13 396 4 832. . P /E

4 66 604 4 832 13 78P /E . / . .

That is, the PE ratio at the end of the fourth year should be 13.78 so that the investor could earn areturn of 13%.

69. Valuation of Cig DivisionUsing sales = P/S × Sales

= 1.5 ×30 = 45Using Assets = 15 × 1.2 = 18Using Operating Income = P/E × operating Income = 2 × 20 = 40

Average Value of the Cigarette division =45 18 40 34.33

3

Valuation of FMCG divisionUsing sales = 16 × 2.2 = 35.2Using Assets = 14 × 1.8 = 25.2Using Operating Income = 3 × 14 = 42Average = 34.13Valuation of PaperUsing Sales = 40 × 2 = 80Using Assets = 60 × 1.2 = 72Using Operating Income = 12 × 12 = 144Average = 98.67As per the Sum of Parts Approach , value of ITC = 34.13 + 34.33 + 98.67 = 167.13 LacsGiven the current market value of ITC i.e. 80 Lacs it seems to be trading cheap & a long position isadvisable

71.(i) Number of shares to be issued : 5,00,000

Subscription price ` 20,00,000 / 5,00,000 = ` 4

VALUATION OF RIGHT SHARES

70. NO SOLUTIONS


CW Solutions


Ex-right Pr ice 1,30,00,000 20,00,000 1015,00,000

Value of right = 10 4 32

Or = ` 10 – ` 4 = ` 6

(ii) Subscription price ` 20,00,000 / 2,50,000 = ` 8

Ex-right Pr ice 1,30,00,000 20,00,000 1212,50,000

Value of right 12 8 14

Or = ` 12 – ` 8 = ` 4(iii) Calculation of effect of right issue on wealth of Shareholder’s wealth who is holding, say 100

shares.a. When firm offers one share for two shares held.

Value of Shares after right issue (150 X ` 10) ` 1,500Less: Amount paid to acquire right shares (50X`4) ` 200

`1,300b. When firm offers one share for every four shares held.

Value of Shares after right issue (125 X ` 12) ` 1,500Less: Amount paid to acquire right shares (25X`8) ` 200

`1,300c. Wealth of Shareholders before Right Issue `1,300

Thus, there will be no change in the wealth of shareholders from (i) and (ii).

73. Ex-right value of a share = (NPo + S) / (N+1)Where,N is number of existing shares required for a rights sharesPois the cum rights price per shareS is the subscription price52 ≤ (4 × 55 + S)/(4+1)S ≥ 52 × 5 4×55 ≥ 40

74. (i) Current market price of shares already in issue : Earnings Per Share = 75,00,000 /4,00,000 =`18.75P/E Ratio = Market Price Per Share/Earnings Per Share = 8 Market price per share = 8 × `18.75= `150

72. NO SOLUTIONS


CW Solutions


(ii) Price at which rights issue will be made " `150× 75% =`112.50(iii) Number of new shares that will be issued:

= 202,50,000/112.50 = 1,80,000(iv)Ex-rights price is`150 × 4,00,000/5,80,000+112.50×1,80,000/5,80,000 4,00,000 × 15%/12.5%=`103.44 + `41.9= `145.34

*The price/earnings ratio is given as 8. This would imply an earnings yield of (1/8 = 12.5%). This isassumed to be the yield or rate of return on existing funds.b) Assume that a shareholder holds 20 shares, the rights issue means addition of another 9 shares.

Theoretical, the selling price of the right to purchase one share will be (`145.34 - `112.50), that is`32.84. Let us discuss the two cases first if he opt for taking the right and second if he does nottaking the right but selling it.(i) Taking up the rights: `

Market value of 29 shares at £145.34 each 4,214.86Less : Cost of taking up rights of nine new share at `112.50 each 1,012.50

3,202.36(ii) Selling the rights: `

Market value of 20 shares at £145.34 each 2,906.80Add : Sales of 9 rights at `32.84 each 295.56

3,202.36

75. (i) Let the buyback price be xAmount used for buyback = 30% of 90 = 27 lacs∴No. of shares bought back =

27x∴ No. of shares outstanding after buyback = 10 -

27x

Post buyback share price = 1.1x∴Post buyback market cap =2710 1.1xx

or, 200 =2710 1.1xx

or, 11x - 29.7 = 200or, x = 20.88

(ii) No. of shares re-purchase =27 1.293lacssharesapprox

20.88

BUY BACK OF SHARES


CW Solutions


(iii)Net income = 10 × 3 = 30 lacs∴ No. of shares = 10 - 1.24 = 8.76∴ Post buyback EPS =30 3.42

8.76

76. (i) Let the buyback price be xAmount used for buyback = 30% of 90 = 27 lacs∴ No. of shares bought back =

27x∴ No. of shares outstanding after buyback = 10 -

27x

Post buyback shares price = 1.1x∴ Post buyback market cap =2710 1.1xx

or, 200 =2710 1.1xx

or, 11x - 29.7 = 200or, x = 20.88

(ii) No. of shares re-purchase =27 1.293lacssharesapprox

20.88

(iii) Net income = 10 × 3 = 30 lacs∴ No. of shares = 10 - 1.24 = 8.76∴ Post buyback EPS =30 3.42

8.76

VALUATION OF CLOSED HELD COMPANIES

77. NO SOLUTIONS

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