Ch. 3: Valuation of Bonds and Shares
CHAPTER 3 VALUATION OF BONDS AND SHARES Problem 1
(1) 1-year government bond maturity value (Rs) Market rate of interest PV of the bond: 1,000/1.08 (Rs) (2) Purchase price of bond (Rs) Implied return: (1,000 – 904.98)/904.98
1,000 8% 925.93 904.98 10.5%
Problem 2
Perpetual interest (Rs) Current yield Price of bond (B) (Rs) 140 B = . = 107692 0.13 Required rate New price of bond (B) (Rs) : 140 B = . = 107692 015 .
140 0.13 1076.92
0.15 933.33
Problem 3
Face value (Rs) Annual interest Maturity (years) Maturity value (Rs) Required rate PVAF, 10 year PVF, 10 year PV of interest (Rs) PV of maturity value (Rs): (d x g) PV of 10-year debenture (Rs) n =10
PV of of 10- year year bon bond d=
∑ (1.12) t =1
=
1000 140 10 1000 0.12 5.6502 0.3220 791.03 321.97 1113.00
140 t
t
+
0.14 5.2161 0.2697 730.26 269.74 1000.00
0.16 4.8332 0.2267 676.65 226.68 903.34
1000 , (112 . ) 10
140 × PVAF.12, 10
+
1000 , × PVF.12, 10
140 × 5.6502 + 1,00 000 × 0 .32 3220 = Rs 1,113.00 Similar calculations can be made if the required rate is 14% or 16%. What would happen to the present value of bond if it had a maturity of 5 years? A similar procedure can be followed. PV of a 5-year bond at 12%, 14% and 16% respectively will be as shown below: =
Required rate PVAF, 5 year PVF, 5 year PV of interest (Rs) PV of maturity value (Rs) PV of 5-year debenture (Rs)
0.12 3.6048 0.5674 504.67 567.43 1072.10
0.14 3.4331 0.5194 480.63 519.37 1000.00
Problem 4
Face value (Rs) Interest rate Interest (Rs): (1,000 x 0.16) Price of bond (Rs) Yield = INT B
1000 0.16 160 800 0.200
1300 0.123
1000 0.160
1
0.16 3.2743 0.4761 458.40 476.11 934.51
I. M. Pandey, Financial Management, 9 th Edition, New Delhi: Vikas.
Problem 5 Taxco (three-year maturity): Cash PVF PV flow 9% (Rs) 120 120 1120
0.917 0.842 0.772
110.09 101.00 864.85 1075.94
Maxco (three-year maturity): Cash PVF PV flow 9% (Rs) 60 60 1060
0.917 0.842 0.772
55.05 50.50 818.51 924.06
PVF 12% 0.893 0.797 0.712
PVF 12% 0.893 0.797 0.712
Taxco (eight-year maturity): Cash PVF PV flow 9% (Rs) 120 120 120 120 120 120 120 1120
0.917 0.842 0.772 0.708 0.650 0.596 0.547 0.502
110.09 101.00 92.66 85.01 77.99 71.55 65.64 562.09 1166.04
Maxco (eight-year maturity): Cash PVF PV flow 9% (Rs) 60 60 60 60 60 60 60 1060
0.917 0.842 0.772 0.708 0.650 0.596 0.547 0.502
55.05 50.50 46.33 42.51 39.00 35.78 32.82 531.98 833.96
PVF 12% 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404
PVF 12% 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404
PV (Rs)
PVF 6%
107.14 95.66 797.19 1000.00
0.943 0.890 0.840
PV (Rs)
PVF 6%
53.57 47.83 754.49 855.89
113.21 106.80 940.37 1160.38
PV (Rs)
0.943 0.890 0.840
PV (Rs)
56.60 53.40 890.00 1000.00
PVF 6%
107.14 95.66 85.41 76.26 68.09 60.80 54.28 452.35 1000.00
PV (Rs)
0.943 0.890 0.840 0.792 0.747 0.705 0.665 0.627
PV (Rs) 53.57 47.83 42.71 38.13 34.05 30.40 27.14 428.12 701.94
PV (Rs)
PVF 6% 0.943 0.890 0.840 0.792 0.747 0.705 0.665 0.627
113.21 106.80 10 0.75 95.05 89.67 84.60 79.81 702.70 1372.59
PV (Rs) 56.60 53.40 50.38 47.53 44.84 42.30 39.90 665.06 1000.00
Problem 6 (1) Annual compounding: Annual interest rate 12% Dis. rate - annual Cash Period flow 1 to 5 5
120 1,000
10%
12%
16%
PVF
PV
PVF
PV
PVF
PV
3.791* 0.621
454.89 6 20.92 1075.82
3.605 0.567
432.57 56 7.43 1000.00
3.274 0.476
392.92 476.11 869.03
* Annuity factor
2
Ch. 3: Valuation of Bonds and Shares
(2) Half-yearly compounding: Half-yearly interest rate 6% Dis. rate -half-yearly Period
5%
Cash flow
1 - 10 10
60 1,000
6%
8%
PVF
PV
PVF
PV
PVF
PV
7.722* 0.614
463.30 613.91 1077.22
7.360 0.558
441.61 558.39 1000.00
6.710 0.463
402.60 463.19 865.79
* Annuity factor (3) Quarterly compounding: Quarterly interest rate 3%
Dis. rate -half-yearly Period
2.5%
Cash flow
1 - 20 20
60 1,000
3%
4%
PVF
PV
PVF
PV
PVF
PV
15.589* 0.610
935.35 610.27 1545.62
14.877 0.554
892.65 553.68 1,446.33
13.590 0.456
815.42 456.39 1,271.81
* Annuity factor
Problem 7 Face value Maturity periods (half-yearly) Half-yearly interest rate Interest payment period Maturity value Required rate (half-yearly) Value of interest (Rs) Value of maturity value (Rs) Value of bond (Rs) 20
Value of bond
=
∑ (1.07) t =11
60 t
t
+
Rs 1,000 20 6% 11 - 20 Rs 1,050 7% 214.23 271.34 485.57
1,050 (1.07) n
=
60 × (PVAF20, 7%
=
60 × (10.5940 − 7.0236) + 1,050 × 0.2584 = Rs 485.57
−
PVAF10,7% ) + 1,050 × PVF20,7%
Problem 8 Bond 1 16% 15% 25 100 8.0% 7.5% 50 12.9748 8 103.80 0.0269 2.69 106.49 95 16.86% 8.43%
Interest rate Required rate of return Maturity period (years) Par/maturity value (Rs) Semi-annual interest rate Required rate of return (half-yearly) Compounding periods PVAF (annuity) Half-yearly interest (Rs) PV of interest (Rs) PVF (lump sum) PV of maturity value (Rs) Bond value (Rs) Current market price of bonds (Rs) Annual yields (by trial & error) Semi-annual yield (by trial & error)
Bond 2 14% 13% 15 100 7.0% 6.5% 30 13.0587 7 91.41 0.1512 15.12 106.53 100 14.00% 7.00%
Bond 3 12% 8% 20 100 6.0% 4.0% 40 19.7928 6 118.76 0.2083 20.83 139.59 110 10.76% 5.39%
Bond 4 12% 8% 10 100 6.0% 4.0% 20 13.5903 6 81.54 0.4564 45.64 127.18 115 9.60% 4.82%
Value of a bond that pays interest half-yearly can be calculated by the following equation: 2n
B0
=
∑ t =1
1 2
( INTt )
k (1 + 2d
3
)
t
+
Bn (1 +
k d 2
) 2n
I. M. Pandey, Financial Management, 9 th Edition, New Delhi: Vikas.
Problem 9
1 - year bond (i) Annual yield 95 =
10 + 100
=
1+ y
15%
(ii) Half - yearly yield 95 =
5 1+ y
5 + 100
+
(1 + y)
=
2
7.8%
2 − year bond (i) Annual yield 100 =
10
+
1+ y
10 + 100
=
(1 + y) 2
10%
(ii) Half - yearly yield 100 =
5
5
+
1+ y
(1 + y)
2
5
+
(1 + y)
3
5 + 100
+
(1 + y) 4
=
5%
3 − year bond (i) Annual yield 110 =
10
10
+
1+ y
(1 + y)
2
+
10 + 100 (1 + y)3
=
6.24%
(ii) Half - yearly yield 110 =
5
5
+
1+ y
(1 + y)
2
5
+
(1 + y)
3
5
+
(1 + y)
4
+
5 (1 + y)
5
+
5 + 100 (1 + y)6
=
3.15%
4 − year bond (i) Annual yield 115 =
10 1+ y
10
+
(1 + y)
2
10
+
(1 + y)
3
+
10 + 100 (1 + y)
4
=
5.70%
(ii) Half - yearly yield 115 =
5 1+ y
5
+
(1 + y)
2
5
+
(1 + y)
3
5
+
(1 + y)
4
+
5 (1 + y)
5
+
5 (1 + y)
6
+
5 (1 + y)
7
Problem 10
20 − year bond redeemable in 12 years : Half - yearly interest 5%; periods 24 24
1,000 =
∑ (1 t =1
50 t +
YTC)
t
+
1,150 (1 + YTC) n
YTC = 5.32% 24
1,000 =
∑ (1 t =1
50 t +
YTC)
t
+
1,100 (1 + YTC)
n
YTC = 5.22% 20 − year bond redeemable in 8 years : Half - yearly interest 5%; periods 16 16
1,000 =
∑ (1 t =1
50 t +
YTC)
t
+
1,150 (1 + YTC)
n
YTC = 5.60%
4
+
5 + 100 (1 + y)
8
=
2.87%
Ch. 3: Valuation of Bonds and Shares
Problem 11
Annual interest rate Quarterly interest rate Market price (Rs) Maturity value (Rs) Quarterly periods New interest rate New quarterly interest rate
15% 3.75% 875 1000 60 12.0% 3.0%
Stated yield
Quarterly interest (Rs)
37.50
Market price (Rs) Quarterly yield
875.00 4.34%
Expected yield
Quarterly interest (Rs)
30.00
Market price (Rs) Quarterly yield
875.00 3.50%
Quarterly yields can be found by trial and error. You can also use the Excel formula for rate to calculate yield: = RATE(nper,pmt,pv,[fv],[type],guess)
Problem 12
Value of perpetual preference share =12/0.10 = Rs 120 7
Value of redeemable preference share =
∑ (1.10) 12 t
t =1
=
t
+
110 (1.10) 7
12 × PVAF7 ,10%
+
110 × PVF7,10%
= 12 × 4.868 + 110 × 0.513 = Rs114.87 You can use the Excel formula to calculate value of redeemable preference share: =PV(rate,nper,pmt,[fv],[type])
Problem 13
Expected DPS (Rs) Current share price (Rs) Share price after 1 year (Rs) Required rate PV of share (Rs): DIV1 + P1 3 + 53 = P= 11 . (1 + k e ) 1
3.00 50.00 53.00 0.10
50.91
Return on share: re
=
DIV1
+
( P1 − P0 )
P0
=
3 + 53 − 50 50
=
0.120
5
I. M. Pandey, Financial Management, 9 th Edition, New Delhi: Vikas.
Problem 14
Share price (Rs) Capitalisation rate
Year 0 1 2 3 4 4 Value of the share
75.00 0.12 DPS (Rs)
Share price (Rs)
PVF at 12%
PV (Rs)
70.00
0.8929 0.7972 0.7118 0.6355 0.6355
6.70 5.98 6.41 9.53 44.49 73.10
7.50 7.50 9.00 15.00
It is a desirable investment since the present value of the share is more than its current price.
Problem 15
Current share price DPS Growth rate Required rate Value of the share: DIV 1 P0 = ke − g =
1.5(1.1)
=
165 .
60.00 1.50 0.10 0.12
82.50
012 . − 010 . 0.02 Share should be bought Problem 16
Earnings growth up to 7 years Perpetual growth after 7 years Required rate for 7 years Required rate after 7 years EPS DPS
0.15 0.09 0.12 0.10 4.00 2.00 DPS (Rs) 2.00 2.30 2.65 3.04 3.50 4.02 4.63 5.32
Year 0 1 2 3 4 5 6 7
Present value of dividend growing perpetually after 7 years
P7
PV of Rs 579.88
579.88
=
DIV7 (1 + g n )
(1.10) 10 Value of share
ke
=
−
gn
PVF @ 12%
PV (Rs)
0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4523
=
532 . (109 . ) 010 . − 0.09
579.88 × 0.5132
15.58 + 297.57 = Rs 313.16
6
=
2.05 2.11 2.17 2.22 2.28 2.34 2.41 15.58
=
Rs 579.
Rs 297.57
Ch. 3: Valuation of Bonds and Shares
Problem 17
Current EPS Retention ratio, b Current DPS, DIV0 = EPS0(1 - b) Rate of return, r Required rate, k e Current share price (Rs) Growth, g = b x r Expected EPS (Rs): EPS 1 = EPS0(1+g) = 5 x 1.09 Expected DPS (Rs): DIV 1 = DIV0(1+g) = 2 x 1.09 Expected retained earnings, RE 1 = EPS1 - DIV1 Value of share if g = 0 EPS1 5 = P0 = k e − g 0.13 − 0 Value of share if g = 9% DIV1 2(1+.09 ) 2.18 = = P0 = k e − g 013 . −.09 0.04
=
RE 1 ( r − k e ) k e (k e
−
g)
=
3.27(.15−.13) .13(.13−.09 )
41.92
54.50
Value of growth opportunities, V g (Rs): 54.50 - 41.92 The following formula can be used to find V g: Vg
(Rs) 5.00 0.60 2.00 0.15 0.13 60.00 0.09 5.45 2.18 3.27
=
.0654 .0052
12.58
12.58
Problem 18
Total assets Equity Number of shares Equity per share: 80,000/10,000 Internal rate of return, r Earnings: 10% × 80,000 EPS Capitalisation rate, k Retention ratio, b Dividend per share, DIV: 30% × 0.8 Growth rate, g: b × r Expected DIV: 0.24 × 1.07 PV of share: 0.2568/(0.12 – 0.07)
Rs 80,000 Rs 80,000 10,000 Rs 8 10% Rs 8,000 Rs 0.8 12% 70% Rs 0.24 7% Rs 0.2568 Rs 5.14
Problem 19
Last year's DPS (Rs) Current market price (Rs) Required rate
Growth rate Value of share (Rs)
3 80 0.1 Scenario 1: Scenario 2: Scenario 3: No growth Perpetual growth Different growth rates 0 0.06 3/.10=30 3(1.06)/.1 - .06 = 79.5 68.84 (see below)
7
I. M. Pandey, Financial Management, 9 th Edition, New Delhi: Vikas.
Scenario 3: Different growth rates Growth rate 0.12 0.07 0.04
1-3 years 4-6 years 7 year and onwards
PV of DPS at 10% from year 1 to 6 PV of DPS growing perpetually at the end of 6 years: 5.16(1.04)/(.1 - .04) PV of value of Rs 89.50 received at the end of 6th year: 89.5 x 0.5645 Value of share (Rs): 18.32 + 50.42
Year 0 1 2 3 4 5 6
DPS (Rs) 3.00 3.36 3.76 4.21 4.51 4.83 5.16
PVF
PV (Rs)
0.9091 0.8264 0.7513 0.6830 0.6209 0.5645
3.05 3.11 3.17 3.08 3.00 2.91 18.32
7
5.37
16.667
89.50
0.5645
50.52 68.84
Problem 20
Current DPS (Rs) Current growth rate New growth Capitalisation rate Share price (Rs) if g = 5%, [5(1.05)/(0.15-.05)] Share price (Rs) if g = 10%, [5(1.1)/(0.15-0.1)]
5 0.05 0.10 0.15 52.50 110
When the firm’s growth increases from 5% to 10%, the share prices rises from Rs 52.50 to Rs 110. It is quite logical since price depends on expected dividend and future growth opportunities. Problem 21
Face value (Rs)
Bajaj Hero Honda Kinetic Maharashtra. Scooters
10 EPS Dividend (Rs) rate 11.9 0.50 10.2 0.22 12.0 0.25 20.1
0.25
Market price (Rs) 275.0 135.0 177.5 205.0
DPS Earnings Dividend (Rs) Payout yield yield 5.0 0.420 0.0433 0.0182 2.2 0.216 0.0756 0.0163 2.5 0.208 0.0676 0.0141 2.5
0.124
0.0980 0.0122
Bajaj has the highest current share price but it also pays maximum dividend (as a percentage of its earnings). On the other hand, Maharashtra Scooters has maximum EPS, lowest payout, lowest dividend yield and it is ranked third in terms of share price. Hero Honda has lowest EPS and lowest share price. Kinetic ranks at third place in terms of EPS, DPS and share price. It appears that the market is giving consideration to the companies’ current performance as well as future growth prospects. Problem 22
DPS in year 0 (Rs) DPS in year 10, (Rs) Period (years) Dividend growth rate: [(10.5/3.5) 1/10 -1] Share price (Rs) Expected dividend yield [3.5(1.1161)/75] Capitalisation rate: 0.1161 + 0.0521
3.5 10.5 10 0.1161 75 0.0521 0.1682
8
Ch. 3: Valuation of Bonds and Shares
Problem 23
Current EPS (Rs) Growth Payout Retention ratio: 1 - .4 Capitalisation rate DPS (Rs) Expected EPS: 8.6 x 1.12) Expected dividend: 3.44 x1.12 Expected retained earnings: 9.63 x 0.60 Share value (12% growth) (Rs) Share value (no growth) (Rs) Firm's rate of return: g=r×b
8.60 0.12 0.40 0.60 0.18 3.44 9.63 3.85 5.78 64.21 53.51
0.20
r = g / b =.12/.6 Value of growth opportunities: RE 1 ( r − k e ) 5. 78(.20−.18) Vg = = .18(.18−.12) k e ( k e − g)
=
.1156 .0108
10.70
Problem 24
Face value (Rs) Interest or dividend rate Payment frequency Maturity (years) Compounding periods Maturity value (Rs) Principal amount (Rs crore) Required rate of return PVAF (annuity) PVF (lump sum) Interest/dividend amount (Rs) Perpetual growth rate Market value of each debenture or share (Rs) Total market value (Rs crore)
12% debenture 1000 12% annual 12 12 1000 50 0.10 6.8137 0.3186 120
14% debenture 1000 14% half-yearly 10 20 1000 30 0.06 11.4699 0.3118 70
Pref. Equity share share 100 100 15% annual annual
100 0.135
200 0.15
15
12 0.08
120 x 6.8137 70 x 11.4699 + 1000 x .3186 + 1000 x .3118 15/.135 12/(.15 - .08) = 1136.27 = 1114.69 = 111.11 = 171.43 56.81 33.44 111.11 342.86
Problem 25
Net profit (Rs crore) Number of shares (crore) EPS: 50/2, Rs ROE Capitalisation rate, k Payout Retention ratio, b (1 – payout) Dividend per share, DIV: 60% × 25 Growth rate, g: b × r: 40% × 25% Expected DIV: 25 × 1.10 Current share price, P 0 Expected dividend yield: DIV 1 / P0 Capitalisation rate, k = (DIV 1 / P0) + g
50 2 25 25% 12% 60% 40% 15 10% 16.5 240 6.88% 16.88%
9
I. M. Pandey, Financial Management, 9 th Edition, New Delhi: Vikas.
Problem 26
Net earnings (Rs million)
25
Paid-up capital (Rs million)
200
Par value of share (Rs)
10
Number of shares: paid-up capital/par value of share (mn.)
20
EPS = dividend per share, DIV (assumed): 25/20
1.25
Growth (without investment)
2%
Opportunity cost of capital
10%
Share price: P 0 = (1.25 × 1.02)/ (0.10 – 0.02)
15.94
Investment (Rs million)
10
Earnings from investment (Rs million)
2
Life of investment, years
15
Investment’s NPV: PV of Rs 2 million for 15 years at 10%: 2*7.6061-10 Share price (with investment): 15.94 + 5.21 (million) Problem 27
Earnings (without project), Rs crore Number of shares, crore EPS: 80/5 Required rate of return Share price (without project): 16/0.125 Earnings from project after one year EPS from project: 20/5 Growth in earnings from project after one year Required rate of return Value of growth opportunities: 4/(0.125 – 0.08) Share value with project: 128 + 88.89 EPS after project P/E ratio: 216.89/20
80 5 16 12.50% 128 20 4 8% 12.50% 88.89 216.89 20 10.84
Problem 28
Number of shares, million Net cash profits, Rs million Cash EPS: 80/10 Opportunity cost of capital (a) (i) Retention ratio Return on retained earnings Growth: 40% × 20% Expected Dividend per share, DIV 1: 8 × (1 – 0.40) × 1.08 Share price: 5.18/(0.20 – 0.08) (a) (ii) Retention ratio Return on retained earnings Growth: 60% × 20% Expected Dividend per share, DIV 1: 8 × (1 – 0.60) × 1.12 Share price: 3.58/(0.20 – 0.12) (b) (i) Retention ratio Return on retained earnings Growth: 40% × 24% Expected Dividend per share, DIV 1: 8 × (1 – 0.40) × 1.096 Share price: 5.26/(0.20 – 0.096) (b) (ii) Retention ratio Return on retained earnings
10 80 8 20% 40% 20% 8% 5.18 43.20 60% 20% 12% 3.58 44.80 40% 24% 9.60% 5.26 50.58 60% 24%
Growth: 60% × 24% Expected Dividend per share, DIV 1: 8 × (1 – 0.60) × 1.144 Share price: 3.66/(0.20 – 0.144)
14.40% 3.66 65.37
10
5.21 21.15
Ch. 3: Valuation of Bonds and Shares
Problem 29
Cash EPS (perpetuity), Rs Payout DIV, Rs Opportunity cost of capital (a) Share price: 10/0.15 (b) Expansion opportunity Earnings retention Rate of return Growth: 50% × 18% DIV1: 5 × 1.09 Period of growth Value of growth opportunity:
10 100% 10 15% 66.67 50% 18% 9% 5.45 10
1 1 + g n × 1 − k − g 1 + k 1.09 10 1 = 5.45 × × 1 − 0.15 − 0.09 1.15
V = DIV1 ×
5.45 × 16.67 × 0.4148 = Rs 37.68 Value after growth opportunity: (10 ×1.09 10 /0.15) PV after growth opportunity: 157.80 × 1/1.15 10 39.01 Total share price with growth opportunity: 37.68 + 39.01 76.69 =
11
157.80
I. M. Pandey, Financial Management, 9 th Edition, New Delhi: Vikas.
CASES
Case 3.1: Shyamulu Rao's Investment Decision This case brings out most of the concepts in valuation of shares and bonds. The instructor can ask the students to make the appropriate calculations, and spend the class time in clarifying the concepts and doubts that the students might have. Return from investment in share Investment amount (Rs) Required rate of return Holding period (years) Investment per share Expected EPS1 (Rs) ROE (i) No dividend situation Expected EPS1 (Rs) Retention Growth No growth share price Value of growth opportunities Share price, P0
50,000 15% 10 20 3 15% 0 3 100% 15.0% 20.00 0.00 20.00
Required price for earning 15% return: Investment per share Dividend per share Required rate of return Holding period (years) PVF10, 15%
20 0 15% 10 0.2472
Required price at year 10
80.91
Required price for earning 15% return: (ii) Constant dividend (Rs) Retention Growth Share price, P0
3
Investment per share
20
0% 0%
Dividend per share Required rate of return
3 15%
20.00
Holding period (years)
10
PVAF10, 15% PV of DPS (Rs) PVF10, 15% Required price at year 10
5.019 15.06 0.2472 20.00
Required price for earning 15% return: (iii) Dividend per share Retention Growth Share price, P0
(iv) Dividend per share Supernormal growth
1 67% 10% 20.00
1.6 15%
Investment per share
20
Dividend per share Growth
1 10%
Required rate of return
15%
Holding period (years)
10
PVAF10, 15%, (growth rate 10%) PV of DPS (Rs)
7.1773 7.18
PVF10, 15% Required price at year 10
0.2472 51.87
Required price for earning 15% return: PVF
PV
DPS1
1
1.60
0.870
1.39
DPS2
2
1.84
0.756
1.39
DPS3
3
2.12
0.658
1.39
12
Ch. 3: Valuation of Bonds and Shares
DPS4
4
2.43
0.572
1.39
DPS5
5
2.80
0.497
1.39
Value in year 0 Normal growth Value at year 5 Value at year 0
6.96 10% 61.57 30.61
Share price
37.57
Investment per share
20
Year
Dividend per share Required rate of return Supernormal growth Supernormal growth period (yrs) PV supernormal growth period Normal growth
1.00 15% 15% 5 6.96 10%
6 7 8 9 10
Normal growth period (yrs) PV normal growth period
5 6.10
PVF10, 15% Required price at year 10
DIV 3.08 3.39 3.73 4.10 4.51
PVF 0.4323 0.3759 0.3269 0.2843 0.2472
PV (DIV) 1.33 1.27 1.22 1.17 1.11 6.10
0.2472 28.08
Government bond Redemption value of bond Current value of bond Implied IRR
10,000 2720 13.9%
Reliable Fertiliser bond Implied return 0 1 2 3 4 5 6 7 8 9 10 IRR
-1000 150 150 150 150 150 150 150 150 150 1250 15.5%
Shyamulu will be able to earn 15.5% - more than his required rate of return from bonds of Reliable Fertiliser Company. His risk in investing in bonds would be lower than investing in shares of Ashoka Infotech.
13
I. M. Pandey, Financial Management, 9 th Edition, New Delhi: Vikas.
Case 3.2: Hitech Chem Limited This case highlights the alternative methods of valuing a company and its shares. Issue price (Rs) P/E ratio P/E ratio - industry P/E ratio - Chemical Annual capex (Rs million) S L depreciation rate Average sales (Rs million) Current sales (Rs million) PBIT/sales ratio Revaluation of tangible fixed assets (Rs million) Tax rate
13 18.5 21.75 15 300 10% 15,000 21,500 22% 6,500 35% Expected (Rs mn.)
Hitech's EPS Current sales
Conservative (Rs mn.)*
21,500
16,125
PBIT Interest - 15% bank loan Interest - 12% long-term loan loan
4,730 210 360
3,548 210 360
PBT Tax
4,160 1,456
2,978 1,042
PAT
2,704
1,935
750 3.61
750 2.58
Number of share EPS (Rs) * Lost sales due to patents expiry Hitech's Valuation (i) Book value of equity (equals net worth) (Rs mn.) Number of share Book value per share (Rs)
13,500 750 18.00
(ii) P/E based value PAT (Rs mn.) Hitech's P/E ratio Equity value (Rs mn.) EPS (Rs) Equity value per share (Rs) Chemical industry's P/E ratio Equity value (Rs mn.) Equity value per share (Rs)
2,704 18.50 50,024 3.61 66.70 15.00 40,560 54.08
(iii) Revaluation of assets Tangible fixed assets Patents Net current assets
(Rs mn.) 6,500 0 4500
Total assets Less: Long-tem loan
11,000 3,000
Equity value
8,000
Equity value per share (Rs)
10.67
14
1,935 18.50 35,804 2.58 47.74 15.00 29,031 38.71
