WEBVTT
00:24.580 --> 00:35.210
Welcome to the lectures on Time value of money-Concepts
and Calculations. The topic of the today's
00:35.210 --> 00:39.270
lecture is valuations of shares.
00:39.270 --> 00:45.400
There are many types of shares out of which
preferred shares, ordinary shares, etcetera.
00:45.400 --> 00:54.420
Now, let us see what a preferred share is.
A preferred stock is a class of ownership
00:54.420 --> 01:03.750
in a corporation that has a higher claim on
its assets and earnings than common stock
01:03.750 --> 01:13.409
or common shares. Preferred share generally
have a dividend that must be paid out before
01:13.409 --> 01:21.180
dividends to common share holders and the
share usually do not carry voting rights and
01:21.180 --> 01:25.530
for ordinary shares.
Ordinary shares are the most common types
01:25.530 --> 01:33.790
of shares traded on the equity market. Ordinary
shares, give you full voting rights at annual
01:33.790 --> 01:40.320
general meeting dividends should the company
pay these and a share of the residual economic
01:40.320 --> 01:46.970
value should the company unwind after the
bond holders and preference share holders
01:46.970 --> 01:54.720
are paid. They also allow you to benefit from
capital growth should the company do well.
01:54.720 --> 02:04.390
Valuations of preference shares, preference
shares like debentures are usually subject
02:04.390 --> 02:15.450
to fixed rate of return or dividend. In case
of no stated maturity their valuation is similar
02:15.450 --> 02:22.540
to perpetual bonds. The present value of this
shares PVs is equal to summation t is equal
02:22.540 --> 02:32.700
to one to infinite, D p divided by 1 plus
1 to the power t or is equal to D p by i.
02:32.700 --> 02:41.650
Where, D p is equal to per share dividend,
expected at the end of the year. Which is
02:41.650 --> 02:51.160
fixed i is equal to discounted rate annually.
The value of the redeemable preferential share
02:51.160 --> 02:59.150
is given below, present value of the share
PVs is equal to summation t equals to 1 to
02:59.150 --> 03:08.040
N, D p divided by 1 plus i to the power t
plus MV divided by 1 plus i to the power N.
03:08.040 --> 03:13.791
Where, D p is equal to per share dividend
expected at the end of the year. This is fix
03:13.791 --> 03:24.489
value i equal to discounted rate annual, MV
is equal to maturity value, that is par value
03:24.489 --> 03:31.340
or face value and PVIFA is equal to present
value interest factor for annuity, which is
03:31.340 --> 03:38.710
equal to N brackets 1 plus i to the power
N minus 1, whole divided by i into 1 plus
03:38.710 --> 03:45.130
i to the power N. This is the present value
of annuity and N is the maturity period in
03:45.130 --> 03:53.630
years and PBIF is the present value interest
factor and is equal to 1 by in brackets 1
03:53.630 --> 03:55.950
plus i to the power N.
03:55.950 --> 04:03.569
Computation of value of shares with respect
to following, dividend valuation or dividend
04:03.569 --> 04:10.480
discount models. The first model will consider
a zero growth model; the second model will
04:10.480 --> 04:18.000
consider constant growth model or Gordon model
and third is the variable growth model, now
04:18.000 --> 04:25.720
to start with the zero growth models. In this
approach to dividend valuation assumes a constant
04:25.720 --> 04:37.490
non growing dividend stream, with zero growth
in the amount of dividend. Thus the value
04:37.490 --> 04:49.819
of the share is the present value of a perpetuity
of dividends discounted at discount rate i.
04:49.819 --> 04:59.030
So, the present value of the shares is PVs
is equal to in summation t equal to 1 to infinite
04:59.030 --> 05:10.789
D divided by 1 plus i to the power t and which
is equal to D by i, where D is equal to constant
05:10.789 --> 05:19.030
dividend per share and i is equal to discount
rate or required return of investor. Let us
05:19.030 --> 05:24.809
take an example
Example one Messer’s SJ Internationals per
05:24.809 --> 05:32.919
share dividend remains constant indefinitely
at rupees 8. Assuming required rate of return
05:32.919 --> 05:43.330
that is, discount rate of 20 percent compute
the value of the share of Messer’s SJ International
05:43.330 --> 05:54.740
the solution is PVs equals to D by i is equal
to rupees 8 divided by 0.2, which is the value
05:54.740 --> 06:05.680
of i because i is 20 percent. So, rupees 8
divided by 0.2 comes out to be rupees forty.
06:05.680 --> 06:19.369
The Gordon growth model is used to determine
the intrinsic value of a stock based on a
06:19.369 --> 06:30.409
future series of dividends that grow at a
constant rate given a dividend per share.
06:30.409 --> 06:38.740
That is payable in 1 year and the assumption
that the dividend grows at a constant rate
06:38.740 --> 06:48.710
in perpetuity. The model solves for the present
value of the infinite series of future dividends.
06:48.710 --> 06:56.420
Derivation of the model, the model uses the
fact that the current value of the dividend
06:56.420 --> 07:07.669
payment can be expressed as D 0 in bracket
1 plus g to the power t at discrete time t
07:07.669 --> 07:17.821
is D 0 1 plus g to the power t divided by
1 plus i to the power t. Now when I divide
07:17.821 --> 07:25.179
the dividend with 1 plus i to the power t,
basically I am converting it into its present
07:25.179 --> 07:31.629
value and so the current value of the future
dividend payments, which is the current price
07:31.629 --> 07:38.270
of PVs is the sum of the infinite series.
So, what I am doing that PVs is equal to summation
07:38.270 --> 07:46.509
t is equal to 1 to infinite D 0 1 plus g to
the power t divided by 1 plus i to the power
07:46.509 --> 07:54.759
t. So, the present values of all the dividends
are summed to find out the value, present
07:54.759 --> 08:04.309
value. This summation can be written as PVs
D zero into r dash in brackets 1 plus r dash
08:04.309 --> 08:11.129
plus r dash square plus r dash q and so on
so forth. Where, r dash is equal to 1 plus
08:11.129 --> 08:20.759
g divided by 1 plus i. Clearly the series
in parentheses is the geometric series with
08:20.759 --> 08:32.710
common ratio r dash. So, it sums to 1 by 1
minus r dash, if r dash is less than 1.
08:32.710 --> 08:42.969
Thus PVs is equal to D 0 r dash divided by
1 minus r dash. Substituting the value of
08:42.969 --> 08:53.670
r dash and solving gives PVs is equal to D
0 1 plus g in bracket divided by i minus g
08:53.670 --> 09:05.060
equal to D 1 divided by i minus g. The stable
model is value of the stock D 1 divided by
09:05.060 --> 09:17.800
1 i minus g, where D 1 is the next years expected
annual dividend per share, i is equal to the
09:17.800 --> 09:28.410
investors discount rate, g the expected dividend
growth rate. Note that this is assumed to
09:28.410 --> 09:29.730
be constant.
09:29.730 --> 09:39.440
Now, let us take an example, exercise 2. Messer’s
SJ Internationals has paid following dividends
09:39.440 --> 09:47.430
per share, per year assuming a 20 percent
required return that is, a discount rate and
09:47.430 --> 09:59.450
rupees 5.85 per share dividend in year 7.
Compute the value of the share might as given
09:59.450 --> 10:07.620
that the for year 1, the dividend per share
is 3.3, for the second year the dividend per
10:07.620 --> 10:16.810
year share is 3.63, for third year this is
3.99, for the fourth year this is 3.93, the
10:16.810 --> 10:28.000
fifth year this is 4.83 and sixth year this
is 5.32. Now PVs is equal to D 0 1 plus g
10:28.000 --> 10:38.770
in brackets 1 minus g is equal to D 1, 1 minus
g. D 1 is equal to 1 plus g and D 6 is equal
10:38.770 --> 10:49.300
to D 0 1 plus g to the power 6 or D 1 by D
6 is equal to 1 divided by 1 plus g to the
10:49.300 --> 10:58.460
power 5 or g is equal to D 6 divided by D
1 to the power 1 by 5 minus 1.
10:58.460 --> 11:14.400
So, D 6 is 5.32, this 5.32 and D 1 is 3.3
and 1 by 5 is 0.2 and then minus 1 comes out
11:14.400 --> 11:24.480
to be 0.1 or g is equal to 10 percent and
that is why PVs is equal to 5.85 because D
11:24.480 --> 11:37.010
1 value is 5.85 divided by 0.2 minus 0.1 is
equal to rupees 58.5 per share. This 5.85
11:37.010 --> 11:42.100
has been brought from here and the 7’th
year ok.
11:42.100 --> 11:50.310
Exercise 3; consider a share with an expected
dividend per share, next period of rupees
11:50.310 --> 12:03.160
3.25. A cost of equity is 20 percent and then
expected growth rate is 8 percent forever.
12:03.160 --> 12:10.180
Find the value of the stock or share value
of the share is equal to 3.25 divided by in
12:10.180 --> 12:21.520
the bracket 0.2, which is 20 percent here
and minus 0.08, this is growth rate is 8 percent.
12:21.520 --> 12:28.570
So, divided by 100 is 0.08 and 20 percent
divided by 100 is 0.2. So, 0.2 minus 0.08
12:28.570 --> 12:41.730
is equal to rupees 27.08 per share. Now, let
us see, what are the limitations of the Gordon
12:41.730 --> 12:42.750
growth model?
12:42.750 --> 12:53.090
The main limitation of the Gordon growth model
lies in its assumption of a constant growth,
12:53.090 --> 13:04.190
in dividends per share. It is very rare for
companies to show constant growth in the dividends
13:04.190 --> 13:14.790
due to business cycles and unexpected financial
difficulties or successes. Therefore, the
13:14.790 --> 13:24.570
model is limited to firms showing stable growth
rates. The second issue has to do with the
13:24.570 --> 13:32.920
relationship between the discount factor and
the growth rate used in the model. If the
13:32.920 --> 13:43.070
required rate of return i is less than the
growth rate g of dividends per share. The
13:43.070 --> 13:51.810
result is a negative value rendering, the
model worthless also if the required rate
13:51.810 --> 14:00.420
of the return is the same as the growth rate
the value per share approaches infinite.
14:00.420 --> 14:08.610
Now, let us take a third model which is variable
growth model. The variable growth model is
14:08.610 --> 14:19.230
a dividend valuation approach that allows
for a change in the dividend growth rate.
14:19.230 --> 14:26.760
As a dividend valuation approach, this model
incorporates a change in the dividend growth
14:26.760 --> 14:36.570
rate assuming g 1 is equal to initial growth
rate, g 2 equal to subsequent growth rate
14:36.570 --> 14:44.820
occurs at the end of the year N, the value
of the share can be determined as follows.
14:44.820 --> 14:54.760
Step 1, compute the value of the cash dividends
at the end of each year, that is D t cash
14:54.760 --> 15:02.300
dividend at the end of each year is D t, t
is time during the initial growth period and
15:02.300 --> 15:14.240
initial growth period is year 1 to N. So,
D t is equal to D 0 1 plus g 1 to the power
15:14.240 --> 15:20.820
t and this is for initial growth period year
1 to N.
15:20.820 --> 15:30.090
Step 2, compute the present value of the dividends
during the initial growth period as summation
15:30.090 --> 15:43.600
1 to N D 0 1 plus g 1 to the power t divided
by 1 plus i to the power t when we are dividing
15:43.600 --> 15:50.960
it by 1 plus i to the power t, we are basically
converting into the present value. So, this
15:50.960 --> 16:01.520
is equal to N summation t is equal to N D
t divided by 1 plus i to the power t.
16:01.520 --> 16:11.510
Now, step 3, find the value of the share at
the end of initial growth year P N is equal
16:11.510 --> 16:23.520
to D N plus 1; that means, D at n'th N plus
1st period divided by i minus g 2 this is
16:23.520 --> 16:38.420
the present value of all dividends expected
from year N plus 1 onwards assuming a constant
16:38.420 --> 16:47.380
dividend growth rate g 2 because in the second
part which is N plus 1 onwards, the growth
16:47.380 --> 16:59.570
rate is g 2. The present value p n would represent
the value today of all dividends expected
16:59.570 --> 17:11.550
to be received from year N plus 1 to infinite
and this is equal to D N plus 1 divided by
17:11.550 --> 17:18.459
i minus g 2 into 1 by 1 plus i to the power
N.
17:18.459 --> 17:26.740
So, this converts all dividends, the summation
of the dividends to its present value because
17:26.740 --> 17:36.750
I am multiplying with 1 divided by 1 plus
i to the power N. Step 4, add the present
17:36.750 --> 17:46.960
value components found in step 2 and step
3, to find the value of the shares. The share
17:46.960 --> 17:54.169
value is equal to this is what I have got
in step 2. So, this is here and, what I got
17:54.169 --> 17:57.090
in step 3, this is here.
17:57.090 --> 18:05.850
Now, let us take an example. This is example
4. In the most recent year the annual, that
18:05.850 --> 18:17.789
is in 2012dividend paid by, Messer’s SJ
International is rupees 4 per share. An annual
18:17.789 --> 18:27.940
increase of 12 percent that is, g 1 is expected
over the next 3 years. At the end of the 3
18:27.940 --> 18:37.869
years that is, end of 2015, the dividend growth
rate will slow down to 6 percent. That is
18:37.869 --> 18:50.390
g 2, assuming 14 percent is the rate of return
one, compute the current value at the end
18:50.390 --> 18:59.403
of 2015 of the share of Messer’s SJ International.
Now, let us see this solution. We will solve
18:59.403 --> 19:09.059
this problem step wise. Step 1, determination
of present value of cash dividends received
19:09.059 --> 19:17.919
in first 3 years. Now, if you see this figure
at the end of the first year, the D 0 value
19:17.919 --> 19:27.400
is 4, this is 1 plus g 1 to the power t. That
is one plus g 1to the power 1 is 1.12 and
19:27.400 --> 19:33.950
hence when we multiply this 2, this comes
out to be 4.48 and this is the value of D
19:33.950 --> 19:41.409
t is equal to D 0 1 plus g 1 to the power
t, yet to the power t.
19:41.409 --> 19:48.769
Now, if you find out the present worth factor,
this is 1 divided by 1 plus i to the power
19:48.769 --> 19:59.960
t and the present worth factor is 0.877193
and hence present value of this dividend is
19:59.960 --> 20:10.980
equal to this dividend into this present worth
factor gives you 3.929825. Now, here pictorially
20:10.980 --> 20:18.809
this is shown. At the end of first year this
is 4.48 rupees and when this will be brought
20:18.809 --> 20:27.169
to the present value as D is equal to 0, this
becomes 3.9298. Similarly, in the year ending
20:27.169 --> 20:40.090
2 D 0 value is 4 1 plus g 1 to the power t,
here t becomes 2 becomes 1.2544. When these
20:40.090 --> 20:50.739
two are multiplied, this becomes 5.0176. So,
D 2 is equal to D 0 1 plus g 1 to the power
20:50.739 --> 20:57.799
t and here the value of t will be 2.
So, this is the value. So, now, the present
20:57.799 --> 21:10.480
worth factor for this that is 1 by 1 plus
i to the power 2 whole to the power 2 is 0.769468,
21:10.480 --> 21:20.659
when I multiplied this, with this it becomes
3.86088. Now if I see this pictorially at
21:20.659 --> 21:29.900
the end of the second year this value is 5.017
this is the same value and when this will,
21:29.900 --> 21:35.169
the present worth will be calculated it will
be brought to this 09. When you brought it
21:35.169 --> 21:42.919
to the 09, this becomes 3.8609 which is the
present worth of this value.
21:42.919 --> 21:50.460
Now, if you see the year ending 3, this is
the D 0 is 4 and the growth factor that is
21:50.460 --> 21:59.129
1 plus g 1 to the power t is 1.728, then this
D t is equal to D 0 1 plus g 1 to the power
21:59.129 --> 22:07.899
t is the multiplication of this and this comes
out to be 6.912. Now, if you see the present
22:07.899 --> 22:16.279
worth factor, this is 1 divided by 1 plus
i to the power 3 comes out to be 0.674972
22:16.279 --> 22:25.960
and we multiply this with this, the present
value of this becomes 4.665403 and we add
22:25.960 --> 22:34.390
this 3 present values, it is 12.456108.
So, the sum of the present value of the dividend
22:34.390 --> 22:40.970
for last 3 years, this three years is equal
to this. This is given by the formula this
22:40.970 --> 22:47.779
i t is equal to 1 to N D 0, this is N is 3
here 1 plus g 1 to the power t divided by
22:47.779 --> 22:59.409
1 by 1 plus i to the power t. It is t equals
to N D t 1 plus i to the power t here come
22:59.409 --> 23:07.710
out to be 12.456108. Now step 3, the value
of the share at the end of initial growth
23:07.710 --> 23:11.509
period that is end of 15.
23:11.509 --> 23:20.340
Is D 3 is equal to 6.921. This we have taken
from the step 1 and D N plus 1 that is 4’th
23:20.340 --> 23:27.539
year and our 4’th year is equal to D 2016
is equal to D 3 into the growth rate. This
23:27.539 --> 23:36.279
is g 2 1 plus 0.06 because after the third
year, the growth rate changes to g 2. So,
23:36.279 --> 23:42.460
we have taken the new growth rate 0.06, is
6 percent comes out to be 7.336.
23:42.460 --> 23:53.279
So, by using D 2016 are equal to 7.336 and
14 percent required return and a 6 percent
23:53.279 --> 24:00.390
dividend growth rate. We can calculate the
value of the stock at the end of 2015 as follows;
24:00.390 --> 24:09.929
D N plus 1 divided by i minus g 2 is equal
to 7.336 divided by in bracket 0.14 minus
24:09.929 --> 24:21.039
0.06 is equal to 91.7 and this is p 2015.
Finally, the share value of 91.7 at the end
24:21.039 --> 24:28.649
of 2015 must be converted into the present
value that is end of the 2012. So, we have
24:28.649 --> 24:36.639
to divide it by 1 plus i to the power 3, it
converts into this 91.7 converts into rupees
24:36.639 --> 24:45.009
61.895. Now step 4, the value of the shares
end of initial growth period that is the end
24:45.009 --> 24:53.549
of 12 is the earlier the present value of
the 3.
24:53.549 --> 25:02.279
We have the already calculated, it is 12.456
and 61.895. So, we add them all to rupees
25:02.279 --> 25:10.159
74.351 per share. At last we add the PV of
the initial dividend streams found in step
25:10.159 --> 25:17.390
2 to the PV of the stock at the end of initial
growth period found in step 3, we get this.
25:17.390 --> 25:24.109
Now, other approaches to valuation of shares.
In addition to the dividend valuation approach
25:24.109 --> 25:30.269
discussed above; there are other approaches
for valuation of shares and these are one
25:30.269 --> 25:36.389
book value, second liquidation value and third
price earnings multiples.
25:36.389 --> 25:45.029
Now, book value, the approach uses the book
value per share BVPS as the basis for valuation
25:45.029 --> 25:55.230
of shares. The BVPS is the net worth, that
is equity capital plus reserved and surplus
25:55.230 --> 26:03.809
divided by the number of outstanding equity
shares. Alternatively BVPS is the amount per
26:03.809 --> 26:12.109
share on the sale of the asset of the company
at their exact book value minus all liabilities
26:12.109 --> 26:17.889
including preference shares.
Now, let us take an example to demonstrate
26:17.889 --> 26:25.570
this example 5. Messer’s SJ International
has total asset of rupees 70 crore. Total
26:25.570 --> 26:33.470
liability including preference share is 50
crore and 10, 00,000 shares. Calculate the
26:33.470 --> 26:35.000
book value per share.
26:35.000 --> 26:45.090
So, this is equal to, this is asset 70 crore
minus 50 crore, is liabilities divided by
26:45.090 --> 26:54.380
10, 00,000 is equal to rupees 200. However,
the BVPS is not a good proxy for true investment
26:54.380 --> 27:01.289
value. For one thing, this approach relies
on historic balance in data. Moreover it ignores
27:01.289 --> 27:08.190
the expected earning potential. Similarly,
the BVPS has no true relationship to the market
27:08.190 --> 27:10.369
value of the firm.
27:10.369 --> 27:17.999
Now, the second 1 is liquidation value. This
approach to valuation of share is based on
27:17.999 --> 27:25.720
the liquidation value per share, which is
equal to LVPS is equal to value realized from
27:25.720 --> 27:32.049
liquidating all assets minus amount to be
paid to all creditors and preference share
27:32.049 --> 27:38.159
holders divided by number of the outstanding
shares. Let us take an example to demonstrate
27:38.159 --> 27:44.539
this example number 6. The total assets of
Messer’s SJ International can be liquidated
27:44.539 --> 27:51.789
for rupees 70 crore its total liability including
preference share holders is 50 corers and
27:51.789 --> 27:58.859
1000000 shares. Find the liquidation value
per share. It is 70,000 minus 50 divided by
27:58.859 --> 28:05.570
10, 00,000 is equal to 200.
The LVPS is a more realistic measure than
28:05.570 --> 28:13.720
book value, but it ignores the earning power
of the assets of the firm. Moreover it is
28:13.720 --> 28:20.519
difficult to estimate the liquidation value
of a going concern. For above reasons, the
28:20.519 --> 28:27.499
LVPS is also not a true proxy of the true
investment values.
28:27.499 --> 28:37.879
Now, price oblique earning that is PE ratio.
The price earning PE ratio reflects the amount
28:37.879 --> 28:45.210
investors are willing to pay for each rupee
of earning. The price earning multiple approaches
28:45.210 --> 28:52.229
is a popular technique used to estimate the
firms share value, calculated by multiplying
28:52.229 --> 29:00.779
the firms expected earnings per share by the
average price oblique earning PE ratio of
29:00.779 --> 29:01.779
the industry.
29:01.779 --> 29:09.259
Now, let us take an example, example 7. Messer’s
SJ International is expected to earn rupees
29:09.259 --> 29:18.889
12 per share next year, that is 2017. Assuming
the industry average PE ratio to be 10, what
29:18.889 --> 29:25.269
will be the firms share value? Solution, the
firms share value is equal to expected earning
29:25.269 --> 29:33.490
into average PE ratio. So, is equal to rupees
12 into 10, it comes up to be rupees 120 per
29:33.490 --> 29:40.989
share. The PE multiple approach is a fast
and easy way to estimate a shock value; however,
29:40.989 --> 29:48.620
PE ratio vary widely over time. Third, when
using this approach to estimate stock values,
29:48.620 --> 29:56.789
the estimate will depend more on whether stock
market valuations generally are high or low
29:56.789 --> 30:05.669
rather than on whether the particular company
is doing well or not.
30:05.669 --> 30:13.299
Relationship among decisions returns risk
and share values, any action of the financial
30:13.299 --> 30:20.970
manager that increases the level of expected
return that is D 1 comma g.
30:20.970 --> 30:29.419
Without changing risk I should increase the
share value. Second the action of the financial
30:29.419 --> 30:36.399
manager that reduces the level of expected
return without changing risk should reduce
30:36.399 --> 30:44.879
the share value. Third likewise keeping the
expected return constant, any action that
30:44.879 --> 30:53.259
increases risk required return will reduce
share value. Forth keeping the expected returns
30:53.259 --> 31:00.879
constant and any action that reduces risk
that is required return will increase share
31:00.879 --> 31:08.239
value.
Summary what we have thought in this lecture.
31:08.239 --> 31:12.679
Ordinary shares and preference shares discussed.
31:12.679 --> 31:18.519
Valuation of preferential share discussed.
Valuation of ordinary shares based on dividend
31:18.519 --> 31:24.789
valuation or dividend discount models that
are zero growth, constant growth and variable
31:24.789 --> 31:31.039
growth models discussed. Other approaches
for valuation of shares such as book value,
31:31.039 --> 31:39.220
liquidation value and price earnings multiples
discussed. Relationship among decisions return
31:39.220 --> 31:45.970
risk and share value discussed.
With this lecture I am ending my course. I
31:45.970 --> 32:08.789
hope you should have enjoyed my course and
best luck for you for the examinations.
32:08.789 --> 32:29.779
Thank you.