Example
Mills Company bond which currently sells for Sh.1080, has a 10% coupon rate and Sh.1000 par
value, pays interest annually and has 10 years to maturity. Find YTM of the bond.
10
1
10
)
1
(
)
1
(
1000
100
1080
t
t
k
k
d
d
or,
PVIF
PVIFA
k
k
d
d
10
,
10
,
*
1000
*
100
1080
Trial and error
We know that when K
d
= 10% (equal coupon rate),
then B
0
= 1000. Thus the discount rate to
result in 1080 must be less than 10%. (Try a lower rate if the PV of cash flows at a given rate is
lower than the market price of the bond).
Try 9%
=
100 x 6.418 + 1000 x .422 = 1063.80 (The 9% rate is not low enough to
get Sh.1080).
Next try 8%
=
100 x 6.710 + 1000 x .463 = 1134
Because 1080 lies between 1063.80 and 1134 the YTM must be between 8% and 9%. Because
1080 is closer to 1063.80, the YTM to the nearest whole per cent is 9%.
By using interpolation, we find the more precise YTM value to be 8.77% as follows;

77
Interpolation
1134
1063.80
=
70.20
1080
1063.80
=
16.20
YTM =
9% - 16.20
=
9% - 0.2307692
70.20
=
8.77%)
Using a financial calculator, we get 8.766%.
PREFERENCE SHARES VALUATION
This is a type of stock that promises a fixed dividend but at the discretion of the Board of
directors. It has preference over ordinary shares in the payment of dividends and claims on the
assets it has no maturity date (unless redeemable) and give the fixed nature of the dividend is
similar to a perpetuity.
Thus the PV of a preferred stock,
V
p
,
is
k
D
V
p
p
p
(4.7)
Where D
p
is the stated annual dividend, per share and k
p
is the appropriate discount rate.
Example
A company had issued a 9% Sh.100 par value preference shares and an investors require a rate of
return of 14% on this investment. Find the value of a preference share to investors.
D
p
=
9%*100 = Sh.9
k
p
=
14
The value of the preference share is,
V
p
=
9/0.14 =
Sh.64.29
Example
A preferred stock paying a dividend of Sh. 5 and having a required return of 13% will have a
value of Sh.38.46 (5÷0.13)
VALUATION OF ORDINARY SHARES
Common shareholders expect to be rewarded through periodic cash dividends and an increasing
share value. It is the expectation of future to dividends and a future selling price (which itself is
based on future dividends) that gives value to a share. Cash dividends are broadly defined to
mean all cash distributions and are the foundation for valuation of shares.
Dividend discount models are designed to compute the intrinsic value of a share under specific
assumptions as to the expected growth patterns of future dividends and the appropriate discount
rate to apply.
Basic stock valuation equation
The value of a share is equal to the PV of all future dividends it is expected to provide over an
infinite time horizon
(from a valuation viewpoint only dividends are relevant).

78
k
D
k
D
k
D
P
s
s
s
1
(
)
1
(
)
1
(
...
2
2
1
1
0
(4.7)
Where
P
0
=
current value of ordinary share
k
s
=
required return on ordinary shares
D
t
=
per share dividend at end of year t.
We illustrate the use of this formula to estimate the value of ordinary stock under three dividend
growth assumptions i.e. zero growth in dividends, constant growth in dividends, and variable
growth phases.

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- Fall '16