Stevan Sijan Stojic
31301654@fsv.cuni.cz
Computational Homework
Problem 1
1
Stevan Sijan Stojic
31301654@fsv.cuni.cz
2
Stevan Sijan Stojic
31301654@fsv.cuni.cz
Problem 2
a) By looking at the two strip bonds, we can see the spot rates for year 1 and 2. Therefore,
we will use interest rate 7% for the first year, and 8% for the second year. Furthermore,
the coupon payments will be $9 ($100*0.09). The price of the bond is:
𝑃𝑉(𝑏𝑜𝑛𝑑) =
9
9
100
+
+
= $101.86
2
1.07 1.08
1.082
b) The yield to maturity is the average rate of return that is earned if the bond is purchased
at current market price, and it is held to maturity. As we already know the price of the
bond, we can easily find the yield to maturity:
$101.86 =
9
9
100
+
+
2
1 + 𝑦 (1 + 𝑦)
(1 + 𝑦)2
𝑦 = 7.95
Yield to maturity is 7.95.
c) We need to find the next year forward rate (f2). We can use the yields from the zerocoupon bonds to find it, because we know that (1.07*f2) = (1.08) ^2. Therefore:
𝑓𝑜𝑟𝑤𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 =
1.082
= 9.01%
1.07
Now we will use the forward rate in order to find the market expectation of the bond
price:
𝐵𝑜𝑛𝑑 𝑃𝑟𝑖𝑐𝑒 =
109
= $99.99 ~ $100
1.0901
d) Since there is a liquidity premium of 1%, the forward rate will be changed. This is
calculated by simply subtracting 1 from the forward rate:
𝑓𝑜𝑟𝑤𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 = 9.01% − 1% = 8.01%
And now we find the new expected bond price with the 8.01% forward rate:
𝐵𝑜𝑛𝑑 𝑃𝑟𝑖𝑐𝑒 =
109
= $100.92
1.0801
If we believe in liquidity preference then our bond price would be $100.92.
3
Stevan Sijan Stojic
31301654@fsv.cuni.cz
Problem 3
a) The DuPont analysis is used to analyze fundamental performance of a company. It is
basically an extended version of the ROE formula, that helps to identify the strengths
and weaknesses of a firm. Thus, it is very useful to investors. The DuPont formula is:
𝐷𝑢𝑃𝑜𝑛𝑡 = 𝑇𝑎𝑥 𝐵𝑢𝑟𝑑𝑒𝑛 ∗ 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝐵𝑢𝑟𝑑𝑒𝑛 ∗ 𝐸𝐵𝐼𝑇 𝑀𝑎𝑟𝑔𝑖𝑛 ∗ 𝐴𝑠𝑠𝑒𝑡 𝑇𝑢𝑟𝑛𝑜𝑣𝑒𝑟 ∗ 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒 𝑅𝑎𝑡𝑖𝑜
where:
𝑇𝑎𝑥 𝐵𝑢𝑟𝑑𝑒𝑛 𝑟𝑎𝑡𝑖𝑜 =
𝑁𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒
$475
=
= 0.64
𝑃𝑟𝑒𝑡𝑎𝑥 𝑝𝑟𝑜𝑓𝑖𝑡 $740
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝐵𝑢𝑟𝑑𝑒𝑛 𝑟𝑎𝑡𝑖𝑜 =
𝐸𝐵𝐼𝑇 𝑀𝑎𝑟𝑔𝑖𝑛 =
𝐸𝐵𝐼𝑇
$760
=
= 0.16
𝑅𝑒𝑣𝑒𝑛𝑢𝑒 $4,750
𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡 𝑇𝑢𝑟𝑛𝑜𝑣𝑒𝑟 =
𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒 𝑅𝑎𝑡𝑖𝑜 =
𝑃𝑟𝑒𝑡𝑎𝑥 𝑝𝑟𝑜𝑓𝑖𝑡 $740
=
= 0.97
𝐸𝐵𝐼𝑇
$760
𝑅𝑒𝑣𝑒𝑛𝑢𝑒
$4,750
=
= 1.61
𝑇𝑜𝑡𝑎𝑙 𝑎𝑠𝑠𝑒𝑡𝑠 $2,950
𝑇𝑜𝑡𝑎𝑙 𝑎𝑠𝑠𝑒𝑡𝑠 $2,950
=
= 1.4
𝑇𝑜𝑡𝑎𝑙 𝑒𝑞𝑢𝑖𝑡𝑦 $2,100
Now DuPont can be calculated:
𝑅𝑂𝐸 = 0.64 ∗ 0.97 ∗ 0.16 ∗ 1.61 ∗ 1.4 = 0.226 = 22.6%
In this case ToyCorp has a pretty low ROE, and this is primarily due to the low EBIT margin.
This is also reflected in the balance sheet where COGS is $2,400 million, which is 50% of
the total revenue. Furthermore, when the other expenses are added the remaining revenue
is only $760 million. So, by using the DuPont analysis this company can see that they have
to lower their expenses if they want to increase the return for their shareholders.
b) ROE or return on equity, shows the profitability of a company in relation to its
stockholders’ equity. The calculation is as follows, and it will give the same result as the
DuPont ROE:
𝑅𝑂𝐸 =
𝑁𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒
$475
=
= 0.226
𝑆ℎ𝑎𝑟𝑒ℎ𝑜𝑙𝑑𝑒𝑟 𝑒𝑞𝑢𝑖𝑡𝑦 $2,100
4
Stevan Sijan Stojic
31301654@fsv.cuni.cz
c) The formula for sustainable growth rate is:
𝑆𝐺𝑅 = 𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝐸𝑞𝑢𝑖𝑡𝑦 ∗ (1 − 𝑃𝑎𝑦𝑜𝑢𝑡 𝑅𝑎𝑡𝑖𝑜)
We already know ROE, and we need the payout ratio, which can be calculated:
𝑅𝑂𝐸 =
𝑁𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒
$510
=
= 0.23 = 23%
𝑆ℎ𝑎𝑟𝑒ℎ𝑜𝑙𝑑𝑒𝑟 𝑒𝑞𝑢𝑖𝑡𝑦 $2,200
Now the payout ratio should be calculated
𝑃𝑎𝑦𝑜𝑢𝑡 𝑟𝑎𝑡𝑖𝑜 =
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑
0.6
=
= 0.306
𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 1.96
The sustainable growth rate will be:
𝑆𝐺𝑅 = 0.23 ∗ (1 − 0.306) = 0.15962 = 15.96%
This means that ToyCorp will grow by 15.96% annually with its current revenue, without
financing growth with additional equity or debt.
Problem 4
a) From the setup we know that g is 25%, and k is 20%. First off, we will need to calculate
the price of dividends in the next three years:
𝐷𝐼𝑉1 = $1 ∗ 1.25 = $1.25
𝐷𝐼𝑉2 = $1.25 ∗ 1.25 = $1.5625
𝐷𝐼𝑉3 = $1.5625 ∗ 1.25 = $1.953125
The intrinsic value is obtained by adding up the present value of all the future cash flow
from the dividends, and the present value of the price when the stock is sold. So:
𝑃𝑉(𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠) =
$1.25 $1.5625 $1.953125
+
+
= $3.25
1.2
1.22
1.23
After the first three years, we will have a constant growth of 5%, thus we can use the
constant growth DDM to find the present value of the stock when it is sold. After finding
the price (Div4=P4) we will discount it with k=20%
𝑃𝑉(𝑠𝑡𝑜𝑐𝑘 𝑝𝑟𝑖𝑐𝑒) =
𝐷𝑖𝑣4
$1.953125 ∗ (1.05)
=
= $7.19
3
(𝑘 − 𝑔) ∗ (1 + 𝑘)
(0.2 − 0.05) ∗ (1.2)3
The Intrinsic value of the stock will be
𝑉0 = $3.25 + $7.19 = $11.16
5
Stevan Sijan Stojic
31301654@fsv.cuni.cz
b) Since market price is equal to the intrinsic value, we can easily calculate the expected
dividend yield with its formula:
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑦𝑖𝑒𝑙𝑑 =
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑(𝐷𝐼𝑉1)
$1.25
=
= 0.112 = 11.2%
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒(𝑉0) $11.16
c) The dividend growth model can be used to find the price one year from now:
𝐷1 + 𝑃1
𝑉0 =
1+𝐾
$11.86 =
$1.25 + 𝑃1
= 𝑃1 = $12.14
1 + 0.2
So, the share price one year from now will be $12.14. Now the capital gain needs to be
calculated, so that it can be compared to the dividend yield and the market capitalization
rate:
𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑔𝑎𝑖𝑛 =
𝐸(𝑃1) − 𝑃0 $12.14 − $11.16
=
= 8.79%
𝑃0
$11.16
The capital gain of 8.79% is not consistent with the dividend yield or the market
capitalization rate.
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