Stock Valuation with Non-Constant Growth

This assignment focuses on valuing a stock using the Dividend Discount Model (DDM) under the scenario of non-constant growth. It presents a step-by-step calculation of the stock price in five years, considering varying dividend growth rates for the first three years followed by a constant 8% growth rate. The solution involves calculating the present value of future dividends and the terminal value of the stock at year three.

Running head: INVESTMENT AND PORTFOLIO MANAGEMENT
Investment and portfolio management
Name of the student
Name of the university
Author note

1INVESTMENT AND PORTFOLIO MANAGEMENT
Table of Contents
Question 1..................................................................................................................................2
Question 2..................................................................................................................................4
Question 3..................................................................................................................................5
Question 4..................................................................................................................................6
Reference and Bibliography.......................................................................................................9

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Question 1
(a) Benchmark index for tracking the performance of securities/stock exchange
 Australia – S&P/ASX 50
 USA – NYSA Arca Major market Index
 Hong Kong – Hang Seng Index
 Japan – Nikkei 225
 England – FTSE 100
 China – SSE Composite Index
(b) Major asset classes and asset allocation
Stable fund – the stable fund is more conservative investment which is aimed at
outperformance of cash and boosting the returns through blending the cash with specific
shares. Main goal of various investors are to increase the cash without increasing the
considerable risk (Huang, Li & Shi, 2016). The major asset class under stable fund is cash
that includes term deposits, bank deposits, cash management trusts and cheque and savings
accounts. This is suitable for the investors those have the short-term preference and lower
risk tolerance level. It offers low and stable risk income, generally in form of the regular
payments of interest equally. Under stable fund the potential return as well as the risks both is
low. No minimum timeframe is recommended for this fund.
Balanced fund – the balanced fund invests in the combination of specific selected fixed
incomes, shares and the commodity investments in Australia and international market for
providing long-term growth without much downs and ups. The major asset class under
balanced fund is fixed interest that includes corporate bonds, government bonds, hybrid
securities and mortgage securities (Samudhram, Siew, Sinnakkannu & Yeow, 2016). It is
more volatile as compared to the cash, still it can be considered as relatively stable. It

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operates generally in the same way of loan. Return on income is normally in form of regular
payment of interest for the agreed time period. Recommended time frame for this asset is
minimum 1 to 3 years. Under stable fund the potential return as well as the risks both is
moderate.
Growth fund – the growth fund’s main objective is to offer long term growth of capital
through investing in the high quality and large Australian organizations. It offers well-
diversified investing portfolio in wide range of the industry sectors. The major asset class
under growth fund is property that includes direct investment in commercial, residential and
industrial property and the indirect investment like vehicles. It may also include equities that
include international equities and Australian equities. Growth funds generally has the high
return as well as the risk involved is high (Bateman et al., 2014) The property is of long term
nature, generally 7 years or more and the exit and entry cost involved with this is
considerably high. The returns under equity fund include the capital loss or growth and the
income through the dividends. Further, the equities are considered to be most volatile class of
asset over the long term time frame. However, it involves the part ownership for any
company that enables the investor to share profits and the future growth.
Typical asset allocation
Asset class High
growth
Growth Diversified Socially
responsible
Balanced
fund
Stable
fund
Australian equities 30% 22% 26% 16% 6%
International equities 37% 29% 24% 21% 7%
Alternatives 28% 28% 26% 28% 29%
Fixed income 0% 10% 18% 20% 20%
Cash 5% 10% 6% 15% 38%
Total 100% 100% 100% 100% 100%

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Justification for asset allocation
For allocating the assets, an active strategy is adopted to avail the advantages from the
market conditions through temporary decreasing or increasing the exposures to the particular
class of asset. This will help in protecting the investors from the risks of overexposures to the
expensive market and get the additional return through increasing the exposures to class of
assets while they will be attractive.
Question 2
Taking into consideration the 1st derivative of the bond or any security that offers
fixed income, the price (P) with regard to the yield to maturity (R) delivers the following –
(dP/P) / [dR/(1+R)] = - D
Economic interpretation of the above equation is D is the measure of percentage
change in price of the bond for the given change in percentage with respect to yield to
maturity that is the interest elasticity (Khalil et al., 2014). Further, the above equation can be
written as follows for providing the practical application –
dP = -D[dR/(1+R)] P
To be stated in other ways, if the duration factor is known, the change in the bond
price owing to the small changes in the rate of interest, R, may be forecasted through the
above formula.

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Question 3
(a) Duration, modified duration and the dollar duration
Duration –
Duration of the treasury bond of $ 1,000 that is paying the semi-annual coupon rate of
10% per annum and selling at par at present with 11 years of maturity will be as follows –
Period Cash flow Period*cash flow
PV of $1 @
5% PV of cash flow
1 $ 50.00 $ 50.00 0.95238 $ 47.62
2 $ 50.00 $ 100.00 0.90703 $ 90.70
3 $ 50.00 $ 150.00 0.86384 $ 129.58
4 $ 50.00 $ 200.00 0.82270 $ 164.54
5 $ 50.00 $ 250.00 0.78353 $ 195.88
6 $ 50.00 $ 300.00 0.74622 $ 223.87
7 $ 50.00 $ 350.00 0.71068 $ 248.74
8 $ 50.00 $ 400.00 0.67684 $ 270.74
9 $ 50.00 $ 450.00 0.64461 $ 290.07
10 $ 50.00 $ 500.00 0.61391 $ 306.96
11 $ 50.00 $ 550.00 0.58468 $ 321.57
12 $ 50.00 $ 600.00 0.55683 $ 334.10
13 $ 50.00 $ 650.00 0.53032 $ 344.71
14 $ 50.00 $ 700.00 0.50507 $ 353.55
15 $ 50.00 $ 750.00 0.48102 $ 360.77
16 $ 50.00 $ 800.00 0.45811 $ 366.49
17 $ 50.00 $ 850.00 0.43630 $ 370.86
18 $ 50.00 $ 900.00 0.41552 $ 373.97
19 $ 50.00 $ 950.00 0.39573 $ 375.94
20 $ 50.00 $ 1,000.00 0.37689 $ 376.89
21 $ 50.00 $ 1,050.00 0.35894 $ 376.89
22 $ 1,050.00 $ 23,100.00 0.34185 $ 7,896.74
Total $ 13,821.15
Therefore, the duration will be ($ 13,821.15/$ 1,000) / 2 = 6.91
Modified duration –
Modified duration = D / (1 + R/2)

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= 6.91 / (1+ 0.10/2) = 6.581
Dollar duration –
Dollar duration = MD * P = 6.581 * $1,000 = $ 6,581
(b) Estimated price change if –
Interest rate increases by 10 basis point that is, 0.10%
Estimated price change = - dollar duration * change in rate
= - 6,581 * 0.001 = - $ 6.581
Therefore, the new prices will be $ 1,000 - $ 6.581 = $ 993. 419
Interest rate decreases by 20 basis point that is, 0.20%
Estimated price change = - 6,581 * - 0.002 = $ 13.162
Therefore, the new price will be $ 1,000 + $ 13.162 = $ 1,013.162
Rate change Estimated price Actual price Error
+0.001 $993.419 $993.369 0.099
-0.002 $1,013.162 $1,013.364 -0.203
Question 4
Under constant growth –
Current price of the share –
P0 = ?, D = 0.20, g = 0.08, R = 0.16
P0 = D1 / (R – g)

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= $0.20 (1.08)1 / (0.16 - 0.08)
= $0.216 / 0.08 = $ 2.7
Share price in 5 years –
P5 = D6 / (R – g)
= $0.20 (1.08)6 / (.16 - .08)
= $0.20 * 1.587 / 0.08
= $3.9675
Under non-constant growth -
The dividend is expected to grow at the rate of 205 for next three years and thereafter
it will settle down at 8% per year.
Price of the stock at year 3 will be –
P3 = D3 (1 + g) / (R – g)
= D0 (1 + g1)3 (1 + g2) / (R – g)
= $0.20(1.20)3(1.08) / (.16 – .08)
= 0.373 – 0.08
P3 = $ 4.666
The stock’s price today will be the PV of 1st three dividends plus PV of the year three
stock price. Therefore, the stock price today will be –
P0 = $0.20(1.20) / 1.16 + $0.20 (1.20)2 / (1.16)2 + $0.20 (1.20)3 / (1.16)3 + $4.666 / (1.16)3

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= 0.207 + 0.214 + 0.221 + 2.989 = $ 3.631