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Unformatted text preview: ARE 171a I Homework3 E g ! Fall2011 1. (12) Jennifer’s portfolio consists of three stock holdings, with their portfolio weights shown: Nucor'Befense Systems (35%) Vista Travel (40%) Tom's Toothpaste (25%)
These stocks' returns are affected by the state of international relations, as follows: I all. 0 called mmcui'mﬁ  ‘ State of the worldﬁ Major int‘l. hostilities Minor int’ i tensions Peaceful relations J W ' W s‘ k grog—z I ht 0.30 0.50 0.20 expecled return sl ma CV Wm we, 9/ M10
oc: o ooweg g, \_ _. Hm». I EMRQW‘W“
Nucor 0.35 i as 14% 6% 17.80% 16.38% 0.92032 0.4m] W
Vista 0.40 : 40% 12% 18% 3.60% 15.62% 4.337605 Wm (\M
Tom's 0.25 l 9% 11% 12% 10.60% 1.11% 0.105052 KL M [Place
i \ W
Portfolio “ 8.2326 ‘— 10.32% 2.1396 0.206457 w “re
V a) w i K 5N MI. W,“ ~— ; P «
[LP run (2 RP (7‘3 (WP A11, I ~ L... R WM
called hWPm uwuhrp Ii) “Ufa/W a.(1) Do these stocks' returns appear to be correlated, and if so, in which direction? (consider each pair of 2, verbal answers only) Yes, Vista and 1059‘s are positively corLelatgd with each other, since they both perform best in times of (V T > 0
peace, and worst in times of war. vista and T_om's are each negatively correlﬂeg with Nucor, since i 4
Nucor‘s return increases as war becomes more likely, and is at a minimum during times of peace. rv) N < O I FT N o b. (6)) Find the expected rate of return, standard deviation of return, and coefﬁcient of variation of each stock, if held alone.
Which has the highest expected rate of return? Which has the lowest CV? As shown above, Nucor has the highest expected return; and Tom's has the lowest CV.
Vista doesn't look attractive, given its low expected return and high CV. Based on its sigma and mean return, it is dominated by Tom's. c. (5) Now ﬁnd the expected rate of return, standard deviation of return, and CV for Jennifer’s portfolio.
Also from above: W
Portfolio prar = 10.32% sigma p = 2.13% CV = .2065
Notice that, due to the very poor performance of Vista during periods of war, and its large share of the total portfolio,
this particular portfolio is still not as attractive as owning Tom‘s by itself. if the chance of war :rasn'tso high, this would not be
the case. {2 . 0:47.16“ .51 misit e’Z( Yd): i032°5€ is the portfolio’s expected value equal to the weighted average of the 3 stocks' individual returns? j u
as shown above: (do; {(44 9014 P .
in the table above, l calculated prar as the sum of (prob of each state) x (Rp in that state) P («WM RP 'f‘ PMMSGEF 1" PF,“ (4 2
Now let‘s see if this is equal to the sum of (share of each stock in portfolio)x (Rbar for that stock) ‘ ‘ .
The answer should be yes, or we have made a calculation error. (7
wn‘Rnbar + wv’vaar + wt‘lttbar = .35‘1739‘ + «93.6% + .25‘10.6% = 10.32% (check) I 0: g 2 0 is the portfollo's standard deviation equal to the weighted average of the 3 stocks' individual std. deviations? No, it should be less. So let's check:
tr p = (.30“(8.3510.32)A2+.5(12.4510.32)'*2+.25"(8.110.32)"2)'*.5
=2.13 weighted average of each stock's individual sigma, weighted by its
share in the portfolio, wouid be: wn'slgma n + wv‘slgma v + wt‘slgma t = .35‘16.38% + .4‘15.62% + .25‘1.11% a
12.26% We see that the portfolio standard deviation of return is much lower than a weighted average of the
individual stocks' standard deviations of return. This is because the returns are not perfectly positively
correlated. it is especially effect to blend Nucor with the other two, since its returns move in the opposite
direction from the others, thus helping to stabilile average returns. However, in this particular case, we have the rather attractive Tom's stock, which has a nice, quite stable return that actually
dominates this particular portfolio's performance. We could build a better portfolio than this one, by simply
blending Nucor and Tom's. its mean return would be between 10.6 and 17.8%, while its std. dev. wouid be
less than the weighted average of sigma n and sigma t. 2. a. CV Lux =oL/RLbar = 9/10 0.9
. CV Ben =oB/RBbar = 1 5/8 0.625 lf held alone. Ben's Wholesale Foods has a lower CV, thus is less risky per unit of expected return.
b. 2 2 1 ‘2 "z 
(P  M at ’“ ‘00 (B ’r ZWLWB maﬁa? ~ wEHLH (I'wtlz(5z)+.2w,_(l'wt.l (.2) (1)151
: 103(801 25* 5‘0 W1, + 26‘ m1 +18tJL—lgw:Z 6P1 03(81129161 + (13’93w1, 4+ 2§ f
2. ".1 if? 1 2683940 ~31 = 0
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\ _ v“ ___._.._.._ .—« _ * .——. ..._ mt. ‘._. ._. .____ ...._ ._.. ._ w. _ q A firm’s balance sheet as of Dec. 31“, 2010 is shown below: (all values in millions) Assets 12312010
Cash 50 Other current assets 155
Net ﬁxed assets £0
Total assets 545
Liabilities and shareholders equity
Current liabilities 85
Long term debt 135
Shareholders' equity 125 Total liab and s. equity 545 \\ a. During 2011, the firm’s sales were $700 m., cost of good sold was $400 m, depreciation was $88 m., interest paid was
$12 m., and taxes paid were 25% of EAT. A dividend of $50m was issued to shareholders. Using this information,
prepare the 2011 income statement.‘ Also ﬁnd 2011 EPS and dividend per share, assuming there are 2°million shares outstanding. If the firm previously (in 2010) had EAT of $105 m., and paid dividends of $45m, also with 2°million shares
outstanding, ’what was the rate of growth in EPS between 2010 and 2011? What was the rate of growth in div. per share? b. Now that 2011 has come to an end, we need to prepare the balance sheet for 12312011. Using the 2010 balance
sheet above, the 2011 income statement from part a, and the information below, write the 1231—2011 balance sheet. During the 2011 calendar year, the ﬁrm paid off $10 million in longterm bond principal. It increased its holdings
of cash by $5m, and increased other current assets by $15 m. Its current liabilities increased by $5 m. (Hint: to finish
the balance sheet, you will need to calculate the change in net fixed assets such that the balance sheet balances. ) How much did the firm invest in new fixed assets? (1} ‘i “mew— 16“ Sub») 700‘ k 6‘ W
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