Chapter 11 BUSI 530
Whatisthediscountrateonthestock?
Discount rate9.70selected answer correct%
Whatpriceshouldshebewillingtopayforthestocktoday?
1.TophedgefundmanagerSallyBuffitbelievesthatastockwiththe
samemarketriskastheS&P500willsellatyear endatapriceof$49.
Thestockwillpayadividendatyear endof$3.00.Assumethatrisk free
Treasurysecuritiescurrentlyofferaninterestrateof2.1%.
AverageratesofreturnonTreasurybills,governmentbonds,and
commonstocks,1900–2015(figuresinpercentperyear)areasfollows.
Portfolio
Treasury bills
Treasury bonds
Common
stocks
Average Annual
Rate of Return (%)
3.8
5.3
11.
4
Average Premium (Extra
return
versus Treasury bills) (%)
1.
5
7.
6
Some values below may show as rounded for display purposes, though unrounded
numbers should be used for the actual calculations.
Based on the historical risk premium of the S&P 500 (7.6%) and a risk-free rate of
2.1%, one would predict an expected rate of return of 9.70%. If the stock has the
same systematic risk, it also should provide this expected return. Therefore, the stock
price equals the present value of cash flows for a 1-year horizon.
$3.00 +
P0
49=
= $47.40
1.097
(Enter your answer as a
percent rounded to 2 decimal places.)
(Do not
round intermediate calculations. Round your answer to
2 decimal places.)
Stock price$47.40selected answer correct
Explanation
2.Astockissellingtodayfor$60pershare.Attheendoftheyear,i
t paysadividendof$3pershareandsellsfor$72.
a.Whatisthetotalrateofreturnonthestock?(Enter your
answer as a whole percent.)
b.
Rate of return25selected answer correct%
b.Whatarethedividendyieldandpercentagecapitalgain?
Nowsupposetheyear endstockpriceafterthedividendispaidis
$54.Whatarethedividendyieldandpercentagecapitalgaininthis
case?
d.Isthereanychangeinthedividendyieldcalculatedinparts(b)and
(c)?
(Enter
your answers as a whole percent.)
Dividend yield5selected answer correct%
Capital gains yield20selected answer correct%
c.
(Negative amounts should be indicated by a minus
sign. Enter your answers as a whole percent.)
The dividend
yield is
unaffectedselected answer
correct
Dividend yield5selected answer correct% Capital
gains yield(10)selected answer correct%
; it is based
on the
initial priceselected answer
correct
Explanation
Some values below may show as rounded for display purposes, though unrounded
numbers should be used for the actual calculations.
a.
Total percentage
=(Capital gain + Dividend) / Initial
returnshare price
=[($72 – 60) + $3] / $60
=0.25, or 25%
b.
Dividendividend / Initial share
yield=Dprice
=$3 / $60
=0.05, or 5%
Capital gainsCal gain / Initial
yield=apitshare price
=($72 – 60) / $60
=0.20, or 20%
c.
Dividend
=Dividend / Initial share
yield price
=$3 / $60
=0.05, or 5%
Capital gainsapit
ld=Cal gain / Initial yieshare price
=($54 – 60) / $60
=–0.10, or –10%
d.
The dividend yield is unaffected by the ending share price because the yield is based
on the initial price.
b. What is your real (inflation -
adjusted)rateofreturniftheinflationrate is5%?
3.Youpurchase100sharesofstockfor$25ashare.Thestockpaysa
$2persharedividendatyear end.
Whatistherateofreturnonyourinvestmentiftheend of yearstock
priceis(i)$23;(ii)$25;(iii)$26?
a.
(Leave no cells blank - be
certain to enter "0" wherever required. Enter your
answers as a whole percent.)
(Do not round intermediate calculations. Enter
your answers as a percent rounded to 2 decimal places.
Negative amounts should be indicated by a minus sign.)
Stock PriceRate of Return
230selected answer correct%
258selected answer correct%
2612selected answer correct%
Stock PriceReal Rate of Return
23(4.76)selected answer correct%
252.85selected answer correct%
266.67selected answer correct%
Explanation
Some values below may show as rounded for display purposes, though unrounded
numbers should be used for the actual calculations.
a.
(i)
Capital gain + Dividend($23 − 25) + $2
Rate of return===0%
Initial share price$25
(ii)
($25 − 25)
Rate of
+ $2
return==0.08, or 8%
$25
(iii)
($26 − 25)
Rate of
+ $2
return==0.12, or 12%
$25
b.
(i)
1 + Nominal rate of return1 + 0
Rate of return=−1 = −1 = −0.0476, or −4.76%
1 + Inflation rate1 + 0.05
(ii)
1 + Nominal rate of return1 + 0.08
Rate of return=−1 = −1 = 0.0286, or 2.86%
1 + Inflation rate1 + 0.05
(iii)
Scenario
Recession
Normal
economy
Boom
Rate of return
=
Rate of
Return
Probabili Stock Bond
tyss 0.20 –5% 19%
0.6020 10
0.2027 4
1 + Nominal rate of return
1 + Inflation rate −1 = 1.1
2
1.0
5
Some values below may show as rounded for display purposes, though unrounded
numbers should be used for actual calculations.
a.
Interest rates tend to fall at the outset of a recession and rise during boom periods.
Because bond prices move inversely with interest rates, bonds provide higher returns
during recessions when interest rates fall.
b.
rstock = [0.2 × (−5%)] + (0.6 × 20%) + (0.2 × 27%) = 16.4%
−1 = 0.0667, or 6.67%
4.Considerthefollowingscenarioanalysi
s:
a. IsitreasonabletoassumethatTreasurybondswillprovidehigher
returnsinrecessionsthaninbooms?
Yes
b.Calculatetheexpectedrateofreturnandstandarddeviationforeach
investment.
(Do not round intermediate calculations. Enter
your answers as a percent rounded to 1 decimal place.)
Stocks
Bonds
Expected Rate of ReturnStandard Deviation
16.4selected answer11.0selected answer
% %
correct correct
10.6selected answer
%4.8selected answer correct%
correct
Explanation
rbonds = (0.2 × 19%) + (0.6× 10%) + (0.2 × 4%) = 10.6%
Variance (stocks) = [0.2 × (−5 − 16.4)2] + [0.6 × (20 − 16.4)2] + [0.2 × (27 − 16.4)2]
= 121.84
Standard deviation = 121.841/2 =11.04%
Variance (bonds) = [0.2 × (19 − 10.6)2] + [0.6 × (10 − 10.6)2] + [0.2 × (4 − 10.6)2]
= 23.04
Standard deviation = 23.041/2 = 4.80%
Stocks have both higher expected return and higher volatility. More risk-averse
investors will choose bonds, while those who are less risk-averse might choose
stocks.
