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Unformatted text preview: — Lecture 9 _* _.__.*_—i__ r ‘ hwiim ,ﬁ, ,_
——~—~ 7 “7 @ Lecture 9 _ ESE6? Time Value of Money  Part III How can we compute the amount of interest and principal for each loan payment?
MOLE W (a) (C) (e) Principal Ending Example 23' You take a P ' d B ' ' R d t' B  rice
 car roan f eno egmning e uc lOl't a a
payments The Payments occur t$$5'000‘“atw'” be pand orrm three annual Barance Payment to) — (d) (b)  (e)
7% 3 e and of each year and the annual interest 1
meme"? ‘ 1 ,3 Wow zww
. W4
sum rm 3"“ “4 l 05710 liftI3 ib‘ayis 17% 0. x!
m» m new w. —
What lS the amount of each paYment? H _ TOTALS g 7578/ 767 _
,  ow
PV: 5 000 much Of 936“ Payment is interest expense? 3 U” x 37 z 350 3 a ‘ ’
' ‘ ‘ ‘ ‘f '. .
.l '{WWJ‘i x .0712‘HJ3 r
r 2 0(0 Lit .l._ . r 7,! ‘l' JT
Points to note: [7915‘ x ‘07 ﬂu”; '
M = l 1. The cash paid out each year is the same.
2. The Ending Balance after the last payment is $0.
N = W73 :47 3. The total Principal Reduction is $5,000. the original amount borrowed.
4. The Total Payments is the same as the total interest paid plus the totat principal repaid. ‘4‘“ PV=$PMT[J ‘W WW)” '
HM , which We want to solve for PMT' Computing the Outstanding Balance on an Amortizing Loan
How can we determine the balance on the loan at any point in time? PMTLLH 9“ . \
[l—l/(I+r/M)N ‘ ~ﬂﬁ 11%5 Cit/inoytlZCbhm Wk;
r/M E‘ “073 R
0.01 . I h of 
com ute the amount of e the three annual a m . In addition, we can use the followmg short—cut:
or 3” amortizin loamIS fonnllla can be used to
Q  Richard T. Bliss, Babson University lgRichamnB A  andTerryDNingiamiU 'w,‘
FIN 301 A — ' ‘IISBamemvel'Slty  D , m natty
._ .8 Fall 2011 3‘” Te"? 0 chon. Miami University \ 59 FIN 301A,B — Fall 2011 Lecture 9 The halance on an amortizi
remaining payments. “9 ‘08“ ‘ at any POil'It in time  is simply the PV of the How much of the third monthly payment is interest? Example 24: You bought a carthree years ago for $10,000. You borrowed the money om' Principal
you just made the smasgggggnnﬁg fhaeigdgfWlntrlpayments ﬁat12% annual interest. Beginning Raduc‘uon
Immediately after you make the payment? . 3 IS the remaining balance on the loan Balance
TIMELINE: or. 2" I“ ‘5'" 48 r
to [4 P P ‘3
First we need to compute the monthly payment;
PvalOJmN r: ll M: I; I .\2
r M = * l N = u 3) El Practice: The Rock (aka The People’s Champ) signs papers today to buy J. Lo’s old
PM? PV [am mansion for $15 million. He plans to hold the home for two years and then sell it for ' 2‘“) $20 million. He has arranged a 15—year mortgage on the house calling for monthly
‘W payments at a 5% annual interest rate. How much money will The Rock net after he fng t—l/(1+r/M)N]= [inf1:318 r [M T“ sells the home in two years? Assume he has just made his 24rh payment on the
/”’ mortgage. I ' :“l 6.. 9m A l
A 1 WW}
lgﬁgk ,kai :. pml ..c_:_ J
L. —_} J A_
NOW we can use the sho a . 
rtcut above gm “r, ‘ x3 .\ lulli
Paymems are left on the loan? to compmethe’emalning balance How many L [K L _ K? H
P = l _ _ ‘7';
MT W "*1 M: “L i i“: “a ‘ M”
r 1 FM“ ‘1' N 4'2" I ‘ ;
PW”in = M tile—K t? L a l 1 HM 3: a, Wmlol 2
~ ll ’ 5 JI
‘ \2._ © — Richard T. Bliss, Babson University © Rum and Tony D. Nixon, Miami University
' ’ d T. Bliss, Babson University '
FIN 301 AB  Fall 2011 W Ten? D. Nixon. Miami University 71 FiN 301 AB  Fall 2011 E:——“ ' “'*— _
L sture I 7 m __   m— “VaW" '_ _:—Lecture 10 m e w Example 1: CDUYW IMQ‘igqg‘f‘ 7mg? : \ﬁm 1 I
You are interested in investing in a bond with an annualgoupon ﬂeﬂgfiezﬁ percent. Coupon payments are made on a semiannualhﬁasis.’ Thé'ﬁond has a face value of
$1,000 and 7 years to maturity. Similar bonds are currently yieﬁing 10 percent to their
owners. How much should you be willing to pay for this bond? The valuation (pricing) of bonds and stock is a straight forward application of the time
value of money (TVM) concepts we have just studied. r  ’r
Bonds and stock arej t ' f h ﬂ W TIMEL'NEi l——I5H_g_.__:_r__,
us series 0 cas ows. hat kinds of cash flows are rece‘ d It; .
from bonds? What kinds of cash ﬂows are received from stock? we 72 7M ‘75 735 [312%
gawk“Cme Poﬁhow'roﬂi \Dlle
. : [Wm
, —  ~  . Mural
Stools alum dle WINK Wired Mm PM W“ x mufﬁn rm Mo K may
_ COUPON PAYMENT = M ; ———i——_..
[POSJUQ
YTM = l0 = 72.5 G
Regardless of the assets nam .
(today) Of its cash flows, e. the current Value Of any 38381 rs the present Value M = 2.
N = in i W l BOND VALUATION BOND PRICE: 7L§[__LL+_—i] +Q+—l°)'+ : 112171 Bond Timeline: [W Bond Value = SCOUPON PMT [:39 + YTM KM)” W] + szCE MLUE [on L (I + YTJLI I M l” PM, You are considering buying the bond listed above when suddenly, the yield on similar bonds jumps to 20 percent. Will the bond’s price increase or decrease? Why? Coupon payment) with a "e that bonds are simply a TEClﬂl‘k’. LinW’s: relicuhmiﬂ lump Sum {the face value). ‘ i it l
(Note: Coupon patrment is an; all“ A fed“! “mm WK w” T ‘31 a) ” J‘ "x J o  mama T. Bliss, Bataan Univth
., _ . and'l' DN' Min "Univ ‘
Nu— FIN 301 A,B  Fall 2011 o . mam T 355,, mm um  my mm, an Emmy
‘ W 72 “m”? 0' “mm” “M” . T3 FIN 301 A,B — Fall 2011 4_ when a hands yield (required ra FIN 301 AB — Fall 2811 ‘ E" "W" _
e we m Lemmﬂ [EEL‘m—w_ﬁ I page 7;}
El Pra t. : ' I  . _
I c rceT WhaEEFtE bond 8 new price wrth the 20 percent yield? ‘ PREFERRED STOCK VALUATION L [A bnﬂt
“$3125 “ W“ N i too " V ,J + gee)“ (5.1317 i
‘2. 7— The value of preferred stock is also determined by its cash flows. Preferred stock
: T17. g; twice"? Pays a 5'6? eeeee _£*___EEJP;I_s_§§@1ﬂ — r
. H f__,,
i i : 1t;  E BI
, I, . Preferred stock timeline: r.
v .3 4m  1;? 9,: H T
53‘ W M“
* 1“ EA T
doth; Q: What formula have we used up to now to account for just this type ofcas'h flow Purchase. What IS the bond ' '    2 t5 ,7 I“. VHF”; 8 price If the yield on srmllarbonds becomes 14.5 percent? stream? ._ f‘ﬂ“,r'yrm'.ﬁ
a 3 7;. 7‘, I W5: _ qum'rgi C1;
11:.“ 1‘ ' . 14  . 7! a v 
. . .. _ A' W 43$ 'L~
a .7 Lmi
Dp
Preferred Stock Value = VP =
:9
Where: 0,, = the constant preferred stock dividend
rp = the cost (required rate of return) of the preferred stock Things to note on bond pricing: Note: As with other perpetuities. this formula gives you the vaiue of the preferred stock
one period prior to receipt of the ﬁrst preferred dividend payment. Example 2: M, Herb Enterprises pays an annuat preferred dividend of $1.75 and the required rate of
return on simiiar ﬁnancial instruments is 8.3 percent. How much shoutd you be willing to
pay for a share of Herb’s preferred stock? Assume the ﬁrst dividend is to be received in one year. price Is greater than Its face (ma © v Ricl'nrd T. Babsmt Hubentry
I 9_mtmlrmauw MTcrryD.Ntson,Misnul}mrccmy
74 and Terry D. Nixon, Mum; UM I. 75 FIN 301 A13 — Fat! 201 1 — Lecture 10 _ 1'6 —Lemure m n  77
Practice: If you receive the dividend from example 2 immediately, how much should where. QSSLli‘upliul 2
you now be Willing to pay for a share of Herb’s preferred stock? Why? ' l) is inﬁdel ﬂ\ Q} k 1 Do = the dividend paid at the start of constant growth a, . “J  t s— '2 l' ‘5 ‘ 5‘ l5 3 _ rs = the cost (required rate of return) of common stock 1) y a g = the constant growthrateaof the dividend
l ) iZiwz'f _ "—
Example 3: You own a share (ﬁt—Tb, Inc’s corllmnoen stock and have—lj‘usftjtecéiveﬁja $3.00 dividend
(i.e., it is currently in your pocket), and you expect dividends tEgTUW‘by 12 percent per 5 COMMON STOCK VALUATION year hereafter. If you require a 16 percent rate of return on this particular investment,
how much should you be willing to pay for a share of thls stock? Common stock valuation is a slight! '  "‘1 ‘ "ll 1“ 7’
_ I Y more compilcated task than either bonds or  M“ l “"0
grained stock because leldend payments are van'abjeminrnatgre common Stock TIMELINE' ‘ A __ .1 "
WI elldsare typically not ConstanL. Simple annuity and perpetuity formulas  ill t be Ell—l“;
enough to value common stock. w no D _ _' , A.
o  3
Never fear” Given you knowledge of th
I e valuation of lum =
perpeturtles we wrli stlll be able to value common stock 95::21233lggglflztlsngrgggt; g 1
Constant growth rate r5 = ll
If we are able to assum  
(g)! the valuation of corfnigitSiEFkabZIlggfsendts are going to grow at a constant % rate COMMON STOCK PRICE = all .
familiar. a 35" W'th whlch you should already be Rm) : 1)] :44
n l 1— a ‘5
Cost t ' ' ‘3 “we ._. _
n an 9"th “melme Q: What is the value of a share of RTC's common stock It leldends are not predicted to
CH 9; grow? “  ll‘l‘C‘.) l‘l ’tsu‘ I I H
In general how would you valué‘l; ’ ‘k “l
In, ‘. 77h ‘ ommorlst . Q; I‘ rﬂ_
rate? T" “1 "1M lili‘l‘l'} 00k that IS Supposed t0 grow at a constant A: fig—q : ll l5 l5
(Rn ‘llG ‘ V
l‘ 9)
Common Stock Value (With all constant growth)_ P E[Do(1+ g) D
 = I
(rs—g) [G's—3)]
e  Richard T. Bliss, Babson University
© _ . T. BBS, Baum I and Terry D. Nixon, Miami Urdrem'ty
FIN 301 A,B —F ti 201 “’dm" . . . . 
a 1 “may 0 NmmMmrUm‘ﬂ” 77 FIN 301 A,B  Fall 2011 76 — m7ff’ "" " imp ENE 10 “in 1 a 879
Mm El Practice: Seuss & Sons, Inc. has just paid a dividend of $3.00 per share. They will
increase dividends by 5% per year for two years. They will then increase dividends
Example 4: Suppose that the Goku Corp. has just paid you a dividend of $1.50. You by 4% for two years. Aftewvards, dividends will grow pyji for the foreseeable
think that their dividend payments will grow by 8 percent in the ﬁrst year, 10 percent in future. If the appropriate rate of return on their stock isyjjf/E how much _shouid you
the second year, and will then grow by 11 percent thereafter. Given their current level of be Willing to Pay for tit/EEC in four V935? Assume YOU hat/e JUSt recewed the
risk, you require a return of 14 percent on your investment in their stock. How much diVidend they Wi” Payk®mm now should you be willing to pay for a share of their stock? I withf iii w a *2. at s face up. [.1351 I‘lig’uj g 3.1;: may; j 35‘i47i37b
Q: The dividend payments are not initial! ‘ TamC ‘5 S e
_ ygrowm b aconstantra . 7733”
this Stream of cashﬂows? 9 V te How can we value
A? Ll‘ J x l w 1 ﬁatj.
MW? “mm9 U“ m «J . \ yum} pgm‘wt) 1 Limaoh
~ll  ~03
D1 _' ‘ _ ‘r a
l L; [32 .l 03. “? 1 q r
l r _ \ “H L. 0 \ L J ’ _\
S \r ’Y u _H_ Ian“ 1 t t r
‘1' '3 . ‘ivul' ul  '
COMMON STOCK PRICE = ' ’ '
‘ ‘. A 1 ' f l .:_'_...s_..# at. __
.. 9:.“ 4 m. H:  ,; _ ‘\
:erZ L l v
_ﬂ f .__* _ w y
l t . . . a ’ Z
r_:.lul mm rim 3‘75 ‘
© — Richard T. Biiss, Babson Univeth
K and Terry D. Nixon, Lﬁaﬂﬁ [inﬁnity
0.  7 I'd“!
L F'“ 3‘” A'B'Fa'mo” 78 mkt'fcwd'giﬂimww ' . 79 FIN 301A,BFall2011 Lectu 1 7' """_ ' ' .__.,__
g“! 0 :Lemn Common stock valuation with a known end price RISK AND RATES OF RETURN In the unlikely scenario that we know a price we can sell common stock at in the future, valuation of common stock becomes an easy task. . computing expected returns Example 5: Recently you were struck by a lightning bolt. Upon awakening from your ' Standard deﬂation as a measure 0f “3k
03m: yﬁu found that you had gained the super power to predict future prices of common  risk aversion _3 00 (a the other superheroes laugh at your power). Using your power, you know that . . ‘ "1 exaCﬂY 3 years, you can sell your share of XTC, Inc. for $30. In the meantime you . dlverSiﬁcatlon expect to receive a dividend of $2.00 in one year, $2.25 in two years, and $2.25 in three years immediately before sellin the stock. If '
investment! how much should it] pay forthe ﬁgcfglgraig return of 7 percent on your Remember risk is deﬁned as unceﬁaint of outcome NOT the chance of com lete loss.
\ i 7— :3 Before considering the concept of risk, we look at return, speciﬁcally,
l 1 “ES, 1‘ 1 expected return ~ “WWW Wﬁhﬂd {mmME me_
4r '9:
Fire y, j g ,r 7’" T: 2 Example: Stock A has the following possible returns for the coming year:
WIT“. ' r 9 ‘Fl “h : ! I Q .
“ tint \ LU r , ﬁx" Economic State Boom Average De ressron
m
Expected Return = (return in Boom x prob. of Boom) + (return in Average x prob. of Average) +
(return in Recession x prob. of Recession) + (return in Depression x prob. of Depression),
7' = expected rate of return =
Expected Return = r = 2 {Outcome x Probability}
= P1r1+ P2r2+ . . . + PM}.
3 'IC‘ '5 51¢ '4‘ 9—}?X 311. egg 1;
© 7 Richard T. Blis, Baboon University
and Terry D. Nixon, MinnLi Univcmty
9  ' ‘ ' I :
Fm 301 AB — Fall 2011 as“??? 33m 31 FIN 301 AB — Fall 2011 80 ...
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This note was uploaded on 04/04/2012 for the course FIN 301 taught by Professor Schaeff during the Fall '08 term at Miami University.
 Fall '08
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