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**Unformatted text preview: **ECF2331 Tepic 2
Interest Rates and the Bend Market [I] Discounting and Present Value [II] Measuring Interest Rates [III] The Band Market Disceunting Future Payments Principal = $1DD
I: [1.11] =1D% In one year $1DDs{1+D.1D} = $11IC]|
9' In two years $11Ds{1+ﬂ.1ﬂ}= $121
= $1ss:i;{1+i:r.1i:iiE in three years $121 s{1+ﬂ.1ﬂ}= $133
= 1131131131-1'{1+[lh1ﬂ]3 In N years $1DD s {1+D.1D}“ — Each dellar receiyedrpaid in the future is iess
yaiuahie than a deliar receiyedrpaid new — The payment receiyed in the future needs te he
disceunted hack ta teday’s yaiue fer a meaningful cemparisen Present Value i‘r Present Value [PU] c-f a future amc-unt c-f payment is the current wc-rth c-f
future cash fic-ws {CF} given a speciﬁed rate pf interest if}. CF PV=—
(1+.i)ﬂ 3% After cc-nyerting each stream c-f future payment tc- its present yaiue. we can
cpmpare payments scheduied at different times. $10G $110 $121 CF
Year 0 1 2 n W 100 11D!{1+i) 121,I"(1+i}2 GFI(1+i]“ YTM an A Simple Lean 5-“- The lender prdyides the ladrrewer with a given amdunt effunds called the principal; 5-“- The funds. aldng with an additidnal payment fer the interest. must be repaid tn the
lender in a single payment at the maturity date. PM“ = amdunt borrowed = $1131] CF = cash flow in one year = $111] a: number dfyears = 1
$1113 {1+ i)‘
n+n$1aa=$11a
1+l = 1.1 $100 = i=ﬂ.1=1ﬂ% Interest Rate = VTM = 10% YTM an A Fixed-Payment Lean 3-“- The lender prdyides the bdrrdwer 1with a giyen amdunt effunds called the principal; i=- The same cash flew payment, censiating at part dfthe principal and interest, needs
td he made eyery peridd thrdughdut the life dfthe lean. P9 = Lean Value = $19,999 Fixed yearly payment = $9,439.29 :1 = number pfyeara until maturity = 29 $9,439.29 $9,439.29 $9,439.29 $9,439.29 mean = —_+—_+—_+..._‘
$ 1 +1 (1 +11)2 [1 + 1113 (1 +1)“ i=?% Interest Rate = VTM = 7% YTM on a 10%-coupon-rate bond maturing in 10 years
(face value = $1,000) 1L‘E'ielilis to Maturity an a lﬂﬁ-EnupuII-Rate Bend Hatuting in Ten Years
[Face Value = $1,000) Price of Bond ($11 Yield to 11".laltllrilj.Ir (‘11:)
1,200 T.13
1,100 0.40
1,000 10.00
900 11.?5
800 1131 3* Price of the pond is negative re iated to WM 3* If coupon pond price = face wraiue, ‘r‘TM equais the coupon rate. 3* If coupon pond price is beiow its face vaiue, ‘r‘TM is greater than the coupon rate; If coupon bond price is above its face vaiue, ‘r‘TM is iess than the coupon rate. Other Bonds is A discount bond is bought at a price below its face value {at the discount) and the
face value is re paid at maturity date. No coupons — also called zero-coupon bond. Face Value = $1 .ﬂﬂﬂ [to be repaid in one yea r} Current Price = $9DD $1,ooo _
$soo= 1+, —r WM=I=11.1%
i 3* A consol or perpetuity has no maturity date and does to repay the principal,
but instead proyides ﬁxed coupon payment foreyer. P = Price of the consol {i.e. today's yalue} E: ﬁxed coupon payment
i: ”field to maturity of the consol For long—term bonds. matu rlty date is far a way. Hence. i=CrF' can be used to
approximate WM. Thls approximation ls called the current yield. Rate ef Return vs. Interest Rate Irv Rate of return an a hand measures hc-w well eff an inyestc-r is lay awning the hand. Irv Rate of return equals the payments tcu the hc-lder at the hand [e.g. $1DD} plus the
change in value dfthe lacund [e.g. $2DD}. expressed as a fractic-n c-f its initial purchase price.
FHCE 1I.I"E:ilUIl'-i = $1.UDD Rate _ $113.] + ($1’2ﬂﬂ _ $1,0ﬂﬂ]
Yearly cc-upc-n payment = $1DD 01” $1.0ﬂﬂ Return = sass Selling price in cmeyear’s time = $1.33!? Irv Rate of return _ +
frc-m ttc- t+I Rate at
Cprrent Capital
"field Gain :rr Rate of return dues n_et necessarily equal the ‘I'TM. Irv A rise in interest rates means a fall in hand prices. which can result in capital less and
therelay a lewer rate c-f return. Irv The risk cufinterest rate changes is called interest rate risk. Trading Icing-term hands
inyc-lyes mere risk than trading shcurt—term hands. Nominal vs. Real Interest Rates Nominal interest rate is not adjusted for inflation. Real interest rate is adjusted for inflation so it more accurately reflects
the true cost of borrowing. Fisher Equation f = nominal interest rate
fr = real interest rate
a” = expected inﬂation rate Ex ante real interest rate is adjusted for expected changes in the
aggregate price level. Ex post real interest rate is adjusted for actual changes in the
aggregate price level. 1,0013
{maﬁa} 95D
ii= 5.3%} 900
{i=11.1%} {FF-1:33;; Equiiihrium am
[i = 25.0%} THEE
if: 33.D%] "-"n-"I'l-"I L::-:.-: :-.-'=..-=.~.-_. |'.‘-'I'.'"H'|-H."|I'.1. ii'I-S—j- tilt—MW! :':-'I-:T.'&.': FIE-1'." .'-_'-. 11:: f1" 1m 2m 3m 4m 5m Eiuan‘lity uf Bands. 5
iii billinns} Shift in Demand Curve fer Bends “Uhatfacters
Price of Bonds. P shift D-cu FVE tetheright? An increase in the demand fer
bends E-HIHE the. bend demand
curve rightward. Expected
Interest Expected
I Return on
Hands Expected lnﬂaﬁen Quantity of Bonds, 3 Price cf Bends. P Shift in Supply Curve fer Bends Quantity cf Bends, B What factors
shift S-curve tn the right ? of Preﬁtahility
Investments I Arr rncreese in the supc-Iy' c-f
trends shlﬁs the b-ﬂl'ld Supﬂly‘
c: L] we rig h 1. we r cl. Expected
lnflatiun Government
Budget
Deﬁcit Response to A Change in Expected Inﬂation Price Di 3mm1 p Step 2. end ehiite
the bend eueelyr
eurue ngt'itwerd . . _ Step ii- eeueing P
the price ei bends. te tell and the
equilibrium Step 1. A rise in interest rate te nee. P2 expected inlletien
ehihe the trend
demand cu we leftward . _ _ Quantity of Bonds. 5 Fisher Effect: when expected inﬁetien rises. interest rates will rise [e.g. prices will fall} Response to A Business Cycle Expansion Price of Bands, F Step 2. and shifts- the bend
Eierhenrj curve rigiwhmard. hut _ 5
by a lesser arr'leuh‘t . . . E 1 Ste; 1 . A business cycle
e:—;pensten shifts. the bend supply curve rightward . . .
I
BE _- .--. .- , -_ _._
:JEE'E: :3. Eu the grim: hf t:::‘.-:='!~’_1:E. fats and the eel_1§!éb:+'=-s_ih"- “IE-"EST r‘EiE' H1393. Quantity of Bonds, 5...

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