(ICF)Jim Cook

Cook-Hauptman Associates, Inc. (USA)

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(Sessions am: 8:30-12:00, pm: 1:30-5:00): , , , , : ; (Sessions am: 8:30-12:00, pm: 1:30-5:00): . : : (Sessions am: 8:30-12:00, pm: 1:30-5:00): : : (Sessions am: 8:30-12:00, pm: 1:30-5:00): : , , , eBay : .

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: 10,000, 2 3 ?012100001188131090012950 = ( ) * ( 1 + ) RMB; 9%

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: 310,000, ?012772291743841810000 = ( ) / ( 1 + ) RMB

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:

Vt+T = Vt * (1 + r ) T

V(t+T) = V(t) * (1 + r) T ()

V(T) = V * (1 + r) T (t0)

FV = PV * (1 + r) T

:r ()T Vt t ( t=0, PV)Vt+T t+T ( FV)

: t 0, +. , t

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?: 5000 RMB,10%,?

T :Vt+T = Vt * ( 1 + r ) T

10000 RMB= 5000 RMB * (1.10 ) T

(1.10 ) T = 2 = 10 log(2) = 10T * log(1.1)

T = log(2) / log( 1.10 )

= 7.27

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?: 600,000. 200,000, ?

r :Vt+T= Vt * (1 + r ) T

600000= 200000 * (1 + r ) 15

(1 + r ) 15= 600000/200000 = 3

(1 + r )= 3 (1/15) = 3 .06666 = 10 .06666 * log103

log10(1 + r) = .06666 * log10 3 = .0318

(1 + r )= 10 .0318 = 1.076 r = (1+r) 1 = 1.076 1 = 7.6%

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: 5, 4%, 7%. 1, ?

PV : FV = PV * (1 + r ) T

r is not 3%, but 2.8846% or 1 + ( 1.07 / 1.04 )

1000000 * (1 + .04) 5 = PV * (1 + .07) 5 PV = 1000000 * (1.04 ) 5 / (1.07) 5

PV = 121665 / 1.40255 = 86745

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: , ?

FVYr = PV * ( 1 + r / 4 ) 4 * Yr

FV2 = 10000 * (1+.09/4) 4 * 2 = 11948 not 11881 RMB

FV3 = 10000 * (1+.09/4) 4 * 3 = 13060 not 12950 RMB

PV = 10000 / (1+.09/4) 4 * 3 = 7657 not 7722 RMB

10 = 5 x (1+.1/4) 4 * Yr Yr = log2/(4*log1.025) = 7.02 7.27 Yrs

(1 + r / 4 ) = 3 4 * Yr = 10(1/(4*15))*log3) = 1.01848 r = 7.4% 7.6 %

10 6 = PV * ((1+.07/4) 4 * 5 / (1.04) 5) PV = 85996 86261

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(AIR)Bank, Annual Interest Rate is X% at m*X/12% every m monthsThe stated rate was X%, but the EAR is (1+m*X/12)^12/m - 1The simple treatment; off a little bit from the compounded

(EAR): EAR = (1 + AIR / m ) m 1 (This should be the rate for internal decisions)

: Bank says, AIR is 8.00%, compounded quarterly It means, Effective Annual Interest Rate is 8.24% Advertisement says, EAR is 8.24%, compounded quarterly It means, Quarterly compounding rate is 2.00%

FV = PV * e r * T V(0+T) = V(0) * e r * T (e= 2.71828)

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MBA

, . ,

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I ()PV = C/(1+r)1+C/(1+r)2 C/(1+r) = C * 1 / (1+r) t = C/r

: . , , ? C/R. (C). r (), : P/E? ?

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II PV = C0 * [ ( 1 + g ) t - 1 / ( 1 + r ) t ] = C0 / ( r g )

(annual fixed payout for fixed duration)PV = C * [ [ 1 / (1 + r ) t ] - [ 1 / (1 + r ) T + t ] ] = C * [ (1 / r ) - 1 / (r * (1+ r ) T ) ] = C / r * [ 1 - 1/ (1+r) T ] FV = C / r * [ (1+r) T 1 ]

(constant payout / period for fixed duration)PV = n * ( C / r ) * [ 1 - 1 / (1 + r / n ) n * T ] : n = /

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(face amount paid upon maturity) PV = Face / ( 1 + r ) T where T = periods until maturity

(periodic payments plus maturity) PV = n * C / r * [ 1 - 1 / (1 + r / n ) n * T ] + Face / (1 + r ) T

note: n is times paid per year (could even be , if paid every other year) C is the regular coupon payment and r is the discount rate

(given the market price, whats the yield)note: you have to solve the above equation for r which is difficult for r>2and impossible, in the general case, for r>6Procedure: Set up a NPV in a spreadsheet and when NPV = 0 the discountrate is the Bond Yield to Maturity.

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(NPV): (0)

LIBR: ()

:NPV = - C0 + C1/(1+r) + C2/(1+r)2 + ... + CT/(1+r)T

(1T), (C0 T=0)

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: 111.300 , 112.645 , ?

= ( / ) * ( ) / = -

= 4 * ( 112.645 111.300 ) / 111.300 = .048

: 4.8% . 4.8% . : ,??

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Note: r = rational prime interest rate in country of subscript for period given by the forward duration where annual is EAR computed.

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Value of US bond = $1,000,000 * 1.05 = $1,050,000

Value of Japan bond = $1,000,000 * 112.645 = 112,645,000 yen exchange 112,645,000 yen * 1.0025 = 112,927,000 yen bond pmt 112,927,000 yen / 107.495 = $1,050,500 exchangeExample - You have the opportunity to invest $1,000,000 for one year. All other things being equal, you have the opportunity to obtain a 1 year Japanese bond (in yen) @ 0.25 % or a 1 year US bond (in dollars) @ 5%. The spot rate is 112.645 yen:$1 The 1 year forward rate is 107.495 yen:$1 Which bond will you prefer, why? With and without transaction costs?

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2%,2.5%, ? : 112.645Yen=$1Es = 107.68

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+ 1+ 1 ? ?

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