1. SINGLE CASH FLOWPART 1PROBLEMS**SINGLE CASH FLOW1. PRESENT VALUE1. PRESENT VALUEINPUTINPUTSingle Cash Flow$1,000.00CSingle Cash Flow$1,673.48CDiscount Rate / Period6.0%rDiscount Rate / Period7.8%rNumber of Periods5nNumber of Periods4nPRESENT VALUE USING A TIME LINEPRESENT VALUE USING A TIME LINEPeriod012345t Period01234t Cash Flows$0.00$0.00$0.00$0.00$0.00$1,000.00CiCash Flows$0.00$0.00$0.00$0.00$1,673.48CiPresent Value of Each Cash Flow$0.00$0.00$0.00$0.00$0.00$747.26PviPresent Value of Each Cash Flow$0.00$0.00$0.00$0.00$1,239.21PviPresent Value$747.26PVPresent Value$1,239.21PVPRESENT VALUE USING THE FORMULAPRESENT VALUE USING THE FORMULAPresent Value$747.26Present Value$1,239.21PRESENT VALUE USING THE PV FUNCTIONPRESENT VALUE USING THE PV FUNCTIONPresent Value$747.26Present Value$1,239.212. FUTURE VALUE2. FUTURE VALUEINPUTINPUTSingle Cash Flow$747.26PVSingle Cash Flow$932.47PVDiscount Rate / Period6.0%rDiscount Rate / Period3.9%rNumber of Periods5nNumber of Periods4nFUTURE VALUE USING A TIME LINEFUTURE VALUE USING A TIME LINEPeriod012345tPeriod01234tCash Flows$747.26$0.00$0.00$0.00$0.00$0.00PviCash Flows$932.47$0.00$0.00$0.00$0.00PviFuture Value of Each Cash Flow$1,000.00$0.00$0.00$0.00$0.00$0.00FviFuture Value of Each Cash Flow$1,086.67$0.00$0.00$0.00$0.00FviFuture Value$1,000.00FVFuture Value$1,086.67FV

FUTURE VALUE USING THE FORMULA FUTURE VALUE USING THE FORMULAFuture Value$1,000.00Future Value$1,086.67FUTURE VALUE USING THE PV FUNCTIONFUTURE VALUE USING THE PV FUNCTIONFuture Value$1,000.00Future Value$1,086.67

PV = C / (1+r)tPV = C / (1+r)n = - PV(r,n,t1,C)FV = C*((1+r)^(n-ti)

2. ANNUITYPART 1PROBLEMS**ANNUITY1. PRESENT VALUEINPUTSingle Cash Flow$80.00CDiscount Rate / Period6.0%rNumber of Periods5n

ANNUITY VALUE USING A TIME LINEPeriod012345t Cash Flows$0.00$80.00$80.00$80.00$80.00$80.00CiPresent Value of Each Cash Flow$0.00$75.47$71.20$67.17$63.37$59.78PviPresent Value$336.99NPV

ANNUITY VALUE USING THE FORMULAPresent Value$336.99

ANNUITY VALUE USING THE PV FUNCTIONPresent Value$336.99

2. FUTURE VALUEINPUTSingle Cash Flow$80.00PVDiscount Rate / Period6.0%rNumber of Periods5n

ANNUITY VALUE USING A TIME LINEPeriod012345tCash Flows$0.00$80.00$80.00$80.00$80.00$80.00PviPresent Value of Each Cash Flow$0.00$101.00$95.28$89.89$84.80$80.00FviPresent Value$450.97FV

ANNUITY VALUE USING THE FORMULAPresent Value$450.97

ANNUITY VALUE USING THE PV FUNCTIONPresent Value$450.97

*SYSTEM OF FOUR ANNUITY VARIABLESINPUTSingle Cash Flow$80.00CDiscount Rate / Period6.0%rNumber of Periods5nPresent Value$336.99PVPAYMENTPayment using the FormulaPayment using the PMT FunctionDISCOUNT RATE / PERIODdiscount Rate / Per using the Rate FunctionNUMBER OF PERIODNum of Period using the NPER FunctionPRESENT VALUEPeriod012345t Cash Flows$0.00$80.00$80.00$80.00$80.00$80.00CiPresent Value of Each Cash Flow$0.00$75.47$71.20$67.17$63.37$59.78PviPresent Value using a Time Line$336.99NPVPresent ValuePresent Value

NPV = C / (1+r)tNPV = C*((1- (1+r)-n)/r)= - PV(r,n,C,t1)FV = C*((1+r)^(n-ti)NPV = C*(((1+r)n)-1)/r)=PV(r,n,C,t1)

6. BOND VALUATIONPART 1**BOND VALUATION
Author: NH GI TRI PHIUAnnual Percentage RateINPUTSRate Convention: 1 = EAR, 0 = APR0Annual Coupon Rate (CR)
Author: li sut hng nm5.0%Yield to Maturity (kd)9.0%Number of Payments / Year (NOP)
Author: S Thanh ton / nm2Number of Periods to Maturity (N)8Face Value (M)
Author: Mnh gi $1,000OUPUTSDiscount Rate / Period (DR)4.5%Coupon Payment (INT)$25CALCULATE BOND PRICE USING THE CASH FLOWSPeriod012345678Time (years)0.00.51.01.52.02.53.03.54.0Cash Flows$25.00$25.00$25.00$25.00$25.00$25.00$25.00$1,025.00Present Value of Cash Flow$23.92$22.89$21.91$20.96$20.06$19.20$18.37$720.76Bond Price$868.08CALCULATE BOND PRICE USING THE FORMULABond Price$868.08

CALCULATE BOND PRICE USING THE PV FUNCTIONBond Price$868.08$868.08FALSECALCULATE BOND PRICE USING THE PRICE FUNCTION (under APR)Bond Price$868.08

6.2 Maturity**BY YIELD TO MATURITYINPUTSRate Convention: 1 = EAR, 0 = APR0Annual Coupon Rate (CR)
Author: li sut hng nm5.0%Yield to Maturity (kd)9.0%Number of Payments / Year (NOP)2Number of Periods to Maturity (N)8Face Value (M)$1,000OUPUTSDiscount Rate / Period (DR)4.5%Coupon Payment (INT)$25CHART OUTPUTSYield to Maturity (Annualized)1.0%2.0%3.0%4.0%5.0%6.0%7.0%8.0%9.0%10.0%11.0%12.0%13.0%14.0%15.0%16.0%17.0%18.0%19.0%20.0%Discount Rate / Period0.5%1.0%1.5%2.0%2.5%3.0%3.5%4.0%4.5%5.0%5.5%6.0%6.5%7.0%7.5%8.0%8.5%9.0%9.5%10.0%Bond Price$1,156$1,115$1,075$1,037$1,000$965$931$899$868$838$810$783$756$731$707$684$662$640$620$600

6.3 Dynamic**DYNAMIC CHARTINPUTSRate Convention: 1 = EAR, 0 = APR00Annual Coupon Rate (CR)
Author: li sut hng nm3.0%600.0%Yield to Maturity (kd)1.5%300.0%Number of Payments / Year (NOP)22Number of Periods to Maturity (N)501Face Value (M)$1,000

OUPUTSDiscount Rate / Period (DR)0.8%Coupon Payment (INT)$15

TIME TO MATURITY123456789101112131415161718192021222324252627282930Number of Period to Maturity2.04.06.08.010.012.014.016.018.020.022.024.026.028.030.032.034.036.038.040.042.044.046.048.050.052.054.056.058.060.0Bond Price of a Coupon Bond$1,015$1,029$1,044$1,058$1,072$1,086$1,099$1,113$1,126$1,139$1,152$1,164$1,177$1,189$1,201$1,213$1,224$1,236$1,247$1,258$1,269$1,280$1,291$1,301$1,312$1,322$1,332$1,342$1,352$1,361Bond Price of Par Bond$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000

1. Annual tng --> Coupon Bond gim, INT tng, biu i ln2. Yield tng ---> Coupon Bond gim, DR tng, biu i xung3. Number of Payments tng ---> Number..Maturity tng, INT tng, DR gim4. Face value tng --> INT tng, coupon Bond tng, Par Bond tng, Biu tng5. Par Bond khng ph thuc, khng thay i theo Time6. Annual tng --> Yield ???

6.4 SYSTEM **SYSTEM OF FIVE BOND VARIABLESAnnual Percentage RateINPUTSRate Convention: 1 = EAR, 0 = APR0Annual Coupon Rate (CR)
Author: li sut hng nm5.0%Yield to Maturity (kd)9.0%Number of Payments / Year (NOP)2(1) Number of Periods to Maturity (N)8(2) Face Value (M)$1,000(3) Discount Rate / Period (DR)4.5%(4) Coupon Payment (INT)$25(5) Bond Price$868.08(1) Number of Periods to Maturity (N)Number of Periods to Maturity using the NPER Function8(2) Face Value (M)Face Value using the FV Function$1,000Face Value using the Formula$1,000(3) Find Discount Rate / Period (DR)Discount Rate / Period using the Rate Function4.5%(4) Coupon Payment (INT)Coupon Payment using the PMT function$25Coupon Payment using the Formula$25(5) Bond Price Bond Price using the PV Function$868.08Bond Price using the Formula$868.08

PROBLEMS**PROBLEMS
Author: NH GI TRI PHIUAnnual Percentage RateINPUTSabcdeRate Convention: 1 = EAR, 0 = APR000Annual Coupon Rate (CR)
Author: li sut hng nm4.6%0.5%100.0%Yield to Maturity (kd)8.1%1.0%200.0%Number of Payments / Year (NOP)
Author: S Thanh ton / nm222Number of Periods to Maturity (N)101086839250050Face Value (M)
Author: Mnh gi $1,000$1,000$1,000$1,000$763$1,000$1,000

OUPUTSDiscount Rate / Period (DR)4.1%3.2%4.5%5.7%3.8%4.3%0.5%Coupon Payment (INT)$23$40$27$30$45$37$3Bond Price$858.41$1,067.55$880.00$865.00$872.00$887.00

CALCULATE BOND PRICE USING THE CASH FLOWSPeriod012345678910Time (years)0.00.51.01.52.02.53.03.54.04.55.0Cash Flows$23.00$23.00$23.00$23.00$23.00$23.00$23.00$23.00$23.00$1,023.00Present Value of Cash Flow$22.10$21.24$20.42$19.62$18.86$18.12$17.42$16.74$16.09$687.79Bond Price$858.41

CHART OUTPUTSYield to Maturity (Annualized)1.0%2.0%3.0%4.0%5.0%6.0%7.0%8.0%9.0%10.0%11.0%12.0%13.0%14.0%15.0%16.0%17.0%18.0%19.0%20.0%Discount Rate / Period0.5%1.0%1.5%2.0%2.5%3.0%3.5%4.0%4.5%5.0%5.5%6.0%6.5%7.0%7.5%8.0%8.5%9.0%9.5%10.0%Bond Price$1,175$1,123$1,074$1,027$982$940$900$862$826$792$759$728$698$670$643$618$593$570$548$527Number of Periods to Maturity using the NPER Function39eFace Value using the FV Function$763dDiscount Rate / Period using the Rate Function5.7%cCoupon Payment using the PMT function$27bBond Price using the PV Function$1,067.55aTIME TO MATURITY123456789101112131415161718192021222324252627282930Number of Period to Maturity2.04.06.08.010.012.014.016.018.020.022.024.026.028.030.032.034.036.038.040.042.044.046.048.050.052.054.056.058.060.0Bond Price of a Coupon Bond$995$990$985$980$976$971$966$962$957$953$948$944$939$935$931$926$922$918$914$910$906$901$897$894$890$886$882$878$874$871Bond Price of Par Bond$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000

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