Quick Qestions (fast points Both Bond Bill and Bond Ted have 9.4 percent coupons
ID: 2642284 • Letter: Q
Question
Quick Qestions (fast points
Both Bond Bill and Bond Ted have 9.4 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 5 years to maturity, whereas Bond Ted has 22 years to maturity. Requirement 1: If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places (e.g., 32.16).) Requirement 2: If rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of these bonds? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)Explanation / Answer
First Calculate Yield to Maturity of Both Bonds:
Bond Bill:
FV = 1,000, PMT = 1,000*9.4%*.5 = 47, Nper (N) = 5*2 = 10, PV = 1,000 and Rate = To be calculated where FV is face value, PMT is semi-annual interest payment, Nper is period, PV is current selling price) and rate is Yield to Maturity.
Using EXCEL/Financial Calculator, we get the following equation to calculate Yield to Maturity:
Yield to Maturity = Rate(Nper,PMT,PV,FV)*2 = Rate(10,47,1000,1000)*2 = 9.40% (we multiply the equation by 2 to find annual YTM)
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Bond Bill:
FV = 1,000, PMT = 1,000*9.4%*.5 = 47, Nper (N) = 22*2 = 44, PV = 1,000 where FV is face value, PMT is semi-annual interest payment, Nper is period, PV is current selling price) and rate is Yield to Maturity.
Using EXCEL/Financial Calculator, we get the following equation to calculate Yield to Maturity:
Yield to Maturity = Rate(Nper,PMT,PV,FV)*2 = Rate(44,47,1000,1000)*2 = 9.40% (we multiply the equation by 2 to find annual YTM)
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Requirement 1: Calculate % Change When Interest Rates Rise by 2%:
Bond Bill
FV = 1,000, PMT = 1,000*9.4%*.5 = 47, Nper (N) = 5*2 = 10, PV = To be calculated, Rate = 9.40-2 = 11.40%/2 where FV is face value, PMT is semi-annual interest payment, Nper is period, PV is current selling price) and rate is Yield to Maturity
To calculate price, we use another EXCEL/Financial Calculator Equation:
revised Price = PV(Rate,Nper,PMT,FV) = PV(11.40%/2,10,47,1000) = $925.34
% Change in Price = (Revised Price - Original Price)/Original Price*100 = (925.34 - 1,000)/(1000)*100 = -7.47%
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Bond Ted
FV = 1,000, PMT = 1,000*9.4%*.5 = 47, Nper (N) = 22*2 = 44, PV = To be calculated, Rate = 9.40+2 = 11.40%/2 where FV is face value, PMT is semi-annual interest payment, Nper is period, PV is current selling price) and rate is Yield to Maturity
To calculate price, we use another EXCEL/Financial Calculator Equation:
revised Price = PV(Rate,Nper,PMT,FV) = PV(11.40%/2,44,47,1000) = $839.87
% Change in Price = (Revised Price - Original Price)/Original Price*100 = (839.87 - 1,000)/(1000)*100 = -16.01%
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Table When, Interest Rates Rise by 2%:
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Requirement 3:Calculate % Change When Interest Rates Fall by 2%:
Bond Bill
FV = 1,000, PMT = 1,000*9.4%*.5 = 47, Nper (N) = 5*2 = 10, PV = To be calculated, Rate = 9.40-2 = 7.40%/2 where FV is face value, PMT is semi-annual interest payment, Nper is period, PV is current selling price) and rate is Yield to Maturity
To calculate price, we use another EXCEL/Financial Calculator Equation:
revised Price = PV(Rate,Nper,PMT,FV) = PV(7.40%/2,10,47,1000) = $1,082.33
% Change in Price = (Revised Price - Original Price)/Original Price*100 = (1,082.33 - 1,000)/(1000)*100 = 8.23%
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Bond Ted
FV = 1,000, PMT = 1,000*9.4%*.5 = 47, Nper (N) = 22*2 = 44, PV = To be calculated, Rate = 9.40-2 = 7.40%/2 where FV is face value, PMT is semi-annual interest payment, Nper is period, PV is current selling price) and rate is Yield to Maturity
To calculate price, we use another EXCEL/Financial Calculator Equation:
revised Price = PV(Rate,Nper,PMT,FV) = PV(7.40%/2,44,47,1000) = $1,215.63
% Change in Price = (Revised Price - Original Price)/Original Price*100 = (1,215.63 - 1,000)/(1000)*100 = 21.56%
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Table When, Interest Rates Fall by 2%:
%Change in Price Bond Bill -7.47% Bond Ted -16.01%Related Questions
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