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Exam 15: Bond Valuation and Sinking Funds

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A $100 000,7.5% bond with semi-annual coupons redeemable at 106 is bought three years before maturity to yield 8% compounded semi-annually.What is the purchase price?

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FV = $100 000(1.06)= $106 000; P/Y = C/Y = 2; PMT = $100 000 FV = $100 000(1.06)= $106 000; P/Y = C/Y = 2; PMT = $100 000 = $3 750; n = 3(2)= 6 PP = 106000.00(1.04)<sup>-6</sup> + 3750.00 = $3 750; n = 3(2)= 6 PP = 106000.00(1.04)-6 + 3750.00 FV = $100 000(1.06)= $106 000; P/Y = C/Y = 2; PMT = $100 000 = $3 750; n = 3(2)= 6 PP = 106000.00(1.04)<sup>-6</sup> + 3750.00 FV = $100 000(1.06)= $106 000; P/Y = C/Y = 2; PMT = $100 000 = $3 750; n = 3(2)= 6 PP = 106000.00(1.04)<sup>-6</sup> + 3750.00

Bonds in denominations of $10 000 redeemable at par in six years and four months are offered for sale.If the coupon rate is 6.5% payable quarterly and the expected yield is 8% compounded quarterly,determine a)the market price; b)the accrued interest; c)the cash price.

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FV = $10 000; PMT = 10 000(0.065)(0.25)= $162.50; a)The interest date preceding the purchase date is 6.5 years before maturity. n = 6.5(4)= 26; P/Y = 4; C/Y = 4; I/Y = 8; i = FV = $10 000; PMT = 10 000(0.065)(0.25)= $162.50; a)The interest date preceding the purchase date is 6.5 years before maturity. n = 6.5(4)= 26; P/Y = 4; C/Y = 4; I/Y = 8; i = <sub> </sub>= 0.02 PP = 10000(1.02)<sup>-26</sup> + 162.50 Market price = $9 245.46 b)The accrued interest two months later = 0.01625; t = = 0.5 c)Cash price = $9 245.46 + 81.25 = $9326.71 = 0.02 PP = 10000(1.02)-26 + 162.50 FV = $10 000; PMT = 10 000(0.065)(0.25)= $162.50; a)The interest date preceding the purchase date is 6.5 years before maturity. n = 6.5(4)= 26; P/Y = 4; C/Y = 4; I/Y = 8; i = <sub> </sub>= 0.02 PP = 10000(1.02)<sup>-26</sup> + 162.50 Market price = $9 245.46 b)The accrued interest two months later = 0.01625; t = = 0.5 c)Cash price = $9 245.46 + 81.25 = $9326.71 FV = $10 000; PMT = 10 000(0.065)(0.25)= $162.50; a)The interest date preceding the purchase date is 6.5 years before maturity. n = 6.5(4)= 26; P/Y = 4; C/Y = 4; I/Y = 8; i = <sub> </sub>= 0.02 PP = 10000(1.02)<sup>-26</sup> + 162.50 Market price = $9 245.46 b)The accrued interest two months later = 0.01625; t = = 0.5 c)Cash price = $9 245.46 + 81.25 = $9326.71 Market price = $9 245.46 b)The accrued interest two months later FV = $10 000; PMT = 10 000(0.065)(0.25)= $162.50; a)The interest date preceding the purchase date is 6.5 years before maturity. n = 6.5(4)= 26; P/Y = 4; C/Y = 4; I/Y = 8; i = <sub> </sub>= 0.02 PP = 10000(1.02)<sup>-26</sup> + 162.50 Market price = $9 245.46 b)The accrued interest two months later = 0.01625; t = = 0.5 c)Cash price = $9 245.46 + 81.25 = $9326.71 FV = $10 000; PMT = 10 000(0.065)(0.25)= $162.50; a)The interest date preceding the purchase date is 6.5 years before maturity. n = 6.5(4)= 26; P/Y = 4; C/Y = 4; I/Y = 8; i = <sub> </sub>= 0.02 PP = 10000(1.02)<sup>-26</sup> + 162.50 Market price = $9 245.46 b)The accrued interest two months later = 0.01625; t = = 0.5 c)Cash price = $9 245.46 + 81.25 = $9326.71 = 0.01625; t = FV = $10 000; PMT = 10 000(0.065)(0.25)= $162.50; a)The interest date preceding the purchase date is 6.5 years before maturity. n = 6.5(4)= 26; P/Y = 4; C/Y = 4; I/Y = 8; i = <sub> </sub>= 0.02 PP = 10000(1.02)<sup>-26</sup> + 162.50 Market price = $9 245.46 b)The accrued interest two months later = 0.01625; t = = 0.5 c)Cash price = $9 245.46 + 81.25 = $9326.71 = 0.5 FV = $10 000; PMT = 10 000(0.065)(0.25)= $162.50; a)The interest date preceding the purchase date is 6.5 years before maturity. n = 6.5(4)= 26; P/Y = 4; C/Y = 4; I/Y = 8; i = <sub> </sub>= 0.02 PP = 10000(1.02)<sup>-26</sup> + 162.50 Market price = $9 245.46 b)The accrued interest two months later = 0.01625; t = = 0.5 c)Cash price = $9 245.46 + 81.25 = $9326.71 c)Cash price = $9 245.46 + 81.25 = $9326.71

A $100 000 bond is redeemable at 105 in 20 years.If interest on the bond is 5% payable semi-annually,what is the purchase price to yield 6% compounded semi-annually?

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FV = 100 000(1.05)= $105 000; PMT = 100000(0.05) FV = 100 000(1.05)= $105 000; PMT = 100000(0.05) = $2500; n = 20(2)= 40; P/Y = C/Y = 2; i = = 0.03 PP = 105 000(1.03)<sup>-40</sup> + 2500 = $2500; n = 20(2)= 40; P/Y = C/Y = 2; i = FV = 100 000(1.05)= $105 000; PMT = 100000(0.05) = $2500; n = 20(2)= 40; P/Y = C/Y = 2; i = = 0.03 PP = 105 000(1.03)<sup>-40</sup> + 2500 = 0.03 PP = 105 000(1.03)-40 + 2500 FV = 100 000(1.05)= $105 000; PMT = 100000(0.05) = $2500; n = 20(2)= 40; P/Y = C/Y = 2; i = = 0.03 PP = 105 000(1.03)<sup>-40</sup> + 2500 FV = 100 000(1.05)= $105 000; PMT = 100000(0.05) = $2500; n = 20(2)= 40; P/Y = C/Y = 2; i = = 0.03 PP = 105 000(1.03)<sup>-40</sup> + 2500

A sinking fund of $100 000 is to be created by equal annual payments at the beginning of each year for 12 years.Interest earned by the fund is 5.5% compounded annually. a)Compute the annual deposit into the fund. b)Construct a sinking fund schedule showing totals.

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Question 4

A $200 000,6% bond with semi-annual coupons redeemable at par March 1,2009,was purchased on November 15,1999,to yield 5% compounded semi-annually.What was the purchase price of the bond?

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Question 5

What is the amount of premium/discount amortized or accumulated for the second payment interval of a $1500 bond that sold for $1627.32? The bond rate is 6.95% compounded semi-annually and the yield rate is 6% compounded semi-annually.

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Question 6

A $150 000 bond bearing interest at 6% payable semi-annually is bought eight years before maturity to yield 4.5% compounded annually.If the bond is redeemable at par,what is the purchase price?

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Question 7

Ten $10 000,4% bonds with interest payable semi-annually and redeemable at par are purchased 18.5 years before maturity.Find the premium or discount and the purchase price if the bonds are bought to yield 7%.

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Question 8

A $50 000 bond bears interest at 4.5% payable semi-annually and is redeemable at par on November 4,2022.The bond is sold on March 20,2013,to yield 5.5% compounded semi-annually.What is the cash price?

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Question 9

A $1 000 000,9% bond with interest payable annually is redeemable at 104 in 5 years.What is the purchase price to yield 8% compounded quarterly?

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Question 10

A $250 000,7% bond redeemable at par with interest payable semi-annually is bought 4 years before maturity.Determine the premium or discount and the purchase price if the bond is purchased to yield: a)6.5% compounded semi-annually b)8% compounded semi-annually

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Question 11

What is the annualized cost of the debt for a sinking fund that has semi-annual deposits and it is set up to pay off a debt of $20 000 over a period of 5 years? The sinking fund earns 4.6% compounded annually and the loan rate on the debt is 9.2% compounded quarterly.

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Question 12

A $40 000 bond with semi-annual coupon payments at 5.5% compounded semi-annually is redeemable at par in 12 years.Calculate the yield rate if the bond is purchased at 102.5.

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Question 13

Find the gain or loss on the sale without constructing a bond schedule for three $100 000,5.5% bonds with quarterly coupons redeemable at par on September 1,2017,bought on May 1,2011,to yield 6% compounded quarterly.The bonds were sold on January 21,2014,at 93.5.

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Question 14

Nick buys a $25 000,5.4% bond with quarterly interest coupons,3 years before maturity,to yield 7% compounded quarterly.Construct a schedule of accumulation of discount.

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Question 15

A $100 000,9.0% bond with semi-annual coupons redeemable at par on March 1,2015,was purchased on September 22,2007,to yield 10.00% compounded semi-annually.What was the purchase price?

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Question 16

OPG is required to create a sinking fund of $8.1 billion 80 years from the start of the plant by making equal deposits at the end of every month throughout the 50 years life of the Pickering plant.If the interest is compounded 7.2% monthly,what is the accumulated value at the end of the mid-life of the plant (after 25 years)?

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Question 17

To redeem a $10 000.00 promissory note due in 12 years,SEJE has set up a sinking fund earning 8% compounded semi-annually.Equal deposits are made at the beginning of every six months.What is the size of the semi-annual deposits?

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Question 18

A $50 000 bond bearing interest at 5.5% payable semi-annually is redeemable at par on August 10,2033.The bond is sold on the primary market on December 10,2013,to yield 5% compounded semi-annually.Determine a)calculate the market price; b)the accrued interest; c)the cash price.

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Question 19

A $100 000,8.75% bond with interest payable annually is redeemable at 103 in four years.What is the purchase price to yield 7% compounded quarterly?

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