Deck 15: Bond Valuation and Sinking Funds

Question 1

A $5000 bond that pays 6% semi-annually is redeemable at par in 14 years. Calculate the purchase price if it is sold to yield 8% compounded semi-annually.

Answer 1

PMT = = $150
PP = 5000 + 150 PP = 1667.39 + 2499.46
PP = $4166.85
Programmed solution: The purchase price is 1667.39 + 2499.46 = $4166.85

Question 2

Bonds in denominations of $100 000 redeemable at 104 are offered for sale. If the bonds mature in ten years and six months and the coupon rate is 5.5% payable quarterly, what is the market price of the bonds to yield 7.2% compounded quarterly?

Answer 2

FV=100 000(1.04)=$104 000; PMT=100 000(0.055)0.25 =$1375.00; n=10.5(4)=42; P/Y=4; C/Y=4; I/Y=7.2; i= =0.018;
The purchase price on the interest date preceding the date of purchase
PP = 104 000(1.018)-42 + 1375 = 49 161.67 + 40 279.22 = $89 440.89

Question 3

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?

Answer 3

FV=$150 000; PMT=150000(0.06)0.5=$4500; n=8(2)=16; P/Y=2; C/Y=1; c= =0.5; i= =0.045
p = - 1 = 0.0222524
PP = 150000(1.0222524)-16 + 4500 = 150000(.7031853) + 4500(13.3385481)
= 105477.77 + 60023.46 = $165 501.23

Question 4

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?

Question 5

Six $1500 bonds with 4.5% coupons payable semi-annually are bought to yield 5% compounded monthly. If the bonds are redeemable at par in eight years, what is the purchase price?

Question 6

A $200 000 bond is redeemable at 108 in 14 years. If interest on the bond is 5.5% payable semi-annually, what is the purchase price to yield 4% compounded semi-annually?

Question 7

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.

Question 8

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?

Question 9

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?

Question 10

A $100 000, 4% bond with semi-annual coupons is redeemable at 108. What is the purchase price to yield 5.5% compounded semi-annually seven years before maturity?

Question 11

A $25 000, 6% bond redeemable at par is purchased 11 years before maturity to yield 6.9% compounded semi-annually. If the bond interest is payable semi-annually, what is the purchase price of the bond?

Question 12

A $100 000 bond bearing interest at 8% payable semi-annually is bought five years before maturity to yield 6% compounded annually. If the bond is redeemable at par, what is the purchase price?

Question 13

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?

Question 14

A $50 000 bond bearing interest at 6.5% bond payable semi-annually matures in 10 years. If it is bought to yield 5.7% compounded semi-annually, what is the purchase price of the bond?

Question 15

A $150 000 bond redeemable at par on October 1, 2026, is purchased on January 15, 2014. Interest is 6% payable semi-annually and the yield is 7.5% compounded semi-annually.
a) What is the market price of the bond?
b) How much interest has accrued?
c) What is the cash price?

Question 16

What is the purchase price of a $10 000, 3.5% bond with semi-annual coupons redeemable at 104 in seven years if the bond is bought to yield 2.5% compounded semi-annually?

Question 17

A $200 000.00, 6% bond with semi-annual coupons is redeemable at par. What is the purchase price of the bond six years before maturity to yield 8% compounded semi-annually?

Question 18

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?

Question 19

A $5000, 6.5% bond with semi-annual coupons redeemable at 108 is bought two years before maturity to yield 6% compounded semi-annually. What is the purchase price?

Question 20

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.

Question 21

A $1000, 6.5% bond redeemable at par in four years bears coupons payable annually. Compute the premium or discount and the purchase price if the yield, compounded annually, is 7.5%.

Question 22

A $1 000, 7% bond redeemable at par in eight years bears coupons payable annually. Compute the premium or discount and the purchase price if the yield, compounded annually, is:
a) 6.5%
b) 7.5%
c) 8.5%

Question 23

A $10 000, 7.2% bond with semi-annual coupons is purchased 3 years before maturity. Calculate the discount or premium if the bond is sold to yield 6% compounded semi-annually.

Question 24

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

Question 25

Find the gain or loss on the sale without constructing a bond schedule for six $5000, 9.5% bonds with interest payable semi-annually redeemable at par bought twenty-one years before maturity to yield 10.5% compounded semi-annually. The bonds were sold three years later at 103.625.

Question 26

A $5000, 6.25% bond with interest payable annually redeemable at par in eight years is purchased to yield 7.5% compounded annually. Find the premium or discount and the purchase price and construct the appropriate bond schedule.

Question 27

A $100 000 bond, redeemable at 110 in seven years with 6.75% coupons payable annually, is bought to yield 7.25% compounded annually.
(i) Determine the discount and the purchase price.
(ii) Construct a schedule of accumulation of discount.

Question 28

A $100 000.00, 7.2% bond with quarterly coupons redeemable at par is purchased 11 years before maturity to yield 6% compounded semi-annually. Determine the premium or discount.

Question 29

A $5000.00 6.5% bond redeemable at 109 with interest payable annually is purchased six years before maturity to yield 7% compounded annually. Construct the appropriate bond schedule.

Question 30

Three $25 000, 6% bonds with semi-annual coupons redeemable at par were bought eight years before maturity to yield 7% compounded semi-annually. Determine the gain or loss if the bonds are sold at 89.625 four years later.

Question 31

Find the gain or loss on the sale without constructing a bond schedule for a $100 000, 8% bond with semi-annual coupons redeemable at par purchased eleven-and-a-half years before maturity to yield 9% compounded semi-annually. The bond was sold five years later at 99.125.

Question 32

Bonds with a face value of $130 000 redeemable at par bearing 4.5% coupons payable quarterly are sold six years before maturity to yield 5.25% quarterly. Determine
a) the premium or discount;
b) the purchase price?

Question 33

Find the gain or loss on the sale without constructing a bond schedule for a $50 000, 6% bond with semi-annual coupons redeemable at par purchased twelve years before maturity to yield 10% compounded semi-annually. The bond was sold five years later at 99.375.

Question 34

A $1000, 6% bond redeemable at par with semi-annual coupons was purchased 10 years before maturity to yield 5% compounded semi-annually. The bond was sold 3 years later at 102. Calculate the gain or loss on the sale of the bond.

Question 35

Nine $10 000, 4% bonds with interest payable semi-annually and redeemable at par are purchased 8.5 years before maturity. Find the premium or discount and the purchase price if the bonds are bought to yield 6%.

Question 36

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%.

Question 37

A $50 000, 4% bond with semi-annual coupons is purchased three years before maturity. Calculate the discount or premium if the bond is sold to yield 6% compounded semi-annually.

Question 38

A $50 000.00, 8% bond with quarterly coupons redeemable at par is purchased five years before maturity to yield 4% compounded semi-annually. Determine the premium or discount.

Question 39

A $125 000 bond, redeemable at par in three years with 7.5% coupons payable quarterly, is bought to yield 6% compounded quarterly.
(i) Compute the premium or discount and the purchase price.
(ii) Construct a schedule for amortization of premium.

Question 40

Twenty $5 000 bonds redeemable at par bearing 6% coupons payable quarterly are sold eight years before maturity to yield 5.5% compounded annually. What is the purchase price of the bonds?

Question 41

A $100 000, 6.0% bond with semi-annual coupons redeemable at par is bought 17.5 years before maturity at 74.25. What was the approximate yield rate?

Question 42

A 50 000 bond that pays 5% semi-annually is redeemable at par on July 15, 2025.It is quoted at 97.5 on December 2, 2013. Determine the yield rate.

Question 43

A 4.5% annuity bond of $500 000 with interest payable quarterly is to be redeemable at par in seven years.
a) What is the purchase price to yield 6% compounded quarterly?
b) What is the book value after 6 years?
c) What is the gain or loss if the bond is sold six years after the date of purchase at 99.625?

Question 44

A $25 000, 8% bond with semi-annual coupons, redeemable at par in 12 years, is purchased to yield 6% compounded semi-annually. Determine the gain or loss if the bond is sold two years later at

Question 45

A $100 000, 8% bond with semi-annual coupons redeemable at par on April 25, 2018, was purchased on June 25, 2009, at 94.125. What was the approximate yield rate?

Question 46

A $10 000.00, 5% bond with semi-annual coupons redeemable at 105 in 23 years is purchased at 102.5. What is the approximate yield rate?

Question 47

To redeem a $100 000.00 promissory note due in 12 years, Flinstone Inc. has set up a sinking fund earning 7.25% compounded semi-annually. Equal deposits are made at the beginning of every six months.
a) What is the size of the semi-annual deposits?
b) How much of the maturity value of the fund is deposits?
c) How much is interest?

Question 48

A sinking fund amounting to $115 000.00 is to be created by making payments at the beginning of every six months for 6 years. Interest earned by the fund is 6.5% compounded semi-annually. Determine the size of the semi-annual payments and prepare a sinking fund schedule showing totals.

Question 49

A $50 000, 6% bond with semi-annual coupons redeemable at par on April 25, 2018, was purchased on June 25, 2009, at 94.378. What was the approximate yield rate?

Question 50

A $40 000.00, 5% bond with semi-annual coupons redeemable at par in 14 years is purchased to yield 7% compounded semi-annually. What is the gain or loss if the bond is sold three years before maturity at 99.75?

Question 51

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?

Question 52

A manufacturing company is planning a $600 000 expansion 6 years from now. By that time the company intends to accumulate 75% of the cost of the expansion by making payments into a sinking fund at the beginning of each of the next six years. Interest paid by the fund is 7% compounded annually.
a) Calculate the size of annual payment into the fund.
b) Calculate the total amount deposited into the fund.
c) Calculate the amount of interest.

Question 53

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.

Question 54

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.

Question 55

A $25 000, 7% bond with semi-annual coupons redeemable at par in twenty-two years is purchased to yield 6% compounded semi-annually. Determine the gain or loss if the bond is sold seven years after the date of purchase at 98.25.

Question 56

Phoenix Corporation is depositing equal sums of money at the beginning of every three months into a sinking fund to redeem a $165 000.00 promissory note due 11 years from now. Interest earned by the fund is 4.6% compounded quarterly.
a) Determine the size of the quarterly payments into the sinking fund.
b) Compute the balance in the fund after 6 years.
c) Compute the increase in the fund during the 25th payment interval.
d) Construct a partial sinking fund schedule showing details of the first three deposits, the last three deposits, and totals.

Question 57

A $50 000.00, 6% bond with semi-annual coupons redeemable at par in 14 years is purchased to yield 8% compounded semi-annually. What is the gain or loss if the bond is sold four years before maturity at 99.25?

Question 58

The Town of Snow Lake issued debentures worth $420 000.00 maturing in 15 years to finance construction of recreational facilities. To redeem the debentures, the town council decided to make equal deposits into a sinking fund at the beginning of every three months. Interest earned by the sinking fund is 6.66% compounded quarterly.
a) What is the size of the quarterly payment into the sinking fund?
b) What is the balance in the fund after six years?
c) How much interest is earned by the fund in the 25th payment interval?
d) By how much will the fund increase in the 43rd payment interval?
e) Prepare a partial sinking fund schedule showing details of the first three payments, the last three payments, and totals.

Question 59

A $250 000, 6.5% bond with semi-annual coupons redeemable at par is bought 17.5 years before maturity at 78.25. What was the approximate yield rate?

Question 60

Cranberry Portage Credit Union borrowed $425 000.00 at 6% compounded semi-annually from League Central to build a sports complex. The loan agreement requires payment of interest at the end of every six months. In addition, the credit union is to make equal payments into a sinking fund so that the principal can be retired in total after 11 years. Interest earned by the fund is 4.14% compounded semi-annually.
a) What is the semi-annual interest payment on the debt?
b) What is the size of the semi-annual deposits into the sinking fund?
c) What is the total annual cost of the debt?
d) What is the interest earned by the fund in the 18th payment interval?
e) What is the book value of the debt after 6 years?
f) Prepare a partial sinking fund schedule showing details, including the book value of the debt, for the first three payments, the last three payments, and totals.

Question 61

A $10000 bond bearing interest at 6% payable semi-annually redeemable at par on March 1, 2002, was purchased on September 30, 1996, to yield 5% compounded semi-annually. Determine the purchase price.

Question 62

What is the size of the sinking fund deposit for a debt that has an original principal of $40 000 over 12 years? The deposits are quarterly and the interest rate on the sinking fund is 4.21% compounded annually.

A) $674.41
B) $667.41
C) $676.41
D) $647.41
E) $694.41

Question 63

A $10000, 8.5% bond with semi-annual coupons redeemable at par on March 1, 2005, was purchased on September 22, 1997, to yield 10.06% compounded semi-annually. What was the purchase price?

Question 64

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.

A) $4.30
B) $5.30
C) $1.40
D) $3.40
E) $2.30

Question 65

Waterton Motel made equal payments at the end of every six months into a sinking fund for 11 years. If the fund had a balance of $100 000.00 after 11 years and interest is 5.4% compounded semi-annually, what was the accumulated balance in the fund after seven years?

Question 66

Annual sinking fund payments made at the beginning of every year for four years earning 4.5% compounded annually amount to $25 000.00 at the end of four years. Construct a sinking fund schedule showing totals.

Question 67

What is the purchase price of a bond that is issued on May 1, 2002 for 22 years at a coupon rate of 9.4% compounded semi-annually? The purchase date of the bond is May 11, 2007 and the yield rate is 8.5% compounded semi-annually. The bond has a face value of $5000 and is redeemable at par.

A) $4513.30
B) $5413.30
C) $5431.30
D) $4531.30
E) $4533.30

Question 68

What is the total increase in the 71st monthly deposit interval of a sinking fund that is for 14 years and the sinking fund earn 4.8% compounded monthly? The original principal was $250000.

A) $1883.94
B) $1383.94
C) $1333.94
D) $1888.94
E) $1880.94

Question 69

What is the quoted price of a bond that has 4.5 years until maturity? The face value of the bond is $5000 and it has a coupon rate of 8.1% compounded semi-annually and a yield rate of 8.6% compounded semi-annually.

A) $4809.32
B) $4998.32
C) $4908.32
D) $4888.32
E) $4898.32

Question 70

What is the purchase price of a bond that has 4 years and 6 months until it matures? The face value of the bond is $3000 and the coupon rate is 5.2% compounded semi-annually. The yield rate is 7.5% compounded semi-annually.

A) $2740.53
B) $2440.53
C) $2770.53
D) $2447.53
E) $2547.53

Question 71

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 $20000 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.

A) $5777.52
B) $5447.52
C) $5477.52
D) $5424.52
E) $5577.52

Question 72

The Cochrane Board of Education financed the acquisition of a new school site through a $400 000 long-term promissory note due in 17 years. Interest on the promissory note is 7.25% compounded semi-annually and is payable at the end of every six months. To provide for the redemption of the note, the board agreed to make equal payments at the end of every six months into a sinking fund paying 5% compounded semi-annually.
a) What is the semi-annual interest payment?
b) What is the size of the semi-annual payment into the sinking fund?
c) What is the annual cost of the debt?
d) Compute the book value of the debt after 3 years.
e) Compute the increase in the sinking fund in the 37th payment interval.
f) Construct a partial sinking fund schedule showing details, including the book value of the debt, for the first three years, the last three years, and totals.

Question 73

The Town of The Pas bought rescue equipment for $176 000. The financing agreement provides for annual interest payments and equal payments at the end of each year into a sinking fund for 13 years. After 13 years the proceeds of the sinking fund will be used to retire the principal. Interest on the debt is 6.5% compounded annually and interest earned by the sinking fund is 5.1% compounded annually.
a) What is the annual interest payment?
b) What is the size of the annual payment into the sinking fund?
c) What is the total annual cost of the debt?
d) What is the book value of the debt after 6 years?
e) Construct a partial sinking fund schedule showing details, including the book value of the debt, for the last three years and totals.

Question 74

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?

Question 75

What is the amount of premium/discount for a bond that has 4 years till it matures? The face value of the bond is $100 000 and it has a bond rate of 6.4% compounded semi-annually. The bond is sold to yield 7.4% compounded semi-annually.

A) $3084.47
B) $3840.47
C) $3048.47
D) $3408.47
E) $3184.47

Question 76

Sepaba Construction made equal payments at the end of every six months into a sinking fund for 15 years. If the fund had a balance of $1000 000.00 after 15 years and interest is 6% compounded semi-annually, what was the accumulated balance in the fund after 10 years?

Question 77

A $100000, 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?

Question 78

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.

Question 79

A $100 000.00, 7% bond with semi-annual coupons redeemable at 105 on November 1, 2001, is purchased on July 23, 1999, to yield 8% compounded semi-annually. Determine the quoted price.

Question 80

What is the amount of premium/discount amortized or accumulated in the first payment interval for a bond that has a face value of $6000 and it sold for $5700? The coupon rate is 9% compounded semi-annually and the market rate is 10.1% compounded semi-annually.

A) $18.75
B) $17.85
C) $11.85
D) $15.75
E) $14.75