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Homework answers / question archive / 1) A bond that has a face value of $3,000 and coupon rate of 3

1) A bond that has a face value of $3,000 and coupon rate of 3

Finance

1) A bond that has a face value of $3,000 and coupon rate of 3.90% payable semi-annually was redeemable on July 1, 2021. Calculate the purchase price of the bond on February 10, 2015 when the yield was 4.40% compounded semi-annually.

 

 

2.A $5,500 bond that carries a 3.50% coupon rate payable semi-annually is purchased 6 years before maturity when the yield rate was 5.00% compounded semi-annually.

a. Calculate the purchase price of the bond.

$

Round to the nearest cent

b. What is the amount of discount or premium on the bond?

 

 

3Raymond purchased a $3,000 bond that was paying a coupon rate of 6.70% compounded semi-annually and had 4 more years to mature. The yield at the time of purchase was 5.20% compounded semi-annually.

a. How much did Raymond pay for the bond?

Round to the nearest cent

b. What was the amount of premium or discount on the bond?

 

 

4.A $7,000 bond had a coupon rate of 5.50% with interest paid semi-annually. Victoria purchased this bond when there were 6 years left to maturity and when the market interest rate was 5.75% compounded semi-annually. He held the bond for 2 years, then sold it when the market interest rate was 5.25% compounded semi-annually.

a. What was the purchase price of the bond?

Round to the nearest cent.

b. What was the selling price of the bond?

Round to the nearest cent.

c. What was Victoria's gain or loss on this investment?

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1) First we calculate Market Price on January 1, 2015 using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,

PV = Market Price of Bond = ?

Rate = 4.40%/2 = 2.20%

Nper = 6 years*2 = 12 periods 

PMT = 3000*3.90%/2 = $58.50 

FV = $3,000

Substituting the values in formula:

=-pv(2.20%,12,58.50,3000)

PV or Market Price of Bond on January 1, 2015 = $2,921.65

 

Now we calculate Accrued Interest for the period from January 1, 2015 to February 10, 2015 (40 days):

Interest Accrued = $58.50*40/181 = $12.93

Here, 181 days is difference between January 1, 2015 to July 1, 2015.

 

So, Purchase Price of Bond on February 10, 2015 = $2,921.65+$12.93 = $2,934.58

 

2) 

a) Computation of Purchase Price of Bond using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,

PV = Purchase Price of Bond = ?

Rate = 5%/2 = 2.50%

Nper = 6 years*2 = 12 periods 

PMT = 5500*3.50%/2 = $96.25

FV = $5,500

Substituting the values in formula:

=-pv(2.50%,12,96.25,5500)

PV or Purchase Price of Bond = $5,076.87

 

b) There is a discount as Purchase price is less than face value.

Discount = $5,500-$5,076.87 = $423.13

 

 

3) 

a) Computation of Purchase Price of Bond using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,

PV = Purchase Price of Bond = ?

Rate = 5.20%/2 = 2.60%

Nper = 4 years*2 = 8 periods 

PMT = 3000*6.70%/2 = $100.50

FV = $3,000

Substituting the values in formula:

=-pv(2.60%,8,100.50,3000)

PV or Purchase Price of Bond = $3,160.64

 

b) There is a premium as Purchase price is higher than face value.

Premium = $3,160.64-$3000 = $160.64

 

 

4) 

a) Computation of Purchase Price of Bond using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,

PV = Purchase Price of Bond = ?

Rate = 5.75%/2 = 2.875%

Nper = 6 years*2 = 12 periods 

PMT = 7000*5.50%/2 = $192.50

FV = $7,000

Substituting the values in formula:

=-pv(2.875%,12,192.50,7000)

PV or Purchase Price of Bond = $6,912.25

 

b) Computation of Selling Price of Bond using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,

PV = Selling Price of Bond = ?

Rate = 5.25%/2 = 2.625%

Nper = (6-2) years*2 = 8 periods 

PMT = 7000*5.50%/2 = $192.50

FV = $7,000

Substituting the values in formula:

=-pv(2.625%,8,192.50,7000)

PV or Selling Price of Bond = $7,062.40

 

c) Computation of Victoria's Gain or Loss:

Gain = $7,062.40-$6,912.25 = $150.16