Question

In: Finance

A $10 000 bond with 5% interest payable quarterly, redeemable at par on November 15, 2030,...

A $10 000 bond with 5% interest payable quarterly, redeemable at par on November 15, 2030, was bought on July 2, 2014, to yield 9% compounded quarterly. If the bond sells at 92.75 on September 10, 2020, what would the gain or loss on the sale be?

   Face value = 10 000.00; b = 1.25%

                   Principal = 10 000.00; i = 2.25%

                   Interest dates are November 15, February 15, May 15, and August 15.

                   The interest date preceding the date of sale is August 15, 2020.

                   The time period August 15, 2020, to November 15, 2030, is 10.25 years: n = 41.

                   b < i → discount

                   The interest payment interval August 15, 2020, to November 15, 2020, is 92 days

                   The interest period August 15, 2020, to September 10, 2020, is 26 days.

Solutions

Expert Solution

Period Discounting Factor
[1/(1.0225^period)]		 Discounting Factor Annuity
(Sum of discounting factor & all previous discounting factors)
1 0.97799511 0.97799511
2 0.956474435 1.934469545
3 0.935427321 2.869896866
4 0.914843345 3.784740211
5 0.894712318 4.679452529
6 0.875024272 5.554476801
7 0.855769459 6.41024626
8 0.836938346 7.247184607
9 0.81852161 8.065706217
10 0.800510132 8.866216349
11 0.782894995 9.649111344
12 0.765667477 10.41477882
13 0.748819048 11.16359787
14 0.732341367 11.89593924
15 0.716226276 12.61216551
16 0.700465796 13.31263131
17 0.685052123 13.99768343
18 0.669977626 14.66766106
19 0.655234842 15.3228959
20 0.640816472 15.96371237
21 0.626715376 16.59042775
22 0.612924573 17.20335232
23 0.599437235 17.80278955
24 0.586246685 18.38903624
25 0.573346391 18.96238263
26 0.560729967 19.5231126
27 0.548391165 20.07150376
28 0.536323878 20.60782764
29 0.52452213 21.13234977
30 0.512980078 21.64532985
31 0.501692008 22.14702186
32 0.490652331 22.63767419
33 0.47985558 23.11752977
34 0.469296411 23.58682618
35 0.458969595 24.04579577
36 0.44887002 24.49466579
37 0.438992684 24.93365848
38 0.429332699 25.36299118
39 0.41988528 25.78287646
40 0.41064575 26.19352221
41 0.401609536 26.59513174
42 0.392772162 26.9879039
43 0.384129254 27.37203316
44 0.375676532 27.74770969
45 0.367409811 28.1151195
46 0.359324999 28.4744445
47 0.351418092 28.82586259
48 0.343685175 29.16954777
49 0.336122421 29.50567019
50 0.328726084 29.83439627
51 0.321492503 30.15588877
52 0.314418095 30.47030687
53 0.30749936 30.77780623
54 0.30073287 31.0785391
55 0.294115277 31.37265438
56 0.287643302 31.66029768
57 0.281313743 31.94161142
58 0.275123465 32.21673489
59 0.269069403 32.48580429
60 0.263148561 32.74895285
61 0.257358006 33.00631086
62 0.251694871 33.25800573
63 0.246156353 33.50416208
64 0.24073971 33.74490179
65 0.235442259 33.98034405
66 0.230261378 34.21060543

May 15, 2014 to November 15, 2030 = 66 Quarters

Flat Price or Clean Price (i.e. Price as on May 15, 2014) = PV of All Coupons + PV of Maturity Value = [Coupon*Annuity Factor] + [Maturity Value*Discounting Factor] = [10000*1.25%*34.2106] + [10000*0.23026] = 4276.325 + 2302.6 = $6578.925

Invoice Price or Dirty Price (as on July 2, 2014) = Flat Price + Accrued Interest till Purchase Date = 6578.925 + [10000*1.25%*48/92] = 86578.925 + 65.22 = $6644.145

Therefore, Purchase Price = $6644.145

Value as on August 15, 2014 = $6644.145 + Coupon for July 2 to August 15 i.e. 44 days = 6644.145 + (10000*1.25%*44/92) = 6644.145+59.78 = $6703.925

Period Compounding Factor
[1.0225^period]		 Compounding Factor Annuity
(Sum of discounting factor & all previous discounting factors)
1 1.0225 1.0225
2 1.04550625 2.06800625
3 1.069030141 3.137036391
4 1.093083319 4.230119709
5 1.117677693 5.347797403
6 1.142825442 6.490622844
7 1.168539014 7.659161858
8 1.194831142 8.853993
9 1.221714843 10.07570784
10 1.249203426 11.32491127
11 1.277310504 12.60222177
12 1.30604999 13.90827176
13 1.335436115 15.24370788
14 1.365483427 16.6091913
15 1.396206804 18.00539811
16 1.427621457 19.43301957
17 1.45974294 20.89276251
18 1.492587156 22.38534966
19 1.526170367 23.91152003
20 1.560509201 25.47202923
21 1.595620658 27.06764989
22 1.631522122 28.69917201
23 1.66823137 30.36740338
24 1.705766576 32.07316996
25 1.744146324 33.81731628

August 15, 2014 to August 15, 2020 = 24 Quarters and 25 Coupons will be received.

Future Value of Purchase Price as on August 15, 2020 = Value as on August 15, 2014 as above *Compounding Factor = 6644.145*1.7058 = $11333.58

Future Value of Coupons received as on August 15, 2020 = Coupon*Annuity Factor = (10000*1.25%*33.8173) = $4227.1625

Sales Value = 10000*92.75% = $9275

Gain/(Loss) = Sales Value + FV of Coupons - FV of Purchase Price = 9275 + 4227.1625 - 11333.58 = $2168.5825

jeff jeffy answered 1 year ago
Next > < Previous

Related Solutions

A $50 000, 11% bond with semi-annual coupons redeemable at par on April 15, 2022, was...
A $50 000, 11% bond with semi-annual coupons redeemable at par on April 15, 2022, was purchased on June 25, 2015, at 92.375. What was the approximate yield rate?
A $1000 bond, redeemable at par, with annual coupons at 10% is purchased for $1050. If...
A $1000 bond, redeemable at par, with annual coupons at 10% is purchased for $1050. If the write-down in the book value is $20 at the end of the 1st year, what is the write-down at the end of the 4th year
Mr. Simpson buys a $1000 bond paying bond interest at j2= 6.5% and redeemable at par...
Mr. Simpson buys a $1000 bond paying bond interest at j2= 6.5% and redeemable at par in 20 years. He desires a yield rate of j4= 7%. (a) How much did he pay for the bond? (b) After exactly 5 years he sells the bond. Interest rates have dropped and the bond is sold to a buyer to yield at j1 = 5%. Find sale price. (other answer here is not correct)
11.A 8-year bond with a face value of $2000 is redeemable at par and earns interest...
11.A 8-year bond with a face value of $2000 is redeemable at par and earns interest at 9.2% convertible semiannually. If the yield rate is 6.9% convertible semiannually, find the book value 4 months after the payment of the 7th coupon. (Use simple interest for time between coupon payments.) Value = $ (3 decimal place)
A $3500 bond paying interest at j1 = 10% matures on June 1, 2030. On July...
A $3500 bond paying interest at j1 = 10% matures on June 1, 2030. On July 22, 2004, it was purchased for $3551 plus bond interest. On April 3, 2009, it was sold for $3443 plus bond interest. Estimate the yield j1 by the method of averages.
Cain buys a 3-year $1000 10% bond with annual coupons, redeemable at par. The price assumes...
Cain buys a 3-year $1000 10% bond with annual coupons, redeemable at par. The price assumes an annual effective yield rate of 8%. First, find the price of this bond. Every time Belial receives a payment, he deposits the money into a savings account, with an annual effective interest rate of i. At the end of three years, he puts the last payment he receives from the bond into the savings account and observes that overall, his yield rate was...
A $5000 semi-annual coupon bond paying interest at 12.4%/year compounded semi-annually is redeemable at par in...
A $5000 semi-annual coupon bond paying interest at 12.4%/year compounded semi-annually is redeemable at par in 16 years. It is callable at 115 at the end of 8 years and at 111 at the end of 11 years. Determine the price to guarantee a yield rate of 13.4%/year compounded semi-annually.
(1 point) A $3500 bond paying interest at j1j1 = 10% matures on June 1, 2030....
(1 point) A $3500 bond paying interest at j1j1 = 10% matures on June 1, 2030. On July 22, 2004, it was purchased for $3551 plus bond interest. On April 3, 2009, it was sold for $3443 plus bond interest. Estimate the yield j1j1 by the method of averages.
Calculate the value of a $1,000​-par-value bond paying quarterly interest at an annual coupon interest rate...
Calculate the value of a $1,000​-par-value bond paying quarterly interest at an annual coupon interest rate of 8% and having 15 years until maturity if the required return on​ similar-risk bonds is currently a 16​% annual rate paid quarterly.
On January 2013, Opera Limited purchased the entire issue of N$ 440 000 redeemable no par...
On January 2013, Opera Limited purchased the entire issue of N$ 440 000 redeemable no par value preference shares, issued by Piano Limited.  The shares offer fixed preference dividends at 10% per annum on the issue price of N$ 22 each.  Dividends are payable annually on 31 December.  Redemption at N$ 26.40 per share (i.e at a premium of N$4 40 per share) is compulsory and scheduled for 31 December 2017  The effective interest rate is...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT