Question

A municipal bond service has three rating categories​ (A, B, and​ C). Suppose that in the...

A municipal bond service has three rating categories​ (A, B, and​ C). Suppose that in the past​ year, of the municipal bonds issued thoughout a​ country, 50 % were rated​ A, 20% were rated​ B, and 30% were rated C. Of the municipal bonds rated​ A, 30% were issued by​ cities, 30% by​ suburbs, and 40% by rural areas. Of the municipal bonds rated​ B, 50% were issued by​ cities, 10% by​ suburbs, and 40% by rural areas. Of the municipal bonds rated​ C, 80% were issued by​ cities,15 % by​ suburbs, and 5% by rural areas. Complete​ (a) through​ (c) below. a. If a new municipal bond is to be issued by a city, what is the probability that it will receive an A rating? b. What proportion of municipal bonds are issued by cities? c. What proportion of municipal bonds are issued by suburbs?

Homework Answers

Answer #1

P(A) = 0.50, P(B) = 0.20, P(C) = 0.30

P(cities|A) = 0.30, P(suburbs|A) = 0.30, P(rural|A) = 0.40

P(cities|B) = 0.50, P(suburbs|B) = 0.10, P(rural|B) = 0.40

P(cities|C) = 0.80, P(suburbs|C) = 0.15, P(rural|C) = 0.05

P(Cities) = P(A)*P(cities|A) +P(B)*P(cities|B) +P(C)*P(cities|C) = 0.50*0.30 + 0.20*0.50 +0.30*0.80 = 0.49

a) probability that a new municipal bond will receive an A rating given that it is from cities, P(A|cities) =

b) proportion of municipal bonds are issued by cities, P(Cities) =

=P(A)*P(cities|A) +P(B)*P(cities|B) +P(C)*P(cities|C)

= 0.50*0.30 + 0.20*0.50 +0.30*0.80 = 0.49

c) proportion of municipal bonds are issued by suburbs , P(Suburbs) =

=P(A)*P(suburbs|A) +P(B)*P(suburbs|B) +P(C)*P(suburbs|C)

= 0.50*0.30 + 0.20*0.10 +0.30*0.15 = 0.215

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A municipal bond service has three rating categories​ (A, B, and​ C). Suppose that in the...
A municipal bond service has three rating categories​ (A, B, and​ C). Suppose that in the past​ year, of the municipal bonds issued thoughout a​ country, 60% were rated​ A, 10%were rated​ B, and 30%were rated C. Of the municipal bonds rated​ A,30 % were issued by​ cities, 50 % by​ suburbs, and 20% by rural areas. Of the municipal bonds rated​ B, 60%were issued by​ cities, 30%by​ suburbs, and 10% by rural areas. Of the municipal bonds rated​ C,...
A municipal bond firm has three rating categories (A, B and C). Suppose that in the...
A municipal bond firm has three rating categories (A, B and C). Suppose that in the past year, of the municipal bonds issued throughout the USA, 55% were rated A, 25% were rated B and 20% were rated C. Of the municipal bonds rated A, 50% were issued by cities, 40% by suburbs, and 10% by rural areas. Of the municipal bonds rated B, 60% were issued by cities, 20% by suburbs, and 20% by rural areas. Of the municipal...
A bond service has three rating categories ( R 1​, R 2​, and R 3​). Suppose...
A bond service has three rating categories ( R 1​, R 2​, and R 3​). Suppose that in the past​ year, of the bonds issued throughout a​ country, 70​% were rated R 1​, 20​% were rated R 2​, and 10​% were rated R 3. Out of these​ bonds, 40​% of the R 1 rated bonds were issued by​ cities,50​% of the R 2 rated bonds were issued by​ cities, and 80​% of the R 3 rated bonds were issued by...
1) The yield to maturity for 10-year bonds is as follows for 3 different bond rating...
1) The yield to maturity for 10-year bonds is as follows for 3 different bond rating categories. AAA 7.5% AA 9% A 12% The bonds of Gallagher Inc. were rated at AA and issued at par last month. The bonds have now been downgraded to A. a) What was the price of the Gallagher bonds when they were issued? (1 mark) b) Determine the new price of the bonds, assuming a 15-year maturity and semiannual interest payments. c) What 2...
The yield to maturity for 10-year bonds is as follows for four different bond rating categories....
The yield to maturity for 10-year bonds is as follows for four different bond rating categories. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. Aaa 8.60% Aa1 8.80% Aa2 9.00% Aa3 10.00% The bonds of Falter Corporation were rated as Aaa and issued at par a few weeks ago. The bonds have just been downgraded to Aa2. Determine the new price of the bonds, assuming a...
Parker Pyrotechnics, Inc. has three bond issues outstanding at 12/31/17: Bond A--$1,000,000, 8% bonds issued on...
Parker Pyrotechnics, Inc. has three bond issues outstanding at 12/31/17: Bond A--$1,000,000, 8% bonds issued on January 1, 2017, due December 31, 2024. Interest is payable June 30 and December 31. Bonds were initially priced to yield 8%. Bond B--$1,000,000, 8% bonds issued on January 1, 2017, due December 31, 2026. Interest is payable June 30 and December 31. Bonds were initially priced to yield 8.5%. Bond C--$1,000,000, 8% bonds issued on February 1, 2017, due January 31, 2022. Interest...
A political party in a certain country has three candidates A, B and C, of whom...
A political party in a certain country has three candidates A, B and C, of whom it will select one to run for presidency. The probabilities of selecting the three candidates from the political party are 25%, 25% and 50% respectively. If A is selected, he has a 40% probability of winning the presidency whereas the same probabilities are 50% and 80% for B and C respectively, provided they are selected. Suppose that the candidate from this party is selected...
Consider a city with three taxi companies, A, B and C. Assume that, after a year,...
Consider a city with three taxi companies, A, B and C. Assume that, after a year, 60% of those who were with provider A stay with A, 20% switch to B and 20% switch to C. Of those who were with B, 55% stay with B, 15% switch to A and 30% switch to C the next year. Of those who were with C, 80% stay with C, 10% switch to A and 10% switch to B the next year....
6–C. Part 1. Internal Service Fund Transactions The Stores and Service Fund of the City of...
6–C. Part 1. Internal Service Fund Transactions The Stores and Service Fund of the City of Monroe had the following account balances as of January 1, 2017: Debits Credits Cash $28,000 Due from other funds 27,000 Inventory of supplies 27,500 Land 18,000 Buildings 84,000 Accumulated depreciation—buildings $30,000 Equipment 46,000 Accumulated depreciation—equipment 25,000 Accounts payable 19,000 Advance from water utility fund 30,000 Net position 126,500 Totals $230,500 $230,500 Required: a. Open a general journal for the City of Monroe Stores and...
Jiminy’s Cricket Farm issued a 30-year, 6 percent semiannual bond three years ago. The bond currently...
Jiminy’s Cricket Farm issued a 30-year, 6 percent semiannual bond three years ago. The bond currently sells for 93 percent of its face value. The book value of the debt issue is $95 million. In addition, the company has a second debt issue on the market, a zero coupon bond with eight years left to maturity; the book value of this issue is $40 million, and the bonds sell for 67 percent of par. The company’s tax rate is 22...