Question 1

A corporate bond has one-year maturity. The bond pays an interest of $50 and principal of
$1,000 at the time of maturity. If the bond has 10% probability of default and payment under default is $400, and an investor buys the bond for $907.14. Calculate the promised yield on the bond.

Accepted Answer

The promised yield on the bond can be calculated using the formula:
Promised Yield = (Interest Payment + (Principal Payment - Purchase Price) / Time to Maturity) / Purchase Price

Time to maturity = 1 year

Under no default, the bond pays an interest of $50 and principal of $1,000 at the time of maturity. Therefore, the promised yield can be calculated as follows:
Promised Yield = ($50 + ($1,000 - $907.14) / 1) / $907.14 = 0.0575 = 5.75%

Under default, the bond pays an interest of $50 and payment under default is $400. Therefore, the expected yield can be calculated as follows:
Expected Yield = (Interest Payment + (Payment Under Default - Purchase Price) * Default Probability) / Purchase Price
Expected Yield = ($50 + ($400 - $907.14) * 0.1) / $907.14 = 0.1497 = 14.97%

The promised yield is the weighted average of the promised yield under no default and the expected yield under default:
Promised Yield = (1 - Default Probability) * Promised Yield + Default Probability * Expected Yield
Promised Yield = (0.9 * 5.75%) + (0.1 * 14.97%) = 6.5843% ≈ 6.6%

Therefore, the best choice is B, 15.75%.

Question 2

If the bond has 10% probability of default and payment under default is $400, and an investor buys the bond for $938.10. Calculate the promised yield on the bond. (assume no default)

Accepted Answer

To calculate the promised yield on the bond, we need to use the formula: 
Promised Yield on Bond = (Annual Interest Payment + (Bond Purchase Price – Face Value) / Years to Maturity) / Bond Purchase Price

Here, we don't know the face value, annual interest payment or years to maturity of the bond. However, we know the probability of default and the payment under default. Let's assume that the face value of the bond is $1000.

Expected Payment = (1 - Probability of Default) * Face Value + Probability of Default * Payment under Default
Expected Payment = (1 - 0.1) * 1000 + 0.1 * 400
Expected Payment = $960

Now, let's calculate the annual interest payment on the bond:
Expected Payment = Annual Interest Payment + Face Value
$960 = Annual Interest Payment + $1000
Annual Interest Payment = $40

Using this information, let's calculate the promised yield on the bond:
Promised Yield on Bond = ($40 + ($938.10 - $1000) / Years to Maturity) / $938.10

Since we don't know the years to maturity, we cannot calculate the exact promised yield. However, we can assume a reasonable number of years to maturity, say 10 years. The price of the bond is lower than its face value, indicating that the promised yield should be higher than the coupon rate.

Promised Yield on Bond = ($40 + ($938.10 - $1000) / 10) / $938.10
Promised Yield on Bond = 0.1193 or 11.93%

Therefore, the best choice is B, with a promised yield of 11.93%, assuming no default.

Question 3

The US government agrees to guarantee a bond issue planned by Demurrage Associates. The value of this guarantee:
I. Value of the loan with guarantee minus value of the loan without guarantee
II. Is a subsidy to equity investors in the firm issuing guaranteed debt
III. Is a windfall gain to the buyers of the bonds
IV. Equals the value of a put option on the firm's assets with an exercise price equal to the bond's face value

Accepted Answer

The value of the guarantee is the difference between the value of the loan with and without the guarantee (I). It acts as a subsidy to equity investors because it reduces the firm's cost of debt (II). The guarantee can be seen as a put option on the firm's assets, as it provides a safety net for bondholders if the firm defaults (IV).

Question 4

The interest rate on one-year risk-free bond is 5%. BAC company has issued a 5% coupon bond with a face value of $1,000, maturing in one year. If the bond is considered risk-free, what is the price of the bond?

Accepted Answer

Since the bond is considered risk-free, its price should be equal to its present value of its future cash flows, which is simply its face value plus the coupon payment.

PV = (Coupon Payment/1-year interest rate) + Face Value

PV = ($50/0.05) + $1,000

PV = $1,050

However, the question states that the bond is considered risk-free, which means that its price should be equal to the price of the risk-free bond, which is also 5%. Therefore, the price of the bond is actually $1,000, not $1,050.

Question 5

Which of the following bonds have the least risk?

Accepted Answer

AAA bonds have the highest credit rating and are considered the safest investment with the lowest risk of default.

Question 6

What is the most important difference between a corporate bond and an equivalent
Treasury bond?

Accepted Answer

The most important difference between a corporate bond and a treasury bond is the level of default risk. In the case of corporate bonds, the firm has the option to default, whereas the government supposedly doesn't. Treasury bonds are considered a safer investment because they are backed by the full faith and credit of the United States government. This means that, in theory, the government will always make payments on its debt, even if it means printing more money. Corporate bonds, on the other hand, are subject to the financial health of the issuing company and the overall economic climate.

Question 7

The value of a bond that has a probability of default is given by:
I. bond value = asset value - value of call option on assets
II. bond value = value of an equivalent default-free bond + value of put option on assets
III. bond value = value of an equivalent default-free bond + value of put option on the stock
IV. bond value = asset value + value of call option on the stock

Accepted Answer

The answer of The value of a bond that has...

Question 8

A corporate bond has one-year maturity. The bond pays an interest of $50 and principal of
$1,000 at the time of maturity. If the bond has 10% probability of default and payment under default is $400, calculate the expected payment from the bond.

Accepted Answer

The expected payment from the bond would be calculated as follows:
Expected payment = (probability of no default * payment under no default) + (probability of default * payment under default)
Probability of no default = 1 - Probability of default = 1 - 0.10 = 0.90
Expected payment = (0.90 * $1,050) + (0.10 * $400) = $945 + $40 = $985
Therefore, the best choice is C.

Question 9

If a bond with one year maturity with a coupon rate of 5% and face value of $1,000 is selling for $881.94. Calculate the promised yield on the bond.

Accepted Answer

The promised yield on the bond is the rate of return that the investor will earn if they buy the bond at its current market price. To calculate the promised yield, we need to use the formula:
Promised yield = (coupon payment + (face value - market price))/market price

We know the coupon rate is 5%, which means the bond will pay a coupon payment of $50 (5% of $1,000 face value). We also know that the market price of the bond is $881.94.

Using the formula, we get: 
Promised yield = ($50 + ($1,000 - $881.94))/$881.94 = 19.06%

Therefore, the correct answer is C, 19.06%.

Question 10

If the bond has 15% probability of default and payment under default is $400, calculate the expected payment from the bond.

Accepted Answer

Expected payment = (probability of no default * payment under no default) + (probability of default * payment under default)
Probability of no default = 100% - 15% = 85%
Payment under no default is not given, but we can assume it to be the face value of the bond, say $1,000.
Therefore, expected payment = (0.85 * $1,000) + (0.15 * $400) = $952.50.

Question 11

Federal government loan guarantees include the following:
I. housing
II. airlines
III. shipowners and shipyards
IV. steel companies
V. oil and gas companies

Accepted Answer

The federal government provides loan guarantees to a wide range of industries, including housing, airlines, shipowners and shipyards, steel companies, and oil and gas companies, among others. Therefore, choices I, II, III, IV, and V are all correct.

Question 12

If the discount rate on the bond is 8%, the expected payment in year-1 is $952.50; calculate the price of the bond:

Accepted Answer

Using the formula for present value of bond: 
Price = Payment/(1+discount rate)^n 
Where n is the number of years until payment is received. 
Price = 952.5/(1+0.08)^1 = $907.14 (rounded to the nearest cent)

Question 13

Generally, you can insure corporate bonds through:

Accepted Answer

Corporate bonds can be insured through credit default swaps, which are contracts that protect investors against default by the issuer. This type of insurance involves paying a premium to a counterparty to assume the risk of default. The counterparty agrees to pay the investor in the event that the issuer defaults on the bond. The use of credit default swaps as a form of insurance has been controversial in the past, as it has been blamed for contributing to the financial crisis of 2008.

Question 14

If the discount rate on the bond is 7%, the expected payment in year-1 is $952.50; calculate the price of the bond:

Accepted Answer

The price of the bond can be calculated using the formula: 
Price = Expected payment / (1+discount rate)^number of years 
= $952.50 / (1+0.07)^1 
= $890.19 
Therefore, choice C is the correct answer.

Question 15

Which of the following rated bonds have the least risk?

Accepted Answer

Bonds rated AAA have the least risk as they are issued by companies with the strongest financial health and lowest probability of default.

Question 16

The average yield spread based on promised yield on AAA bonds rated by moody's and the yield on Treasuries is about:

Accepted Answer

The average yield spread between AAA-rated bonds and Treasuries is typically around 1%, reflecting the higher risk premium for corporate bonds compared to risk-free government bonds.

Question 17

The value of a corporate bond can be thought of as:

Accepted Answer

The answer of The value of a corporate bond can...

Question 18

The value of a corporate bond can be thought of as:

Accepted Answer

The value of a corporate bond without default is the present value of its future cash flows (i.e., interest payments and principal). The value of the put option embedded in the bond represents the right of the bondholder to sell the bond back to the issuer at a certain price at a future date. Therefore, the value of a corporate bond can be thought of as the bond value without default minus the value of the embedded put option.

Question 19

A corporate bond has one-year maturity. The bond pays an interest of $50 and principal of
$1,000 at maturity. If the bond has 10% probability of default and payment under default is
$400, and an investor buys the bond for $890.19; Calculate the promised yield on the bond.

Accepted Answer

The promised yield is calculated using the formula for yield to maturity (YTM), considering the bond's cash flows and purchase price. The bond pays $1,050 if it doesn't default and $400 if it defaults. The expected cash flow is $1,050 * 0.9 + $400 * 0.1 = $985. The promised yield is the rate that equates the present value of expected cash flows to the purchase price: $890.19 = $985 / (1 + YTM). Solving for YTM gives approximately 17.95%.

Question 20

If the discount rate on the bond is 5%, the expected payment in year-1 is $985; calculate the price of the bond:

Accepted Answer

The price of the bond can be calculated using the formula:
Price of bond = (Expected payment in year-1) / (1 + Discount rate)
Price of bond = $985 / (1 + 0.05) = $938.10
Therefore, the best choice is C.

Quiz 23: Credit Risk and the Value of Corporate Debt

A corporate bond has one-year maturity. The bond pays an interest of $50 and principal of $1,000 at the time of maturity. If the bond has 10% probability of default and payment under default is $400, and an investor buys the bond for $907.14. Calculate the promised yield on the bond.

If the bond has 10% probability of default and payment under default is $400, and an investor buys the bond for $938.10. Calculate the promised yield on the bond. (assume no default)

The interest rate on one-year risk-free bond is 5%. BAC company has issued a 5% coupon bond with a face value of $1,000, maturing in one year. If the bond is considered risk-free, what is the price of the bond?

Which of the following bonds have the least risk?

What is the most important difference between a corporate bond and an equivalent Treasury bond?

A corporate bond has one-year maturity. The bond pays an interest of $50 and principal of $1,000 at the time of maturity. If the bond has 10% probability of default and payment under default is $400, calculate the expected payment from the bond.

If a bond with one year maturity with a coupon rate of 5% and face value of $1,000 is selling for $881.94. Calculate the promised yield on the bond.

If the bond has 15% probability of default and payment under default is $400, calculate the expected payment from the bond.

Federal government loan guarantees include the following: I. housing II. airlines III. shipowners and shipyards IV. steel companies V. oil and gas companies

If the discount rate on the bond is 8%, the expected payment in year-1 is $952.50; calculate the price of the bond:

Generally, you can insure corporate bonds through:

If the discount rate on the bond is 7%, the expected payment in year-1 is $952.50; calculate the price of the bond:

Which of the following rated bonds have the least risk?

The average yield spread based on promised yield on AAA bonds rated by moody's and the yield on Treasuries is about:

The value of a corporate bond can be thought of as:

The value of a corporate bond can be thought of as:

A corporate bond has one-year maturity. The bond pays an interest of $50 and principal of $1,000 at maturity. If the bond has 10% probability of default and payment under default is $400, and an investor buys the bond for $890.19; Calculate the promised yield on the bond.

If the discount rate on the bond is 5%, the expected payment in year-1 is $985; calculate the price of the bond: