Question 1

Exhibit 14-10
USE THE FOLLOWING INFORMATION FOR THE NEXT QUESTION(S)
The WallMal Company has entered into a 4-year interest rate swap, with semiannual settlement, to pay a fixed rate of 8% per year and receive 6-month LIBOR. The notional principal is $50,000,000.
-Refer to Exhibit 14-10. Assuming that one year after the swap was initiated the fixed rate on a new 3-year receive fixed pay floating LIBOR swap has fallen to 7% per year, calculate the market value of the 8% fixed rate bond based on $100 face value. Settlement is on a semiannual basis.

Accepted Answer

To calculate the market value of the 8% fixed rate bond based on $100 face value, we need to discount the future cash flows of the bond at the new market interest rate of 7% per year, with semiannual settlements. The bond will pay $4 every six months (8% of $100 annually or $4 semiannually) for the next 3 years, plus the $100 face value at the end of the period. The present value of these cash flows, discounted at 3.5% per period (7% annual rate divided by 2 for semiannual), gives the market value of the bond. $$ PV = \frac{4}{(1+0.035)} + \frac{4}{(1+0.035)^2} + \frac{4}{(1+0.035)^3} + \frac{4}{(1+0.035)^4} + \frac{4}{(1+0.035)^5} + \frac{104}{(1+0.035)^6} $$$$ PV \approx 102.66 $$This calculation shows that the market value of the bond is approximately $102.66, which matches option A.

Question 2

Exhibit 14-10
USE THE FOLLOWING INFORMATION FOR THE NEXT QUESTION(S)
The WallMal Company has entered into a 4-year interest rate swap, with semiannual settlement, to pay a fixed rate of 8% per year and receive 6-month LIBOR. The notional principal is $50,000,000.
-Refer to Exhibit 14-10 Assume that one year later the fixed rate on a new 3-year receive fixed pay floating LIBOR swap has risen to 9% per year. Settlement is on a semiannual basis. Calculate the market value of the FRN based on $100 face value.

Accepted Answer

The market value of a FRN is its par value = $100

Question 3

Exhibit 14-8
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
Exclusive Industries has debentures outstanding (par value $1,000.00) convertible into exclusive's common stock at $30. The coupon rate is 11% payable semiannually and they mature in 10 years.
-Refer to Exhibit 14-8. Calculate the straight-bond value assuming that bonds of equivalent risk and maturity are yielding 13% per year compounded semiannually.

Accepted Answer

P = 55(PVIFA?.?%,??) + 1000(PVIF?.?%,??)
P = 55 (11.0185) + 1000 (.2838) = $889.82
where 11.0185 is the present value of annuity factor and .2838 is the present value factor both calculated for 20 periods at an interest rate of 6.5% per period.

Question 4

Exhibit 14-11
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
An international investment firm buys an interest rate cap that pays the difference between LIBOR and 6% if LIBOR exceeds 6%. Current LIBOR is 5%. The amount of the option is $1,500,000, and the settlement is every 3 months. Assume a 360 day year.
-Refer to Exhibit 14-11. Find the payoff if LIBOR closes at 6.3%.

Accepted Answer

The payoff is calculated as the difference between the closing LIBOR (6.3%) and the cap rate (6%), multiplied by the amount of the option, and then adjusted for the period of the settlement. Since LIBOR closed at 6.3%, which is 0.3% above the cap rate, the calculation is: (6.3% - 6%) * $1,500,000 * (90/360) = 0.003 * $1,500,000 * 0.25 = $11,250.

Question 5

Exhibit 14-10
USE THE FOLLOWING INFORMATION FOR THE NEXT QUESTION(S)
The WallMal Company has entered into a 4-year interest rate swap, with semiannual settlement, to pay a fixed rate of 8% per year and receive 6-month LIBOR. The notional principal is $50,000,000.
-Refer to Exhibit 14-10. Assume that one year later the fixed rate on a new 3-year receive fixed pay floating LIBOR swap has fallen to 7% per year. Settlement is on a semiannual basis. Calculate the market value of the FRN based on $100 face value.

Accepted Answer

The market value of a FRN is its par value = $100

Question 6

Exhibit 14-10
USE THE FOLLOWING INFORMATION FOR THE NEXT QUESTION(S)
The WallMal Company has entered into a 4-year interest rate swap, with semiannual settlement, to pay a fixed rate of 8% per year and receive 6-month LIBOR. The notional principal is $50,000,000.
-Refer to Exhibit 14-10. Indicate the market value of the swap to the WallMal Company.

Accepted Answer

The dealer pays the company = (100 - 97.4211)(50,000,000) = $1,289,450

Question 7

Exhibit 14-11
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
An international investment firm buys an interest rate cap that pays the difference between LIBOR and 6% if LIBOR exceeds 6%. Current LIBOR is 5%. The amount of the option is $1,500,000, and the settlement is every 3 months. Assume a 360 day year.
-Refer to Exhibit 14-11. Find the payoff if LIBOR closes at 4.7%.

Accepted Answer

Payoff = $1,500,000 ´ (90/360) ´ Max(0, 0.047 - 0.06) = 0

Question 8

Exhibit 14-9
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
BioTech Industries has debentures outstanding (par value $1,000) convertible into the company's common stock at $30. The coupon rate is 11% payable semiannually and they mature in 10 years.
-Refer to Exhibit 14-9. Calculate the conversion value of the bond if the stock price is $27.00 per share.

Accepted Answer

The bond is convertible into 33.333 shares of common stock since $1000.00/$30.00 = 33.333 shares.
The conversion value is 33.333 ´ $27.00 = $900.00

Question 9

Exhibit 14-7
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
Black Gold Industries (BGI) is an independent oil producer with production capacity of 500,000 barrels per month. Due to the cost structure of the business, BGI needs to receive $56.50 per barrel in order to remain solvent. On the other side of this situation is Petrochemicals Unlimited (PU) which uses an average of 500,000 barrels of West Texas crude oil in its normal production operations. The nature of PU's business is such that they will financially suffer if they have to pay more than an average of $57.80 per barrel for oil over the next six years. To hedge against their exposure to volatile oil prices, BI and PU contact a swap dealer to arrange the six-year oil swap described below: - $ \quad $ Settlement is made monthly.
- The notional principal is for 500,000 barrels per month.
- The monthly WTI index value is determined as the average of the daily settlement prices for the crude oil futures contract traded on the New York Mercantile Exchange (NYMEX).
- The swap dealer pays BGI $ \$ 57.00 $ per barrel.
- BGI pays the swap dealer the average NYMEX Oil futures price per barrel.
- $ \quad $ PU pays the swap dealer $ \$ 57.50 $ per barrel.
- The swap dealer pays PU dealer the average NYMEX Oi futures price per barrel.
-Refer to Exhibit 14-7. Describe the transaction that occurs between PU and the swap dealer if the monthly average oil futures settlement price is $58.45.

Accepted Answer

The answer of Exhibit 14-7
USE THE FOLLOWING INFORMATION FOR THE...

Question 10

Exhibit 14-7
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
Black Gold Industries (BGI) is an independent oil producer with production capacity of 500,000 barrels per month. Due to the cost structure of the business, BGI needs to receive $56.50 per barrel in order to remain solvent. On the other side of this situation is Petrochemicals Unlimited (PU) which uses an average of 500,000 barrels of West Texas crude oil in its normal production operations. The nature of PU's business is such that they will financially suffer if they have to pay more than an average of $57.80 per barrel for oil over the next six years. To hedge against their exposure to volatile oil prices, BI and PU contact a swap dealer to arrange the six-year oil swap described below: - $ \quad $ Settlement is made monthly.
- The notional principal is for 500,000 barrels per month.
- The monthly WTI index value is determined as the average of the daily settlement prices for the crude oil futures contract traded on the New York Mercantile Exchange (NYMEX).
- The swap dealer pays BGI $ \$ 57.00 $ per barrel.
- BGI pays the swap dealer the average NYMEX Oil futures price per barrel.
- $ \quad $ PU pays the swap dealer $ \$ 57.50 $ per barrel.
- The swap dealer pays PU dealer the average NYMEX Oi futures price per barrel.
-Refer to Exhibit 14-7. Describe the transaction that occurs between PU and the swap dealer if the monthly average oil futures settlement price is $55.50.

Accepted Answer

The answer of Exhibit 14-7
USE THE FOLLOWING INFORMATION FOR THE...

Question 11

Exhibit 14-8
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
Exclusive Industries has debentures outstanding (par value $1,000.00) convertible into exclusive's common stock at $30. The coupon rate is 11% payable semiannually and they mature in 10 years.
-Refer to Exhibit 14-8. Calculate the conversion value if the stock price is $24.00 par share.

Accepted Answer

The bond is convertible into 33.333 shares of common stock since $1000/$30 = 33.333 shares.
The conversion value is 33.333 ´ $24 = $800.00

Question 12

Exhibit 14-7
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
Black Gold Industries (BGI) is an independent oil producer with production capacity of 500,000 barrels per month. Due to the cost structure of the business, BGI needs to receive $56.50 per barrel in order to remain solvent. On the other side of this situation is Petrochemicals Unlimited (PU) which uses an average of 500,000 barrels of West Texas crude oil in its normal production operations. The nature of PU's business is such that they will financially suffer if they have to pay more than an average of $57.80 per barrel for oil over the next six years. To hedge against their exposure to volatile oil prices, BI and PU contact a swap dealer to arrange the six-year oil swap described below: - $ \quad $ Settlement is made monthly.
- The notional principal is for 500,000 barrels per month.
- The monthly WTI index value is determined as the average of the daily settlement prices for the crude oil futures contract traded on the New York Mercantile Exchange (NYMEX).
- The swap dealer pays BGI $ \$ 57.00 $ per barrel.
- BGI pays the swap dealer the average NYMEX Oil futures price per barrel.
- $ \quad $ PU pays the swap dealer $ \$ 57.50 $ per barrel.
- The swap dealer pays PU dealer the average NYMEX Oi futures price per barrel.
-Refer to Exhibit 14-7. Barring default by PU or BGI, how much compensation does the swap dealer receive each month?

Accepted Answer

The answer of Exhibit 14-7
USE THE FOLLOWING INFORMATION FOR THE...

Question 13

Exhibit 14-12
USE THE FOLLOWING INFORMATION FOR THE NEXT QUESTION(S)
The Skalmory Corporation has entered into a 3-year interest rate swap, with semiannual settlement, to pay a fixed rate of 7.5% per year and receive 6-month LIBOR. The notional principal is $10,000,000.
-Refer to Exhibit 14-12. Assume that one year later the fixed rate on a new 2-year receive fixed pay floating LIBOR swap has fallen to 7% per year. Settlement is on a semiannual basis. Calculate the market value of the FRN based on $100 face value.

Accepted Answer

The market value of a FRN is the par value = $100

Question 14

The exercise price of The Canadian Dairy Company is $17. You purchase the warrants for $4.00 each when Canadian Dairy's stock price is $20.00 per share. Each warrant entitles you to purchase one share of CDC stock. Calculate your percentage gain assuming the warrant premium drops by 50% and you sell your warrants when the stock reaches $30.00 per share.

Accepted Answer

V = ($20.00 - $17.00) = $3.00 theoretical value
$4.00 - $3.00 = $1.00 premium
V = ($30.00 - $17.00) = $13.00 theoretical value
V = $13.00 + $0.50 = $13.50 actual value
(13.50 - 4)/4 = 9.50/4 = 237.5%

Question 15

Exhibit 14-9
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
BioTech Industries has debentures outstanding (par value $1,000) convertible into the company's common stock at $30. The coupon rate is 11% payable semiannually and they mature in 10 years.
-Refer to Exhibit 14-9. Calculate the straight-bond value assuming that bonds of equivalent risk and maturity are yielding 14% per year compounded semiannually.

Accepted Answer

P = 55(PVIFA?%,??) + 1000(PVIFA?%,??)
P = 55(10.5940) + 1000(0.2584) = $841.07

Question 16

Exhibit 14-10
USE THE FOLLOWING INFORMATION FOR THE NEXT QUESTION(S)
The WallMal Company has entered into a 4-year interest rate swap, with semiannual settlement, to pay a fixed rate of 8% per year and receive 6-month LIBOR. The notional principal is $50,000,000.
-Refer to Exhibit 14-10. Assuming that one year after the swap was initiated the fixed rate on a new 3-year receive fixed pay floating LIBOR swap has risen to 9% per year, calculate the market value of the 8% fixed rate bond based on $100 face value. Settlement is on a semiannual basis.

Accepted Answer

To calculate the market value of the 8% fixed rate bond based on a $100 face value, we need to discount the future cash flows of the bond at the new market interest rate of 9% per year, considering semiannual compounding (since settlement is on a semiannual basis). The bond has 3 years left until maturity and pays a fixed rate of 8% per year on a $100 face value, which translates to $4 every six months. The present value of these cash flows, plus the present value of the $100 face value at maturity, discounted at the new semiannual rate of 4.5% (half of 9%), gives us the market value of the bond.

Question 17

The common stock of BioTech Industries pays a dividend of $1 per share and has a current market price of $27 per share. The convertible bond is selling for $1100. The payback or breakeven time for the bond is

Accepted Answer

The payback or breakeven time for the bond is calculated by dividing the premium paid for the bond over the stock (the difference between the bond price and the equivalent in stock at current prices) by the annual dividend. The bond is selling for $1100, and if we assume each share is $27, then the equivalent in shares would be $1100 / $27 = 40.74 shares (approximately). The premium paid over buying the shares directly is the difference between the bond price and the cost of buying 40.74 shares directly, which is $1100 - (40.74 * $27) = $1100 - $1100 = $0. However, since the question seems to imply a calculation based on dividends, we might need to reconsider the approach based on dividends or additional information provided. Given the dividend of $1 per share, the calculation should focus on how dividends contribute to the payback period. Without clear information on how the bond converts or its relation to dividends, the direct calculation from the given information is challenging. The correct answer, based on the options provided and assuming a typical scenario where dividends and market price play a role, would involve calculating how long it takes for the dividends to cover the premium of the bond over buying the stock directly. However, with the given data, there seems to be a misunderstanding in the calculation process as the premium directly calculated is $0, and the dividend does not directly contribute to a payback period without a premium over the stock. The correct approach would involve understanding the bond's conversion feature, its relation to the dividends, and any premium over the stock price, which is not directly calculable from the given information. The selection of B as the correct answer is based on a standard approach to calculating breakeven times for convertible bonds, which typically involves comparing the investment's additional cost over direct stock purchase against the income from dividends or interest, but the provided data does not directly support this calculation.

Question 18

Exhibit 14-9
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
BioTech Industries has debentures outstanding (par value $1,000) convertible into the company's common stock at $30. The coupon rate is 11% payable semiannually and they mature in 10 years.
-Refer to Exhibit 14-9. At present, what would be the minimum value of the bond?

Accepted Answer

The minimum value of the bond would be at least the greater of the two values, the straight-debt value or the conversion value. In this case, the minimum value is $900.00 (its conversion value).

Question 19

Exhibit 14-10
USE THE FOLLOWING INFORMATION FOR THE NEXT QUESTION(S)
The WallMal Company has entered into a 4-year interest rate swap, with semiannual settlement, to pay a fixed rate of 8% per year and receive 6-month LIBOR. The notional principal is $50,000,000.
-Refer to Exhibit 14-10. Indicate the market value of the swap to the WallMal Company.

Accepted Answer

The company pays the dealer = (102.6643 - 100)(50,000,000) = $1,332,150

Question 20

Exhibit 14-7
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
Black Gold Industries (BGI) is an independent oil producer with production capacity of 500,000 barrels per month. Due to the cost structure of the business, BGI needs to receive $56.50 per barrel in order to remain solvent. On the other side of this situation is Petrochemicals Unlimited (PU) which uses an average of 500,000 barrels of West Texas crude oil in its normal production operations. The nature of PU's business is such that they will financially suffer if they have to pay more than an average of $57.80 per barrel for oil over the next six years. To hedge against their exposure to volatile oil prices, BI and PU contact a swap dealer to arrange the six-year oil swap described below: - $ \quad $ Settlement is made monthly.
- The notional principal is for 500,000 barrels per month.
- The monthly WTI index value is determined as the average of the daily settlement prices for the crude oil futures contract traded on the New York Mercantile Exchange (NYMEX).
- The swap dealer pays BGI $ \$ 57.00 $ per barrel.
- BGI pays the swap dealer the average NYMEX Oil futures price per barrel.
- $ \quad $ PU pays the swap dealer $ \$ 57.50 $ per barrel.
- The swap dealer pays PU dealer the average NYMEX Oi futures price per barrel.
-Refer to Exhibit 14-7. Describe the transaction that occurs between BGI and the swap dealer if the monthly average oil futures settlement price is $55.50.

Accepted Answer

The swap dealer pays BGI $1.50 per barrel ($57.00 - $55.50) for 500,000 barrels, which equals $750,000.

Quiz 14: Derivatives: Analysis and Valuation

The common stock of BioTech Industries pays a dividend of $1 per share and has a current market price of $27 per share. The convertible bond is selling for $1100. The payback or breakeven time for the bond is