Question 1: Company A has issued 15-year, 10% coupon semi-annual payment non-callable convertible bonds. The bonds have a total nominal value of R250 000 000, with minimum denominations of R1 000 000 each, and each R1 000 000 nominal value is convertible into 80 000 Company A shares. The bond indenture stipulates that Company A will not issue further debt that is senior to the bonds.

The company also has outstanding callable bonds, with five years remaining to maturity. The bonds are callable at R104.0000% of par value in three years and are currently trading at R109.4894%. The coupon rate is 7%, which is paid semi- annually.

A fixed-income portfolio manager has purchased both Company A’s convertible bonds and callable bonds. The fixed-income portfolio manager believes that both the corporate and government bonds’ yield curves, in which Company A is domiciled, support the pure expectations theory of the term structure of interest rates. He discovers that both the yield curves are inverted. The fixed-income portfolio manager has received additional funds of R5 000 000 to invest in one of the bonds. He decides to buy more callable bonds with the additional funds.

What type of covenant do Company A’s convertible bonds have? (1)

What is the total redemption value that Company A will pay at maturity for the convertible bonds? (1)

What is the period coupon payment for an investor who has bought R4 000 000 of Company A’s convertible bonds? (1)

Suppose there are 10 years remaining to maturity and Company A’s shares are trading at R15 per share. The yield-to-maturity on the bonds is 6%. Will the option to convert be profitable for an investor who has bought R1 000 000 of Company A’s convertible bonds? Justify your answer. (3)

What is the premium on callable bonds? (1)

Calculate the yield-to-call on the callable bonds. (1)

Did the fixed-income portfolio manager make the correct decision by allocating the additional funds to callable bonds? Justify your answer. (3)

Question 2 (11 marks)

A South African bank, Bank AA, finds a bond in the South African bond market that it wants to add to its fixed-income portfolio. The bond is an 8% German corporate bond — demoninated in South African local currency — priced for settlement on 21 July 2023. The bond makes semi-annual coupon payments on 15 March and 15 September of each year, and it matures on 15 September 2030.
The stated annual yield-to-maturity is 9.5%. The day-count convention for the corporate bond is 30 .

Another South African bank, Bank ZZ, wants to raise funds to fund its new projects through a bond issuance. The bank wants to issue Bond Z, a 6.2% semi-annual coupon payment bond with a maturity of seven years. The bank has not issued bonds before. The bank’s fixed-income strategist has been asked to price the bond issuance.

The fixed-income strategist gathered the following information for four bonds with similar characteristics and credit risk, with all four bonds paying coupons semi- annually:

1. Bond A: five-year, 4% coupon bond trading at a price of 7834%.
2. Bond B: five-year, 6% coupon bond trading at a price of 7332%.
3. Bond C: nine-year, 3% coupon bond trading at a price of 3168%.
4. Bond D: nine-year, 5% coupon bond trading at a price of 2854%.

The following table displays the bonds in a matrix according to the coupon rate and the time-to-maturity:

 3% coupon 4% coupon 5% coupon 6% coupon 5 years R97.7834% 4.5000% R105.7332% 4.7000% 6 years 7 years Bond Z 8 years 9 years R88.3168% 4.6000% R99.2854% 5.2000%

As a South African bond, Bank ZZ’s bond uses the Actual day-count convention. 365

In which South African bond market did Bank AA find the German corporate bond? (1)

What is the annual equivalent yield on the German corporate bond? (1)

Calculate the full price per €100 of par value for the German corporate bond. (2)

Calculate the accrued interest on the German corporate bond. (1)

Calculate the flat price per €100 of par value for the German corporate bond. (1)

Calculate the price per R100 of par value at which Bank ZZ should issue Bond Z.

• Does Bond A or Bond B have greater interest rate risk? Justify your (2)

Question 3 (11 marks)

 A fixed-income analyst wants to construct a spot rate curve from the Treasury yield curve of Country A. The analyst collated the following information for three Treasury bonds, with a par value of R1 000 that pay coupons annually:   Maturity                 Coupon                  Yield                     Price 1 year                              6%                        6%                     R1 000 2 year                              7%                        7%                     R1 000 3 year                              8%                        8%                     R1 000   In addition, the fixed-income analyst wants to use Country B to analyse the relationship between spot rates and forward rates. The analyst finds zero-coupon government bonds with the following prices per 100 of par value and yields-to- maturity stated on a semi-annual bond basis:

 Maturity Yield Price 1 year 2.7180% R97.3364 2 year 3.0627% R94.1116 3 year 3.5796% R89.9031 4 year 3.4692% R87.1466

What is the shape of the Treasury yield curve in Country A? (1)

Calculate the twi-year spot rate from Country’s A Treasury yield curve. (2)

Calculate the reinvestment income from Year 1 to Year 3 for an investor in Country A who holds the three-year Treasury bond if coupons are reinvested at 8.5%.

What is the relative yield spread for an investor in Country A who is holding a three-year, 6.8% annual coupon payment corporate bond, with a yield-to-maturity of 9.5%? (1)

With reference to Country B, what is the two-year implied forward rate one year from now? (2)

An investor in Country B has a three-year investment horizon. The investor decides to buy the two-year zero-coupon government bond and after two years plans to reinvest the proceeds in another one-year zero- coupon government bond. What is the yield-to-maturity that the investor expects on the one-year zero-coupon government bond two years from now? (2)

Question 4 (11 marks)

An analyst finds Bond A. It is a 5% bond that matures on 15 March 2038 and is priced to yield 6.4% for settlement on 25 June 2023. Coupons are paid semi- annually on 15 March and 15 September. The yield-to-maturity is stated on a street-convention semi-annual bond basis. The bond uses the Actual day-count
Actual convention.

The analyst is also assisting a portfolio manager of a defined benefit pension fund that pays a monthly payout to retirees. The portfolio manager wants to understand how to measure the sensitivity of retirement obligations to market interest rate changes. The current interest rate is 6%. The analyst calculated the following present value of the fund’s liabilities under three interest-rate scenarios:

 Interest-rate scenarios Present value of liabilities 4% R778.8 million 6% R648.2 million 8% R523.6 million

Calculate the Macaulay duration for Bond A and interpret the answer. (3)

What is the modified duration for Bond A? (1)

Suppose, immediately after the analyst had found Bond A, the yield-to- maturity on the bond changed from 6.4% to 7%.

To what risk was the bond exposed? (1)

What is the effect of the change in yield from 6.4% to 7% on the bond’s price? (1)

What is the effect of the change in yield from 6.4% to 7% on the bond’s duration? (1)

Suppose Bond A’s modified duration is now 12.5 years and has a convexity of 132.8. Calculate the total effect on the bond’s price if the yield-to-maturity decreases by 150 basis points. (2)

What is the fund’s effective duration? (2) Question 5 (6 marks)

A semi-annual coupon payment corporate bond with a CCC rating is selling at R1 250. The par value on the bond is R1 000 and the coupon rate is 11%. The bond was issued 20 years ago and was secured by collateral. There are eight years remaining until the bond matures. The issuing company is now facing financial difficulties. Investors believe that the company will continue to meet coupon payments until maturity, but will be forced into bankruptcy, with bondholders receiving only 60% of the par value. The company also has a senior subordinated bond outstanding.

Into what grade of creditworthiness can the corporate bond’s rating be classified? (1)

Calculate the expected yield-to-maturity. (1)

Calculate the promised yield-to-maturity. (1)

Calculate the loss severity on the corporate bond. (1)

Justify whether the company will pay the CCC-rated bond or the senior subordinated bond first. (1)

As a bondholder of the company issue, what financial instrument should you have purchased as a protection against default? (1)

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