### MONDAY: 24 April 2023. Afternoon Paper. Time Allowed: 3 hours.

Answer ALL questions. Marks allocated to each question are shown at the end of the question. Show ALL your workings.

Do NOT write anything on this paper.

**QUESTION ONE**

1. Explain THREE reasons why market participants prefer the swap rate curve as a benchmark of interest rate curve as opposed to a government bond yield curve. (3 marks)

2. Explain how the following relationships between coupon rate and required rate of return affect a bond’s value relative to par value:

Coupon rate and required return are equal. (2 marks)

Coupon rate is lower than required rate of return. (2 marks)

Coupon rate is higher than required rate of return. (2 marks)

3. Hifadhi Ltd., an AAA rated company issued fully convertible bonds on the following terms one year ago:

AAA rated companies can issue plain vanilla bonds without conversion option at an interest rate of 9.5%

**Required:**

Calculate today’s:

Straight value of the bond. (2 marks)

Conversion value of the bond. (2 marks)

Conversion premium. (2 marks)

Percentage of downside risk. (3 marks)

Conversion parity price. (2 marks)

**(Total: 20 marks)**

**QUESTION TWO**

1. Explain TWO shortcomings of yield to maturity (YTM) in bond valuation. (4 marks)

2. A putable bond, that is putable in one year has a face value of Sh.100, with a maturity of 2 years and 7% coupon.

The put option will be exercised if the value of the bond is less than Sh.100.

**Additional Information:**

The value of a non-putable bond is Sh.102.99 and the interest rate today is 4.5749% and is expected to either go up to 7.1826% or down to 5.321%, 1 year from today.

**Required:**

Calculate the present value of the putable bond today. (4 marks)

Determine the value of embedded put option. (2 marks)

3. The following spot and forward rates are available:

1. Current 1 year spot rate is 5.5%.

2. One year forward rate one year from today is 7.63%.

3. One year forward rate two years from today is 12.18%.

4. One year forward rate three years from today is 15.5%

A four-year, 10% annual pay Sh.1,000 par value bond is also available.

**Required:**

Calculate the price of the bond. (4 marks)

4. A short term investor possesses an investment horizon of 6 years. The investor pursues his investment objectives using a 13-year, 9% semi-annual pay coupon bond that is currently priced at a par of Sh.1,000.

**Additional information:**

1. The prevailing yields to maturity are expected to be at 8% for the next 2 years into the investment horizon.

2. Coupons in the first 2 years will be re-invested at 8%.

3. Projected yields to maturity are expected to rise to 10% from year 3 to year 6.

4. Coupons in year 4 to year 6 are expected to be re-invested at 10%.

5. Further yields to maturity for the remaining term of the bond (year 7 to year 13) are expected to be 10.6%.

**Required:**

Coupon and re-investment income for the first 2 years into the investment horizon. (2 marks)

Coupon and re-investment income for year 3 to year 6 of the investment horizon. (2 marks)

Realised rate of return by the investor if he sells the bond at the end of year 6. (2 marks)

**(Total: 20 marks)**

**QUESTION THREE**

1. Distinguish between “liquidity preference theory” and “market segmentation theory”. (4 marks)

2. Janice Nyambura is considering purchasing one of the following newly issued 10 year AAA corporate bonds shown below:

Janice notes that the yield curve is currently flat and assumes that the yield curve shifts in an instantaneous and parallel manner.

**Required:**

Explain the effect on the price of both bonds if yields decline more than 100 basis points. (2 marks)

Analyse under which two interest rate forecasts would Janice prefer Bond B over Bond A. (2 marks)

3. A bond that matures in 6 years, with a coupon rate of 4% and a face value of Sh.1,000 with a yield to

maturity of 3% is priced at Sh.1,056.288. The coupons are reinvested at an interest rate of 2%.

**Required:**

Calculate the realised rate of return for a buy and hold investor. (4 marks)

An investor is considering a 5-year, 7.4% coupon bond that is selling to yield 5.6%. The bond makes

coupon payments semi-annually. The par value of the bond is Sh.1,000.

**Required:**

Calculate the price of the bond. (3 marks)

4. The 1 year, 2 year and 3 year spot rates on Treasuries are 4%, 8.167% and 12.377% respectively. An investor is considering a 3 year, 9% annual coupon corporate bond trading at Sh.89.464. The yield to maturity (YTM) is 13.50% and the YTM of a 3 year Treasury is 12%.

**Required:**

The Z-spread (zero volatility spread). (5 marks)

**(Total: 20 marks)**

**QUESTION FOUR**

1. Distinguish between “duration” and “effective duration” as measures of a bond interest rate risk. (4 marks)

2. A bond with a yield to maturity of 8% and a coupon of 5% paid annually has five years to maturity. The bond has a par value of Sh.100. The bond is priced at Sh.88.02.

**Required:**

Calculate the following durations for the bond:

Macaulay duration. (4 marks)

Modified duration. (2 marks)

3. The annual yield to maturity for the 6 month and 1 year Treasury bill is 4.6% and 5.0% respectively. These yields represent the 6 month and 1 year spot rates. The following Treasury yield curve for bonds priced at par for each issue being Sh.100 has been estimated for six months up to a maturity of 3 years:

**Required**:

The 1.5 year spot rate. (3 marks)

The 2.0 year spot rate. (2 marks)

The 2.5 year spot rate. (2 marks)

The arbitrage free value of a 2.5 year Treasury security with a coupon rate of 8% using spot rates and

yields stated above. (3 marks)

**(Total: 20 marks)**

**QUESTION FIVE**

1. With reference to fixed income contracts, distinguish between the following terms:

“Maintenance covenants” and “incurrence covenants”. (2 marks)

“Affirmative covenants” and “negative covenants”. (4 marks)

2. Highlight THREE factors that might be considered when negotiating financial covenants to ensure that monitoring and testing of such covenants for compliance is not a problem. (3 marks)

3. Wetu Limited plans to retire its outstanding bond. The interest rates prevailing in the market have dropped significantly from the time the bond was issued ten years ago. Wetu Limited intends to know if it is advantageous on its part to retire the bond and issue a new bond.

The following information has been provided:

**Required:**

Advise Wetu Limited on the required net initial cash outlay. (5 marks)

Determine the net annual cash savings, if any, from the old and new bond. (4 marks)

Using the net present value (NPV) method, advise Wetu Limited on whether they should issue the new

bond. (2 marks)

**(Total: 20 marks)**