Question

3. A client of Mr. Richards wants to purchase one of three bonds: a) 10-year corporate bond with a 2.00% coupon, paying annually, and par value of $1,000. b) 7-year corporate bond with a 1.75% coupon, paying annually and par value of $1,000. c) 5-year corporate bond with a 1.50% coupon, paying annually and par value of $1,000. What are the current prices for each of these bonds? How will the value of these bonds change if the respective market rates increase by 50 basis points? How will the value of these bonds change if their respective market rates decrease by 50 basis points? What recommendation would you make about purchasing one of these three bonds? Would you suggest any further analysis that might include the use of a relative interest rate risk measure used for bonds? Excel: Using the Basic TVM setup, calculate the value of these bonds, where FV is the par value, pmt is the current coupon (rate * par / payment frequency), PV is the current price, rate is the current market rate or in this case the coupon and rate changes, NPR is the years * M. For the rate changes, literally, copy the three bonds and then change the Rate to +/- .005 or 50 BPS. Setup a summary to show the average sensitivity of each bond and for the rate changes. Include this summary in the written analysis. Written: Briefly describe the analysis that you have performed detailing the relative prices. Also explain how the value of the bonds change in the up/down rate changes. Provide your recommendation about which bond to buy. Discuss what risk measures should be considered. 4. Mr. Richards wants additional analysis on these bonds. He wants you to assume that a year has transpired and to make the following assumptions about the bonds: each bond is exactly 1 year shorter in term rate levels are 1.75% for 9 years, 1.50% for 6 years and 3 1.25% for 4 years. Calculate the value of each bond and their relative rate sensitivity from a +/- 50 BPS rate change. Excel: Using the Basic TVM setup from question 3. Now change both NPER and rates to those indicated above. Compare the change in value from par. Summarize this potential gain in a table and include it in the written analysis. Written: Briefly describe the analysis that you have performed detailing how the values changed as they rolled down the yield curve. Based on each one of these bonds rolling down the yield curve and having a gain, which bond looks to have the most gain in market value and the highest overall yield? Based on this analysis which bond would you now recommend and what additional analysis should have been performed before purchase? 5. Mr. Richard now wants you to apply the effective duration formula he learned in CFA training to the bonds at issue and 1 year forward from questions 3 and 4. ��������� �������� = ��234567 − ��934567 2 ∗ ��<=>? ∗ 50 He would also like a marginal analysis performed for both the original and the forward bond analysis. This should show the base duration and yield for the shortest bond and then the change in yield and duration for each longer bond. He explains that the 5 year is the base and the change shows the additional risk/reward for buying the longer maturities. Excel: Using the results from questions 3 and 4 and calculate the effective duration as shown in the formula. Be very careful to use the brackets as shown above. The durations for these bonds should all be between 1 and 3 as a range so any larger or smaller values means a formula problem. Perform the marginal analysis for both sets of bonds as indicated above and include the tables in the written analysis. Written: Briefly describe the analysis that you have performed detailing how the effective durations changes as the bonds down the yield curve. Based on the short bonds yield and duration, which bond appears to provide the most marginal yield for the least marginal duration? Look at the years of yield and duration (divided both by the term and then look at the marginal change for the longer bonds.) Based on this analysis which bond would you recommend at issue and why?

Answer 1

	3
	a)	10Year Corporate Bond with 2% Coupon paid annually , Face Value $1000
		Face Value	$1,000
	Pmt	Annual Coupon	$20	(1000*2%)
	Rate	Assuming Market Rate=1.75%	1.75%
	Nper	Number of years	10
	FV	Payment at maturity	$1,000
	PV	Current Price	$1,022.75	(Using PV function of excel with Rate=1.75%, Nper=10, Pmt=-20, Fv=-1000)
		Excel Command: PV(1.75%,10,-20,-1000)
		If market rate increases by 50 basis point (0.5%)
	Rate1	Market Rate=1.75+0.5=	2.25%
	PV1	Value of the Bond	$977.83	(Using PV function of excel with Rate=2.25%, Nper=10, Pmt=-20, Fv=-1000)
		Excel Command: PV(2.25%,10,-20,-1000)
		If market rate decreases by 50 basis point (0.5%)
	Rate2	Market Rate=1.75-0.5=	1.50%
	PV2	Value of the Bond	$1,046.11	(Using PV function of excel with Rate=1.5%, Nper=10, Pmt=-20, Fv=-1000)
		Excel Command: PV(1.5%,10,-20,-1000)
	b)	7Year Corporate Bond with 1.75% Coupon paid annually , Face Value $1000
		Face Value	$1,000
	Pmt	Annual Coupon	$17.50	(1000*1.75%)
	Rate	Assuming Market Rate=1.75%	1.75%
	Nper	Number of years	7
	FV	Payment at maturity	$1,000
	PV	Current Price	$1,000.00	(Using PV function of excel with Rate=1.75%, Nper=7, Pmt=-17.5, Fv=-1000)
		Excel Command: PV(1.75%,7,-17.5,-1000)
		If market rate increases by 50 basis point (0.5%)
	Rate1	Market Rate=1.75+0.5=	2.25%
	PV1	Value of the Bond	$967.95	(Using PV function of excel with Rate=2.25%, Nper=7, Pmt=-17.5, Fv=-1000)
		Excel Command: PV(2.25%,7,-17.5,-1000)
		If market rate decreases by 50 basis point (0.5%)
	Rate2	Market Rate=1.75-0.5=	1.50%
	PV2	Value of the Bond	$1,016.50	(Using PV function of excel with Rate=1.5%, Nper=7, Pmt=-17.5, Fv=-1000)
		Excel Command: PV(1.5%,7,-17.5,-1000)
	c)	5Year Corporate Bond with 1.5% Coupon paid annually , Face Value $1000
		Face Value	$1,000
	Pmt	Annual Coupon	$15.00	(1000*1.5%)
	Rate	Assuming Market Rate=1.75%	1.75%
	Nper	Number of years	5
	FV	Payment at maturity	$1,000
	PV	Current Price	$988.13	(Using PV function of excel with Rate=1.75%, Nper=5, Pmt=-15, Fv=-1000)
		Excel Command: PV(1.75%,5,-15,-1000)
		If market rate increases by 50 basis point (0.5%)
	Rate1	Market Rate=1.75+0.5=	2.25%
	PV1	Value of the Bond	$964.90	(Using PV function of excel with Rate=2.25%, Nper=5, Pmt=-15, Fv=-1000)
		Excel Command: PV(2.25%,5,-15,-1000)
		If market rate decreases by 50 basis point (0.5%)
	Rate2	Market Rate=1.75-0.5=	1.50%
	PV2	Value of the Bond	$1,000.00	(Using PV function of excel with Rate=1.5%, Nper=5, Pmt=-15, Fv=-1000)
		Excel Command: PV(1.5%,5,-15,-1000)
			Current Price	Price with 50	Percentage	Price with 50	Percentage
				BPS increase in market interest	Decrease in Value	BPS decrease in market interest	Increase in Value
	a)	10Year Corporate Bond with 2% Coupon paid annually	$1,022.75	$977.83	-4.39%	$1,046.11	2.28%
	b)	7Year Corporate Bond with 1.75% Coupon paid annually	$1,000.00	$967.95	-3.21%	$1,016.50	1.65%
	c)	5Year Corporate Bond with 1.5% Coupon paid annually	$988.13	$964.90	-2.35%	$1,000.00	1.20%
		Bond c has the lowest risk of change of value due to change in interest rate
		Bond c is recommended