Question

I would like the answers for these case study questions showing clearly how they are calculated.  

Issuer	Face Value	Coupon Rate	Rating	Quoted Price $	Years Until Maturity	Sinking Fund	Call Period
ABC Energy	1000	6%	AAA	809.10	20	Yes	3 Yrs
ABC Energy	1000	0%	AAA	211.64	20	Yes	N/A
Trans Power	1000	10%	AA	1025.00	20	Yes	5 Yrs
Telco Utilities	1000	12%	AA	1300.00	30	No	5 Yrs

1. One of Jill's best clients poses the following question: If I buy 10 of each of these bonds, reinvest any coupons received at the rate of 6% per year, and hold them until they mature, what will my realized return be on each bond investment? How should Jill go about demonstrating the solution to this question?

2. Why is there so much variation in the coupon rates and prices of these various bonds? asks one of Jill's wealthiest clients. How should Jill respond?

Answer 1

1). First, we need to find the Future Value (FV) of the coupons reinvested:

ABC Energy: PMT = coupon rate*face value/2 = 6%*1,000/2 = 30; rate (reinvestment rate) = 6%/2 = 3%; N = 20 years*2 = 40 (since payments are semi-annual), CPT FV. FV = 2,262.04

ABC Energy: FV = 0 since it is a zero-coupon bond

Trans Power: PMT = coupon rate*face value/2 = 10%*1,000/2 = 50; rate (reinvestment rate) = 6%/2 = 3%; N = 20 years*2 = 40 (since payments are semi-annual), CPT FV. FV = 3,770.6

Telco Utilities: PMT = coupon rate*face value/2 = 12%*1,000/2 = 60; rate (reinvestment rate) = 6%/2 = 3%; N = 30 years*2 = 60 (since payments are semi-annual), CPT FV. FV = 4,524.08

The semi-annual realized return is calculated as { [(FV of the coupons reinvested + face value received at maturity)/Bond price]^(1/n) } - 1

So, the annual realized return will be twice of this.

Formula	(a)	(b)	('c)	(d)	{[(a+b)/c]^d}-1	Semi-annual return*2
Issuer	FV of coupons reinvested	Face value	Bond price	Number of payments	Semi-annual return	Annual return
ABC Energy	2,262.04	1,000	809.10	40	3.55%	7.09%
ABC Energy	-	1,000	211.64	40	3.96%	7.92%
Trans Power	3,770.06	1,000	1,025.00	40	3.92%	7.84%
Telco Utlities	4,524.08	1,000	1,300.00	60	2.44%	4.88%

2). Coupon rates depend on the credit rating of the issuer. Higher the credit rating (implies lower risk), lower will be the coupon rate and lower the credit rating (implying higher risk), greater will be the coupon rate. Additionally, bonds will also carry call risk (if they are callable), maturity risk, reinvestment risk and the risk effect of the sinking fund provision. A callable bond with greater maturity period and no sinking fund provision (as given in the table) like Telco Utilities is the riskiest of the lot and that is reflected in its quoted price which is also the highest.