Question

Pelzer Printing Inc. has bonds outstanding with 9 years left to maturity. The bonds have a 8% annual coupon rate and were issued 1 year ago at their par value of $1,000. However, due to changes in interest rates, the bond's market price has fallen to $901.40. The capital gains yield last year was -9.86%.

1. What is the yield to maturity? Do not round intermediate calculations. Round your answer to two decimal places.
      %
   
2. For the coming year, what is the expected current yield? (Hint: Refer to footnote 7 for the definition of the current yield and to Table 7.1.) Do not round intermediate calculations. Round your answer to two decimal places.
      %
   
   For the coming year, what is the expected capital gains yield? (Hint: Refer to footnote 7 for the definition of the current yield and to Table 7.1.) Do not round intermediate calculations. Round your answer to two decimal places.
      %
   
3. Will the actual realized yields be equal to the expected yields if interest rates change? If not, how will they differ?
   1. As long as promised coupon payments are made, the current yield will change as a result of changing interest rates. However, changing rates will cause the price to change and as a result, the realized return to investors will differ from the YTM.
   2. As long as promised coupon payments are made, the current yield will not change as a result of changing interest rates. However, changing rates will cause the price to change and as a result, the realized return to investors should equal the YTM.
   3. As long as promised coupon payments are made, the current yield will change as a result of changing interest rates. However, changing rates will cause the price to change and as a result, the realized return to investors should equal the YTM.
   4. As long as promised coupon payments are made, the current yield will change as a result of changing interest rates. However, changing rates will not cause the price to change and as a result, the realized return to investors should equal the YTM.
   5. As rates change they will cause the end-of-year price to change and thus the realized capital gains yield to change. As a result, the realized return to investors will differ from the YTM.

Answer 1

A	B	C	D	E	F	G	H	I	J	K
2
3		a)
4
5		Face value	$1,000
6		Coupon rate	8.00%
7		Current Price	$901.40
8		Years to Maturity	9	years
9		Annual Coupon	80	=D4*D5
10		Cash flow to investor will be as follows:
11		Year	0	1	2	3	4	5	9
12		Cash flow	($901)	$80	$80	$80	$80	$80	$1,080	=D9+D5
13
14		Yield to maturity is the rate at which if future NPV to Investor will be zero.
15
16		Rate(nper,pmt,PV, [fv],type) function of excel can be used to find the yield to maturity as follows:
17		NPER	9
18		PMT	$80
19		PV	($901.40)
20		FV	$1,000
21
22		Yield to maturity	9.69%	=RATE(D18,D19,D20,D21)
23
24		Thus yield to maturity is	9.69%
25
26		b)
27
28		Current Yield	=Annual Coupon / Price of the bond
29			=$80 / $901.40
30			8.88%	=D9/D7
31
32		Hence the current yield is	8.88%
33
34		Expected Capital gain Yield	=YTM - Current Yield
35			=9.69% - 8.88%
36			0.81%
37
38		Hence Expected Capital gain yield	0.81%
39
40		Expected Capital gain yield can also be found as follows:
41		Expected Capital gain Yield	=(Price after 1 Year - Current Price)/ Current Price
42		After one Year,
43		Time to maturity	8	Years
44		YTM	9.69%
45		Face Value	$1,000
46		Annual Coupon	$80.00
47		Price of bond	=Present value of all the cash flows
48			=$80*(P/A,9.69%,8)+$1000*(P/F,9.69%,8)
49			$908.76	=D46*PV(D44,D43,-1,0)+D45*(1/((1+D44)^D43))
50
51		Expected Capital gain Yield	=(Price after 1 Year - Current Price)/ Current Price
52			=($908.76 - $901.40)/$901.40
53			0.82%	=(908.75-901.4)/901.4
54
55		Hence Expected capital gain Yield	0.82%
56
57		c)
58		Since price of the bond is the present value of cash flows from the bond discounted at interest rate,
59		therefore, change in interest rate will change the price of the bond.
60		Thus both the current price and the future price will change.
61
62		Hence the current yield will change and the realized return will differ from the YTM.
63		Therefore the option (I) is correct.
64