1 Consider three coupon bonds that are identical in terms of their risk of defau
ID: 1172222 • Letter: 1
Question
1 Consider three coupon bonds that are identical in terms of their risk of default, tax treatments, and liquidity; each has a face value of $100 and promises a yield to maturity of 8 percent. However, they differ in terms of their coupon rates (c) and their times to maturity (ni), as follows: Bondi A 10% 3 years B 10% 2 years C 0% 3 years 1.1 Calculate the current prices for each bond i, p,(t), implied by the data provided in the table above. [20 points 1.2 Suppose that one year later, the yield to maturity on each of the bonds remains at 8 percent, implying pA(t+1) $103.57, PB(t+1) 101.85, and pe(t + 1) 85.73. For each bond i = A. B, C, calculate (i) the current yield (re), (ii) the capital gain (g) andiii) the implied one- year rate of return that would be realized if the bond were purchased in period t and then sold one year later at those prices in t+1. [20 points 1.3 Recalculate the one-year rates of return from the investment strategy described in question 1.2 above, with each bond i assuming that its yield to maturity, i, rises to 10 percent, (i-A, B, and C). 20 points] 1.4 Identify and briefly explain two factors, as illustrated by your results, that generally amplify the effects of a given change in market coni- tions on the realized rate of return relative to that which what was expected when the bond was purchased. [20 pointsExplanation / Answer
1) We will use financial calculator to calculate current price or PV:
Bond
A
B
C
FV
100
100
100
PMT
10
10
0
n
3
2
3
I/Y
8%
8%
8%
PV
($105.15)
($103.57)
($79.38)
2a)Current Yield= Annual Interest Payment/ Current Bond Price
Bond
A
B
C
PMT
10
10
0
PV
$103.57
$101.85
$85.73
Current Yield
9.6553%
9.8184%
0.0000%
2b) Capital Gain
Bond
A
B
C
T-1
$105.15
$103.57
$79.38
T
$103.57
$101.85
$85.73
Capital Gain
-1.5842
-1.7165
6.3468
2c) Implied One Year Return
Capital Gain + Coupon Payment/ T-1 Price
Bond
A
B
C
T-1
$105.15
$103.57
$79.38
Capital Gain
-1.5842
-1.7165
6.3468
Coupon
10
10
0
Capital Gain +Coupon
8.4158
8.2835
6.3468
Return
8.0033%
7.9982%
7.99511%
3) Prices of Bond with I/Y at 10%
Bond
A
B
C
FV
100
100
100
PMT
10
10
0
n
2
1
2
I/Y
10%
10%
10%
PV
($100.00)
($100.00)
($82.64)
Therefore, rate of return :
Bond
A
B
C
T-1
$105.15
$103.57
$79.38
T
$100.00
$100.00
$82.64
Capital Gain
-5.1542
-3.5665
3.2614
Coupon
10
10
0
Capital Gain +Coupon
4.8458
6.4335
3.2614
Return
4.6083%
6.2119%
4.10843%
Bond
A
B
C
FV
100
100
100
PMT
10
10
0
n
3
2
3
I/Y
8%
8%
8%
PV
($105.15)
($103.57)
($79.38)
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