ABC Corporation issued 20-year, noncallable, 8% coupon bonds that pays coupon payment semi-annually. Par value is $1,000. Assume market interest rate on these bonds is 5.5%. What is the current price of the bonds?
A. 1300.98
B. 1267.10
C. 1377.27
D. 1271.55
Solution:-
ANS:- A) 1300.98
CALCULATION:-
Coupon rate= 8%
Par value of bond = $1,000
Time to mature = 20 year
Required rate of return (RR)= 5.5%
Coupon payment= Semiannually
Semiannual interest = $1000*8%*1/2= $40
Semiannual required rate of return (RR)= 5.5%*1/2 =2.75%
The current price of the bond can be calculated as follows,
Current market price
= Semiannual interest*PVIFA(RR,N)+Maturity value*PVIF(RR ,N)
=$40*PVIFA(2.75% , 40) +$1000*PVIF(2.75%, 40)
=$40*24.078101+1000*0.33785222
=$1300.98
Please feel free to ask if you have any query in the comment section.
PVIFA calculations:- | |
Peroids | 1/(1+2.75%)^peroids |
1 | 0.97323601 |
2 | 0.947188331 |
3 | 0.921837791 |
4 | 0.897165734 |
5 | 0.873153999 |
6 | 0.849784914 |
7 | 0.827041278 |
8 | 0.804906354 |
9 | 0.783363848 |
10 | 0.762397906 |
11 | 0.741993095 |
12 | 0.722134399 |
13 | 0.702807201 |
14 | 0.683997276 |
15 | 0.66569078 |
16 | 0.647874238 |
17 | 0.630534538 |
18 | 0.613658918 |
19 | 0.597234957 |
20 | 0.581250566 |
21 | 0.565693982 |
22 | 0.550553754 |
23 | 0.535818738 |
24 | 0.521478091 |
25 | 0.507521256 |
26 | 0.493937962 |
27 | 0.480718211 |
28 | 0.467852274 |
29 | 0.45533068 |
30 | 0.443144214 |
31 | 0.431283907 |
32 | 0.419741029 |
33 | 0.408507084 |
34 | 0.397573804 |
35 | 0.386933143 |
36 | 0.376577268 |
37 | 0.366498558 |
38 | 0.356689594 |
39 | 0.347143157 |
40 | 0.337852221 |
Total | 24.07810106 |
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