Once upon a time, the treasurer of “Mighty Corporation” (MCO) decided to issue a bond (hereafter: The bond) The bond would have a 20-year life and promised that the holder of the bond would receive:
The bond is bought by an insurance company. One-year passes, the bond has made its first coupon payment, and the interest rate/yield-to-maturity on the bond falls to 6%.
A) What is the Coupon Yield on the bond?
B) The bond now has 19 years left. Calculate the Macaulay duration of the bond.
A
K = N |
Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k] + Par value/(1 + YTM)^N |
k=1 |
K =19 |
Bond Price =∑ [(8*1000/100)/(1 + 6/100)^k] + 1000/(1 + 6/100)^19 |
k=1 |
Bond Price = 1223.16 |
Using Calculator: press buttons "2ND"+"FV" then assign |
PMT = Par value * coupon %=1000*8/(100) |
I/Y =6 |
N =19 |
FV =1000 |
CPT PV |
Using Excel |
=PV(rate,nper,pmt,FV,type) |
=PV(6/(100),19,-8*1000/(100),-1000,) |
current yield = coupon rate*par value/current price |
Current yield%=(8/100)*1000/1223.16 |
Current yield% = 6.54 |
B
Period | Cash Flow | Discounting factor | PV Cash Flow | Duration Calc |
0 | ($1,223.16) | =(1+YTM/number of coupon payments in the year)^period | =cashflow/discounting factor | =PV cashflow*period |
1 | 80.00 | 1.06 | 75.47 | 75.47 |
2 | 80.00 | 1.12 | 71.20 | 142.40 |
3 | 80.00 | 1.19 | 67.17 | 201.51 |
4 | 80.00 | 1.26 | 63.37 | 253.47 |
5 | 80.00 | 1.34 | 59.78 | 298.90 |
6 | 80.00 | 1.42 | 56.40 | 338.38 |
7 | 80.00 | 1.50 | 53.20 | 372.43 |
8 | 80.00 | 1.59 | 50.19 | 401.54 |
9 | 80.00 | 1.69 | 47.35 | 426.17 |
10 | 80.00 | 1.79 | 44.67 | 446.72 |
11 | 80.00 | 1.90 | 42.14 | 463.57 |
12 | 80.00 | 2.01 | 39.76 | 477.09 |
13 | 80.00 | 2.13 | 37.51 | 487.59 |
14 | 80.00 | 2.26 | 35.38 | 495.38 |
15 | 80.00 | 2.40 | 33.38 | 500.72 |
16 | 80.00 | 2.54 | 31.49 | 503.87 |
17 | 80.00 | 2.69 | 29.71 | 505.06 |
18 | 80.00 | 2.85 | 28.03 | 504.50 |
19 | 1,080.00 | 3.03 | 356.95 | 6,782.13 |
Total | 13,676.89 |
Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year) |
=13676.89/(1223.16*1) |
=11.181602 |
Once upon a time, the treasurer of “Mighty Corporation” (MCO) decided to issue a bond (hereafter:...
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