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PART A: Calculating Yield to Maturity
The yield to maturity is the effective yield on a bond on the basis of the expected coupons and reinvestment of the received coupons till maturity. The same can be calculated as given below:
Par Value |
$1000 |
Given |
|
Price = Initial Investment |
$1000 |
Given |
|
Coupon |
$122 |
Annual Frequency |
|
Tenor of Bond = n |
2 |
Years |
|
Coupon Rate |
12.20% |
Calculated as = 122 / 1000 |
|
Re-invest. Rate of coupon |
12.20% |
Same as coupon rate |
|
Particular |
Year 1 |
Reinvestment |
CF at end of Year 2 |
1st Coupon |
122 |
122 * (1 + 12.2%) |
136.88 |
2nd Coupon + Principal |
1122.00 |
||
Total Investment Value |
1258.88 |
The overall yield can be calculated as:
YTM = (Investment value at end of tenor / Initial Investment) ^ (1 / n) – 1
Hence, YTM = (1258.88 / 1000 ) ^ (1/2) – 1
YTM = 12.2%
PART B: Realized YTM is the interest rate changes i.e. The Re-investment rate of coupon changes
When Re-investment rate of coupon = 8%
Particular |
Year 1 |
Reinvestment |
Total |
1st Coupon |
122 |
122 * (1 + 8%) |
131.76 |
2nd Coupon + Principal |
1122 |
||
Total Cash Flows |
1253.76 |
The overall yield can be calculated as:
YTM = (Investment value at end of tenor / Initial Investment) ^ (1 / n) – 1
Hence, YTM = (1253.76 / 1000 ) ^ (1/2) – 1
YTM = 11.97%
When Re-investment rate of coupon = 9%
Particular |
Year 1 |
Reinvestment |
Total |
1st Coupon |
122 |
122 * (1 + 9%) |
132.98 |
2nd Coupon + Principal |
1122 |
||
Total Cash Flows |
1254.98 |
The overall yield can be calculated as:
YTM = (Investment value at end of tenor / Initial Investment) ^ (1 / n) – 1
Hence, YTM = (1254.98 / 1000 ) ^ (1/2) – 1
YTM = 12.03%
When Re-investment rate of coupon = 10%
Particular |
Year 1 |
Reinvestment |
Total |
1st Coupon |
122 |
122 * (1 + 10%) |
134.2 |
2nd Coupon + Principal |
1122 |
||
Total Cash Flows |
1256.2 |
The overall yield can be calculated as:
YTM = (Investment value at end of tenor / Initial Investment) ^ (1 / n) – 1
Hence, YTM = (1256.2 / 1000 ) ^ (1/2) – 1
YTM = 12.08%
r |
Realized YTM |
8% |
11.97% |
9% |
12.03% |
10% |
12.08% |
PLEASE SHOW SOLUTION IN DETAIL. THANK YOU! Chapter 14 0 Saved Help Save & Exit Submit...
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