Question
In: Finance
Suppose that you buy a Walmart bond with the following features: coupon rate: 6.000% semi-annual coupons...
Suppose that you buy a Walmart bond with the following features:
- coupon rate: 6.000%
- semi-annual coupons
- par of $1,000
- 12 years to maturity
- yield (YTM) of 6.500%
- settlement date: Dec. 31, 2020
- maturity date: Dec. 31, 2032
What is the duration (in years) for this bond?
Solutions
Expert Solution
Duration of the bond calculation:
| Year (t) | Payments (n) | Cash Flow from coupon payments (6%/2 of $1000) | Cash Flow from maturity amount | Total Cash Flow from coupon payments and maturity amount (CF) | Present value (PV) discounted at 6.5%/2 =3.25% semiannual yield to maturity [PV = CF/(1+3.25%)^n] | PV *t |
| 0.5 | 1.0 | $30.0 | $30.0 | $29.06 | $14.53 | |
| 1.0 | 2.0 | $30.0 | $30.0 | $28.14 | $28.14 | |
| 1.5 | 3.0 | $30.0 | $30.0 | $27.26 | $40.88 | |
| 2.0 | 4.0 | $30.0 | $30.0 | $26.40 | $52.79 | |
| 2.5 | 5.0 | $30.0 | $30.0 | $25.57 | $63.92 | |
| 3.0 | 6.0 | $30.0 | $30.0 | $24.76 | $74.29 | |
| 3.5 | 7.0 | $30.0 | $30.0 | $23.98 | $83.94 | |
| 4.0 | 8.0 | $30.0 | $30.0 | $23.23 | $92.91 | |
| 4.5 | 9.0 | $30.0 | $30.0 | $22.50 | $101.23 | |
| 5.0 | 10.0 | $30.0 | $30.0 | $21.79 | $108.94 | |
| 5.5 | 11.0 | $30.0 | $30.0 | $21.10 | $116.06 | |
| 6.0 | 12.0 | $30.0 | $30.0 | $20.44 | $122.63 | |
| 6.5 | 13.0 | $30.0 | $30.0 | $19.79 | $128.67 | |
| 7.0 | 14.0 | $30.0 | $30.0 | $19.17 | $134.20 | |
| 7.5 | 15.0 | $30.0 | $30.0 | $18.57 | $139.26 | |
| 8.0 | 16.0 | $30.0 | $30.0 | $17.98 | $143.87 | |
| 8.5 | 17.0 | $30.0 | $30.0 | $17.42 | $148.05 | |
| 9.0 | 18.0 | $30.0 | $30.0 | $16.87 | $151.82 | |
| 9.5 | 19.0 | $30.0 | $30.0 | $16.34 | $155.22 | |
| 10.0 | 20.0 | $30.0 | $30.0 | $15.82 | $158.24 | |
| 10.5 | 21.0 | $30.0 | $30.0 | $15.33 | $160.92 | |
| 11.0 | 22.0 | $30.0 | $30.0 | $14.84 | $163.28 | |
| 11.5 | 23.0 | $30.0 | $30.0 | $14.38 | $165.33 | |
| 12.0 | 24.0 | $30.0 | $1,000.0 | $1,030.0 | $478.05 | $5,736.63 |
| sum | $958.78 | $8,285.76 | ||||
| Bond's Price↑ | ||||||
| Duration = sum of (PV*t)/sum of PVs = | $8,285.76/ $958.78 | 8.64 |
Duration of the bond is 8.64 years
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