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Assume the face value of the bond is £100 i
Assume the face value of the bond is £100
i. Calculate the Macaulay Duration for an £9 annual coupon bond with 3 years left to maturity if the bond’s yield to maturity is 8%. (Show your calculations)
ii. What is the modified duration of the bond?
iii. If 3 year yields to maturity were to suddenly to increase from 8% to 9% and the bond in problem (i) was selling for £102.58 at 8% yield, what would you expect the bond price to be after the yield increases to 9% ?
Expert Solution
i)
| Time Period | Cash Flow | PV of Cash Flow @ 8% | Time Weighted PV of Cash Flow |
| A | B | C = B / (1 + 0.08)^A | C x A |
| 1 | £ 9.00 | £ 8.33 | £ 8.33 |
| 2 | £ 9.00 | £ 7.72 | £ 15.43 |
| 3 | £ 109.00 | £ 86.53 | £ 259.58 |
Sum of Time Weighed PV of Cash Flows = 283.35
Sum of PV of Cash flows = 102.58
Macaulay's Duration = 283.35 / 102.58 = 2.76
ii)
Modified Duration = Macaulay Duration / (1 + YTM) = 2.76 / (1 + 0.08) = 2.56
iii)
Chage in Yield = 9 - 8 = 1%
% Change in price = Change in Yield x (- Mod. Duration) = 1 x (-2.56) = -2.56%
New Price = 102.58 x (1 - 0.0256) = 99.95
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