In: Finance
An Apple annual coupon bond has a coupon rate of 6.9%, face value of $1,000, and 4 years to maturity. If its yield to maturity is 6.9%, what is its Modified Duration? Answer in years, rounded to three decimal places.
Modified Duration = Duration / (1+YTM)
Duration = Sum [ Weight * Year ]
Year | CF | PVF @6.9% | Disc CF | Weight | Duration |
1 | $ 69.00 | 0.9355 | $ 64.55 | 0.0645 | 0.06 |
2 | $ 69.00 | 0.8751 | $ 60.38 | 0.0604 | 0.12 |
3 | $ 69.00 | 0.8186 | $ 56.48 | 0.0565 | 0.17 |
4 | $ 69.00 | 0.7658 | $ 52.84 | 0.0528 | 0.21 |
4 | $ 1,000.00 | 0.7658 | $ 765.75 | 0.7658 | 3.06 |
Duration | 3.63 |
Modfied duration = Duration / ( 1+YTM)
= 3.63 / ( 1 + 0.069)
= 3.63 / 1.069
= 3.40%
Modified duartion is 3.40%