In: Finance
Question 3
Danielle Motors’ bonds have 5 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 8 percent. The bonds have a yield to maturity of 9 percent.
Required
What is the current market price of these bonds?
Compute the current yield
Compute the duration of the bond
Compute the modified duration and interpret your results
Current market price of the bond
Year | CF | PVF@9% | Disc CF |
1 | $ 80.00 | 0.9174 | $ 73.39 |
2 | $ 80.00 | 0.8417 | $ 67.33 |
3 | $ 80.00 | 0.7722 | $ 61.77 |
4 | $ 80.00 | 0.7084 | $ 56.67 |
5 | $ 80.00 | 0.6499 | $ 51.99 |
5 | $1,000.00 | 0.6499 | $ 649.93 |
Market price of the bond | $ 961.10 |
Current yeild = Annual coupon payment / current market price
= 80 / 961.1
= 8.32%
Duration
Year | CF | PVF@9% | Disc CF | Weights | Weights * Year |
1 | $ 80.00 | 0.9174 | $ 73.39 | 0.0764 | 0.0764 |
2 | $ 80.00 | 0.8417 | $ 67.33 | 0.0701 | 0.1401 |
3 | $ 80.00 | 0.7722 | $ 61.77 | 0.0643 | 0.1928 |
4 | $ 80.00 | 0.7084 | $ 56.67 | 0.0590 | 0.2359 |
5 | $ 80.00 | 0.6499 | $ 51.99 | 0.0541 | 0.2705 |
5 | $ 1,000.00 | 0.6499 | $ 649.93 | 0.6762 | 3.3812 |
Duration | 4.2968 |
Modified Duration = Duration / (1+YTM)
= 4.2968 / (1+ 0.09)
= 4.2968 / (1.09)
= 3.9421
Pls do rate, if the answer is correct and comment, if any further assistance is required.