Question
In: Finance
What is the approximate modified duration of a 22-year bond, making semiannual coupon payments, with a...
What is the approximate modified duration of a 22-year bond, making semiannual coupon payments, with a coupon rate of 5% and a current price of 69.18 per 100 of par value, considering a 50 bps change in discount rate?
Solutions
Expert Solution
| Par Value | $ 100.00 |
| Nper | 44 |
| Coupon (semi annual) | $ 2.50 |
| Coupon Rate | 5% |
| Coupon per year | 2 |
| Years to maturity | 22 |
| Current Price | $ 69.18 |
| Yield to maturity (YTM) | 8.0% |
| Formula Explained | |
| Nper |
Total number of payment periods Coupon per year * years of maturity |
| PMT | Interest Payments, Par value*Coupon rate divided by coupons per year |
| PV | The current price of the bond, which is negative because it’s the cost to buy today |
| FV | Par value, because this is the future value of the bond at maturity |
| Type | 0, default |
| Re annualizing | Coupon per year |
|
|||
| YTM 1 | 8.50% | ||
| YTM 2 | 7.50% | ||
| Price of bond for YTM 1 | $65.42 | ||
| Price of bond for YTM 2 | $73.26 | ||
| Modified Duration | 11.33948121 |
|
Formula for Modified Duration |
(Price of bond with YTM 2 -Price of bond with YTM 1) divided by (2* Initial price* change in yield) |
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jeff jeffy answered 1 year agoRelated Solutions
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