Question

In: Finance

Find the duration of a bond with a settlement date of May 27, 2020, and maturity...

Find the duration of a bond with a settlement date of May 27, 2020, and maturity date November 15, 2031. The coupon rate of the bond is 7.5%, and the bond pays coupons semiannually. The bond is selling at a bond-equivalent yield to maturity of 5.5%. Use Spreadsheet 16.2. (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Macaulay duration
Modified duration

Solutions

Expert Solution

The cash flows for the bond is captured for every period from may 20 to nov 31

Coupon payment of 37.5 (1000X7.5%X1/2) semi annual from may 20 to may 31.

Nov 31, coupon amount 37.5+ redemption 1000 ,total cash flow 1037.5

Discount factor at Yield rate of 5.5%pa or 2.275%(0.00275) for 6 months is calculated by,

Discount factor   =    1/ (1+r)^n

Discount factor multiplied by respective CF gives the discounted Cash flows..

Sum of these DCF will be the price of the bond.

Discounted cash flows are again multiplied by the period to arrive at the time weighted DCF

the sum of this is divided by 2- since its semi annual

mac duration is arrived by dividing the above sum of time weighted DCF by the Price of the bond

modified duration is arrived by dividing the mac duration by (1+r)

accordingly,

excel formula

..


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