Question

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You have the following details about the First Banc Corp. bond: Maturity = 9 years, Coupon rate (annual) = 5.25%, Yield to maturity = 4.2%, Par value = $1,000. Calculate the value of the bond, its duration and modified duration. What will be the change in value if interest rates go up by 1.0%?

Answer 1

All the calculations and formulas used are explained in the below images in detail.

1) Value of the bond = $1000.077

Sol" & Giren, Maturity = 9years. Coupon rate & 5.250%., t. YTM= 4.2% 2 Parvalue = $1000. I . a) Value at the bondir Vo= l + T & I + - t I lo (1 ) 11tr22 (trap on (Art) (ltetin Where, I Interest i... $000 @ 5.251. = 52.56. Pn= $1000. n=9 year I train Ixcitragnea, Pitta, 52.5 T400525) = 0.950 49.875 (1+0.0525/2 = 0.903 I 47.41 45.045 52.5 52.5 52.5 152.5 52.5 42.788 TH0.0525)3 = 0.858 ] T TH0.0525)4 = 0.815 I (H0.05255,0.774 T (H0.0525)6 = 0.736 TH0.05257 = 0.699 40.635 52.5 38.64 36.698 52.5 ( 10.0525) 80.664 34.86 52.5 33 128 (H0.0828) 9 = 0.631 0.631 I DOO 631

P & value of * 7) The bond (14 )9 - 1000.017$.
2) Duration of the bond = 7.4 years.

(b) Duration of the bonds Macauley at - exel (4 *) nx (1 M ) Duration I*(-15) + Maison Ix/1- +3) When This is I = 52.5 ; n = 9; M = $1000 *-5-25.1. dused where there is some interest for all years. 9 x I Calentativ iz! (Irti. te Or I 1x 52.5 52.5 0.950 9-3x+ (+0.0125) 49. 875 94.815 135.135 171.15 0.903 2X52.5 -105 |3x52.5=157.5 L 0.858 4 | 0.815 0.774 203.175 4x52.5 -210 5x52-5-2625 6x52.5 = 315 7x52.5=367.5 0.736 0.699 0.664 231.84 256.883 278.88 8x52.5=420 9x12.5-4725 0.631 298.148 - ( ) - 119.9014

.. Duration = 1,719.901 + 9x 1000 . (1+0.0525) 52-5*(-CHO0259 ) + 1000 0.0525 / (1+0.0525) 9 21,919.901 € 5,678.63 + 630.96 703 369.04 12 37398.531 .7.40.4&s. 1000 & Duration = 7.40 yes.
3) Modified duration of the bond = 7.1 years

4) Value of the bond when interest rates are increased by 1%

19 on lali Tion Modified ducation of the bond:- Macauley Modified duration - Duration (HKTM) When, n= No.of Coupons periods per = 7.4 140.042 year which 11 Os 1 piro - 7-10 yes.

(d) value of the band's I = $10000 6.25% = 62.56 son klhen, it increases by 1% 9. e., 6.25%. 1 year I ((1+raja) = (1 +0.0625) Ix (14157) and Para 62.5 THOO62s) = 0.941 58.813 62.5 (H0.0625) - 0.886 55.375 162.5 (140062533 2 0.834 52.125 4 162.5 (H0.0625) 4 = 0.785 49.063 62.5 (H0.0625150 0.739 46.188 62.5 (H0.0625)6 0.695 43.438 40.875 62.5 ( 10.0625) 8 0.616 162.5 (H0.062549) 0.579 36.188 (HooQ5)92 0.579 16 62.5 (1+0062) 7 - 0.654 38.5 9 000 T L I 579 e value of the be (Hryta (Hr)9 -999-565 $.