## ccra bond chapter

agarwalla.harsha
Posts: 7
Joined: Tue Jul 14, 2015 6:55 am

### ccra bond chapter

1)
a 7% risk free bond is trading at 8% ytm, with \$91 price. find out percentage change in price for 1% change in ytm . duration is 8.2 and convexity 78.2.

2)) a 5year bond paying 8% annual pay coupon is currently trading for 1023.56 Having ytm of 7.42%. calculate effective duration of the bond given 25 basis point in ytm .

3)1. Langley Enterprises sold Rs.35,000 in stock and issued Rs.50,000 in debt this past year. The firm also repaid Rs.24,000 on its loans and paid Rs.5,600 in interest. During the year, Langley paid quarterly dividends which totaled to Rs.12,000 for the year and earned a net income of Rs.38,700. The beginning balances at the start of the year were:
I. Preferred stock Rs. 80,000
II. Treasury stock 4,000
III. Long-term debt 92,000
IV. Accumulated retained earnings 126,500
V. Capital surplus 248,600
VI. Common stock 160,000
What is the book value of stockholders' equity at the end of the year?

edupristine
Finance Junkie
Posts: 981
Joined: Wed Apr 09, 2014 6:28 am

### Re: ccra bond chapter

Solution 1:
Duration effect is = - annual modified duration*(change in YTM)
=-8.2*(0.01) = -0.082 = -8.2%
Convexity effect is = 1/2annual convexity*(change in convexity)^2
= 0.5*78.2*(0.01)^2 = 0.00391= 0.391%
Expected change in price= Duration Effect + convexity Effect
= -8.2% + 0.391%
=-7.809%

Solution 2:
Duration = (V_ - V+)/2*V0*(change in YTM)
Where,
V_ = price of bond if YTM is decreased by change in YTM
V+ = price of the bond if YTM is increased by change in YTM.
V0= Current price= 1023.56
Change in YTM= 25 basis point= 0.0025
The price of the bond at a yield of 7.42% + 0.25% = 7.67%
N = 5; I/Y = 7.67%; FV = 1,000; PMT = 80; CPT => PV = -1013.29
The price of the bond at a yield of 7.42% - 0.25% = 7.17%
N = 5; I/Y = 7.17%; FV = 1,000; PMT = 80; CPT => PV = -1033.88

= (V_ - V+)/2*V0*(change in YTM)
= [-1013.29 – (-1033.88)]/2*1023.56*0.0025
= (-1013.29+1033.88)/ 5.118
= -20.59/ 5.118
Effective Duration =-4.02

Solution 3:
Following are the calculation:-
Shareholder’s Equity:
+ 160000 (Common stock at the end)
+ 35000 (Sold stock)
+ 80000 (Preferred stock)
+ 4000 (Treasury stock)
+ 126500 (Accumulated retained earnings)
+ 248600 (Capital surplus)
+ 38700 (Net income)
-12000 (Dividend paid)
= 680800