Question

Please read before doing this. I have everything down but I'm stuck on b and c. By stuck I mean what would the formula and final answer be in this scenario since it's SEMIANNUAL. I'm only familiar with annual payments regarding durations and price changes, and I'm seeing a lot of different results, too. Please do this on Excel as well.

14. Consider a bond that has a coupon of 8 percent paid semiannually and has a maturity of 5 years. The bond is currently selling for $1,047.25. Use Excel to do the following analysis.

a. What is its yield-to-maturity?

b. Compute its duration.

c. If interest rates are expected to increase by 75 basis points, what is the expected dollar change in price? What is the expected percentage change in price?

Answer 1

a. What is the yield to maturity?
YTM = (Interest + average other cost per annum*) / average fund employed**
*average other cost per annum = (Redemption price - current market price) / life remaining to mature
= (1000-1047.25)/10
-23.625
= -4.725
**average fund employed = Redemption price*.4 + current market price*.6
= 1000*.4 + 1047.25*.6
1028.35
1028.35
YTM = (40+-4.725)/1028.35
0.034302523
0.0343
= 3.43%
3.43% is the half year YTM.Therefore YTM per Year will be 6.86(3.43*2)
Here years to maturity is taken as 10(5*2) and interest as 40(1000*8%/2), since bond makes semi annual payments.
It is general practice to take $1000 as face value of bond when no information provided.
b. Compute its duration?
Time	Cashflow	[email protected]%	Present Value (Cashflow*PVF)	Weight based on present value	Time*Weight
1	40	0.967	38.67	0.0369	0.0369
2	40	0.935	37.39	0.0357	0.0714
3	40	0.904	36.15	0.0345	0.1035
4	40	0.874	34.95	0.0334	0.1335
5	40	0.845	33.79	0.0323	0.1613
6	40	0.817	32.67	0.0312	0.1871
7	40	0.79	31.59	0.0302	0.2111
8	40	0.764	30.54	0.0292	0.2332
9	40	0.738	29.53	0.0282	0.2537
10	1040	0.714	742.28	0.7086	7.0857
Duration =
Time*Weight = 8.4774 = 8.48
c. If interest rates are expected to increase by 75 basis points, what is the expected dollar change in price?What is the expected percentage change in price?
Modified Duration = Duration / (1+YTM)
= 8.48/(1..0343)
8.2
Modified Duration Measures the % change in price for every % change in interest rate. The direction of change are in opposite direction. THat is when the interest increases price decreases and vice-versa.
Here the interest rates are expected to increase by 75 basis points. We know that 100 basic points=1%. 75 basic points = .75%(75/100)
% change in price = Modified Duration * % change in interest rate.
6.15
0.0615
Since the interest rates are expected to increase, price expected to decrease.
Change in price = 1047.25 - (1047.25*6.15%)
982.84
982.84