Question

1. Consider a three-year bond trading at $110.83 that pays a 10% coupon semi-annually and has a yield to maturity (YTM) of 6%.
   1. Calculate the duration of this bond.

b)What will be the final price if the YTM increases from 6% to 7%?

Answer 1

(a.) Calculation of Duration of Bond

Below is the table showing calculation of Duration :

(Weights)	Cah Flows	PVF @3%	Discounted Cash Flows	Weights * Discounted Cash Flows
1	5	0.970873786	4.854368932	4.854368932
2	5	0.942595909	4.712979546	9.425959091
3	5	0.915141659	4.575708297	13.72712489
4	5	0.888487048	4.44243524	17.76974096
5	5	0.862608784	4.313043922	21.56521961
6	105 (100 + 5)	0.837484257	87.93584695	527.6150817
		Total	110.8343829	594.9574952

Assuming Maturity value and face value of Bond = 100

Coupon = 100 * 10% = 10 / 2 = 5 (divided by 2 as coupons are paide semiannually)

TYM % is 6%/2 = 3% (divided by 2 as coupons are paide semiannually)

Duration = Sum of (Weights * Discounted Cash Flows) / Discounted Cash Flows

= 594.9574952 / 110.8343829

= 5.367986718 half years

= 5.367986718 / 2 = 2.683993359 years or 2.68 years

(b.) Calculation of Final Price if the YTM increases from 6% to 7%

Final Price can be calculated using PV function of Excel

=PV(rate,nper,pmt,fv)

where rate is YTM i.e 7%/2 = 3.5% ((divided by 2 as coupons are paide semiannually)

nper is the number of years i.e 3 * 2 = 6 (multiplied by 2 as coupons are paide semiannually)

pmt is coupon payment i.e 100 * 10% = 10/2 = 5

fv is the face value =100

=PV(3.5%,6,-5,-100)

Final price if  if the YTM increases from 6% to 7% is 107.99