Question

Cavu Air Inc., issued 15 Year bonds 2 years ago at a coupon rate of 7.30% percent. The bonds make semi annual payments. If these bonds currently sell for 103 percent of par value, what is the YTM? Settlement date 1/1/2000 Maturity date 1/1/2013 Annual coupon rate 7.30% Coupons per year 2 Face value (% of par) 100 Bond price (% of par) 103

Answer 1

Assume face value of bond (m) = 1000; Period = 6months (Semi annual)

Current bond price (s) = face value*103% = 1000*103% = 1030

Coupon amount per period (c) = 1000*7.3%/2 = 36.5

Periods remaining to maturity (n) = 13years*2 = 26periods

Approximate YTM = [c + (m-s)/n]/[(s+m)/2] = [36.5+(1000-1030)/26]/[(1030+1000)/2] = [36.5-(30/26)]/(2030/2) = [36.5 - 1.153846]/1015 = 35.346154/1015 = 0.0348 = 3.48% per period*2 = 6.96% per annum

Computation of YTM using discounted cashflow model:

Period	Type	Cashflow	PVF @ 3.25%	Discounted cashflow @ 3.25% (Cashflow * PVF @ 3.25%)	PVF @ 3.5%	Discounted cashflow @ 3.5% (Cashflow * PVF @ 3.5%)
1	Coupon	36.50	0.9685	35.35025	0.9662	35.26630
2	Coupon	36.50	0.9380	34.23700	0.9335	34.07275
3	Coupon	36.50	0.9085	33.16025	0.9019	32.91935
4	Coupon	36.50	0.8799	32.11635	0.8714	31.80610
5	Coupon	36.50	0.8522	31.10530	0.8419	30.72935
6	Coupon	36.50	0.8254	30.12710	0.8134	29.68910
7	Coupon	36.50	0.7994	29.17810	0.7859	28.68535
8	Coupon	36.50	0.7742	28.25830	0.7593	27.71445
9	Coupon	36.50	0.7498	27.36770	0.7336	26.77640
10	Coupon	36.50	0.7262	26.50630	0.7088	25.87120
11	Coupon	36.50	0.7033	25.67045	0.6848	24.99520
12	Coupon	36.50	0.6812	24.86380	0.6616	24.14840
13	Coupon	36.50	0.6598	24.08270	0.6392	23.33080
14	Coupon	36.50	0.6390	23.32350	0.6176	22.54240
15	Coupon	36.50	0.6189	22.58985	0.5967	21.77955
16	Coupon	36.50	0.5994	21.87810	0.5765	21.04225
17	Coupon	36.50	0.5805	21.18825	0.5570	20.33050
18	Coupon	36.50	0.5622	20.52030	0.5382	19.64430
19	Coupon	36.50	0.5445	19.87425	0.5200	18.98000
20	Coupon	36.50	0.5274	19.25010	0.5024	18.33760
21	Coupon	36.50	0.5108	18.64420	0.4854	17.71710
22	Coupon	36.50	0.4947	18.05655	0.4690	17.11850
23	Coupon	36.50	0.4791	17.48715	0.4531	16.53815
24	Coupon	36.50	0.4640	16.93600	0.4378	15.97970
25	Coupon	36.50	0.4494	16.40310	0.4230	15.43950
26	Coupon+redemption	1,036.50	0.4353	451.18845	0.4087	423.61755
				1,069.36340		1,025.07185

YTM = Base rate + (ΣDiscounted cashflow @ 3.25%-Current bond price)*Difference in discounting rate/(ΣDiscounted cashflow @ 3.25%-ΣDiscounted cashflow @ 3.5%)

= 3.25% + (1069.3634-1030)*(3.5%-3.25%)/(1069.3634-1025.07185) = 3.25% + (39.3634*0.25%)/44.29155 = 3.25%+0.2222% = 3.4722% per period = 6.9444%

Note: PVF = Present value factor

PVF @ 3.25% for period 1 = 1/[(1+rate)^period] = 1/[(1+0.0325)^1] = 1/1.0325 = 0.9685

PVF @ 3.25% for period 2 = 1/[(1+rate)^period] = 1/[(1+0.0325)^2] = 1/(1.0325^2) = 0.9380

Similarly for further period & PVF @ 3.5% it goes on.