Question

A firm’s bonds currently sell for $1,180 and have a par value of $1,000.  They pay a $105 annual coupon and have a 15-year maturity, but they can be called in 5 years at $1,100.  What is their yield to call (YTC)?

Answer 1

Yield To Call (YTC)= 7.78

Calculation of yield to call

Par value of the bond = 1000

Coupon = 105

Number of years = 12

Price of the bond (market price) = 1180

Callable = 5 years at 1100

YTC = ?

Market price= ∑ coupon/(1+ytc)t+ callable value/(1+ytc)n

Or we can apply the formula

Market price = (Coupon*PVFA) + (callable value*PVF)

Assume YTC is 10%

PVFA for 5 years, 10% = 3.7908

PVF for 5 years, 10% = 0.6209

Market price = (105*3.7908) + (1000*0.6209)

=398.034 + 682.99

Market price of the bond where YTC is 10% = 1081.024

Assume YTC is 7%

PVFA for 5 years, 7% = 4.1002

PVF for 5 years, 7% = 0.7130

Market price = (105*4.1002) + (1000*0.7130)

=430.521+ 784.3

Market price of the bond where YTC is 7% = 1214.821

YTC =

Lowest rate + [(value at lowest rate – market price)/(value at lowest rate – value at highest rate)] * difference in rate

= 7+[(1214.821-1180)/(1214.821-1081.024)]*10-7

= 7+(34.821)/(133.797)]*3

= 7+ 0.78

YTC = 7.78

Calculation of PVF and PVFA

PVF and PVFA for 5 years, 10%
year	pvf @ 10%	PVFA @ 10%
1	0.9091	0.9091
2	0.8264	1.7355
3	0.7513	2.4869
4	0.6830	3.1699
5	0.6209	3.7908
6	0.5645	4.3553
7	0.5132	4.8684
8	0.4665	5.3349
9	0.4241	5.7590
10	0.3855	6.1446
11	0.3505	6.4951
12	0.3186	6.8137
13	0.2897	7.1034
14	0.2633	7.3667
15	0.2394	7.6061

PVF and PVFA for 5 years, 7%
year	pvf @ 7%	PVFA @ 7%
1	0.9346	0.9346
2	0.8734	1.8080
3	0.8163	2.6243
4	0.7629	3.3872
5	0.7130	4.1002
6	0.6663	4.7665
7	0.6227	5.3893
8	0.5820	5.9713
9	0.5439	6.5152
10	0.5083	7.0236
11	0.4751	7.4987
12	0.4440	7.9427
13	0.4150	8.3577
14	0.3878	8.7455
15	0.3624	9.1079

Note- PVFA= present value factors for annuity

           PVF= present value factor