Question

A 6.35% coupon bond with 19 years left to maturity can be called in 11 years. The call premium is 1 year of coupon payments, it is currently offered for sale at $964,000. What is the yield to maturity? (Assume interest payments are semiannual)

Answer 1

YTC:
YTC is the rate at which PV of Cash inflows are equal to Bond price when the bond is held till it is called.

Maturity Value = Face Value + 1 Year Coupon amount

Coupon AMount = $ 1000000 * 6.35% /2

= $ 31750.00

Period	Cash Flow	PVF/[email protected]	PV of Cash Flows	PVF/[email protected]	PV of Cash Flows
1-22	$         31,750.00	15.1671	$       4,81,556.21	14.4511	$          4,58,822.91
22	$    10,63,500.00	0.4692	$       4,98,941.70	0.4220	$          4,48,749.55
PV of Cash Inflows	$      9,80,497.91		$          9,07,572.47
PV of Cash Oiutflows	$      9,64,000.00		$          9,64,000.00
NPV	$          16,497.91		$            -56,427.53

YTC per six months = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 0.5% in Int Rate ] * 0.5%

= 0.035 + [16497.91 / 72925.44 ] * 0.5%

= 0.035 + [0.23 * 0.5% ]

= 0.035 + [0.0011]

= 0.0361

YTC Per anum = IRR per six months * 12 / 6

= 0.0361 * 2

= 0.0723

i.e 7.23 %

YTM:
YTM is the rate at which PV of Cash inflows are equal to Bond price when the bond is held till maturity.

Period	Cash Flow	PVF/[email protected]	PV of Cash Flows	PVF/[email protected]	PV of Cash Flows
1-38	$         31,750.00	22.4925	$       7,14,135.66	20.8411	$          6,61,704.52
38	$    10,00,000.00	0.3252	$       3,25,226.15	0.2706	$          2,70,561.94
PV of Cash Inflows	$    10,39,361.81		$          9,32,266.47
PV of Cash Oiutflows	$      9,64,000.00		$          9,64,000.00
NPV	$          75,361.81		$            -31,733.53

YTM per six months = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 0.5% in Int Rate ] * 0.5%

= 0.03 + [75361.81 / 107095.34 ] * 0.5%

= 0.03 + [0.7 * 0.5% ]

= 0.03 + [0.0035]

= 0.0335

YTM Per anum = IRR per six months * 12 / 6

= 0.0335 * 2

= 0.067

i.e 6.7 %

Pls do rate, if the answer is correct and comment, if any further assistance is required.