Question

What is the yield to maturity of a five​-year, $10,000

bond with a 4.1% coupon rate and semiannual coupons if this bond is currently trading for a price of

$9,227​?

A. 7.09​%

B. 2.95​%

C. 8.27​%

D. 5.91​%

Answer 1

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
1-10	$               205.00	8.7521	$            1,794.17	8.5302	$                1,748.69
10	$         10,000.00	0.7812	$            7,811.98	0.7441	$                7,440.94
PV of Cash Inflows	$            9,606.16		$                9,189.63
PV of Cash Oiutflows	$            9,227.00		$                9,227.00
NPV	$               379.16		$                    -37.37

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%

= 0.025 + [379.16 / 416.53 ] * 0.5%

= 0.025 + [0.91 * 0.5% ]

= 0.025 + [0.0046]

= 0.0296

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

= 0.0296 * 2

= 0.0591

i.e 5.91 %

Option D is correct.

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