Question

In: Finance

What is the yield to maturity of a five​-year, $10,000 bond with a 4.1% coupon rate...

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​%

Solutions

Expert Solution

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.


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