Question

An 8% semiannual coupon bond matures in 4 years. The bond has a face value of $1,000 and a current yield of 8.2287%. What are the bond's price and YTM? (Hint: Refer to Footnote 6 for the definition of the current yield and to Table 7.1) Do not round intermediate calculations. Round your answer for the bond's price to the nearest cent and for YTM to two decimal places.

Answer 1

Part A:

Bond Price = Annual Coupon / Current Yield

= [ $ 1000 * 8% ] / 8.2287%

= $ 80 / 8.2287%

= $ 972.21

Part B:

YTM :

YTM is the rate at which PV of Cash inflows are equal to Bond price when the bond is held till maturity. Yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until it matures. Yield to maturity is considered a long-term bond yield but is expressed as an annual rate.

Period	Cash Flow	PVF/PVAF @ 4 %	PV of Cash Flows	PVF/ PVAF @4.5 %	PV of Cash Flows
1-8	$                 40.00	6.7327	$               269.31	6.5959	$                   263.84
8	$           1,000.00	0.7307	$               730.69	0.7032	$                   703.19
PV of Cash Inflows			$            1,000.00		$                   967.02
PV of Cash Oiutflows			$               972.21		$                   972.21
NPV			$                  27.79		$                      -5.19

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%
= 4 % + [27.79 / 32.98 ] * 0.5%
= 4 % + [0.84 * 0.5% ]
= 4 % + [0.4213 % ]
= 4.42 %

YTM Per anum = IRR per six months * 12 / 6
= 4.4213 % * 2
= 8.8426 %
i.e 8.84 %

PVAF = Sum [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r )^n
r - Int Rate per period
n - No. of Periods

How to calculate PVAF using Excel?
+PV(Rate,NPER,-1)
Rate = Disc rate
NPER - No. of Periods
YTM is 8.84%