The market price is $850 for a 15-year bond ($1,000 face value)with a 6% annual...

The market price is $850 for a 15-year bond ($1,000 face value) with a 6% annual coupon rate. What is the bond's expected rate of return?

Expert Solution

Expected Ret from bond is nothing but YTM.

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

YTM = Rate at which least +ve NPV + [ NPV at that Rate / Change in NPV due to 1% inc in disc rate ] * 1%

Year	Cash Flow	PVF/ PVAF @ 7 %	PV of Cash Flows	PVF/ PVAF @ 8 %	PV of Cash Flows
1-15	$ 60.00	9.1079	$ 546.47	8.5595	$ 513.57
15	$ 1,000.00	0.3624	$ 362.45	0.3152	$ 315.24
PV of Cash Inflows			$ 908.92		$ 828.81
PV of Cash Oiutflows			$ 850.00		$ 850.00
NPV			$ 58.92		$ -21.19

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 7 % + [ 58.92 / 80.11 ] * 1%
= 7 % + [ 0.74 ] * 1%
= 7 % + [ 0.7355 % ]
= 7.74 %

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

Expected Ret from Bond is 7.74%

jeff jeffy answered 2 years ago

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