Question

GE has a 10%, 10-year bond with interest paid annually. If the bond was issued 2 years ago and is currently quoted at 110, calculate the YTM. Show the (condensed) timeline and key steps of two methods. For the NS method, show the abbreviated equation/expression

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.

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

It assumes coupon payments are reinvested at YTM only.

Original Maturity 10 Years

Lapsed period 2 Years

Balance years 8 Years.

Assuming $ 1000 is Face Value.

Year	Cash Flow	PVF/ PVAF @ 8 %	PV of Cash Flows	PVF/ PVAF @ 9 %	PV of Cash Flows
1-8	$                100.00	5.7466	$                        574.66	5.5348	$                     553.48
8	$             1,000.00	0.5403	$                        540.27	0.5019	$                     501.87
PV of Cash Inflows			$                    1,114.93		$                 1,055.35
PV of Cash Oiutflows			$                    1,100.00		$                 1,100.00
NPV			$                          14.93		$                     -44.65

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 8 % + [ 14.93 / 59.58 ] * 1%
= 8 % + [ 0.25 ] * 1%
= 8 % + [ 0.2506 % ]
= 8.25 %

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