Question

savvy sammy just sold a 9.5% coupon bond with 8 years remaining maturity for $1,080. He purchased the bond two years ago, which is when the bond was first issued to the public as a new issue par bond.

1A) What is the YTM for this bond today?

- 9.50%

-5.23%

- 8.89%

- 8.12%

-13.13%

1B) What is the YTM for the bond when it was first issued?

- 9.50%

-5.23%

- 13.13%

- 8.89%

- 8.12%

1C) What is sammy's realized holding period yield (HPY) on his investment?

- 8.12%

- 9.50%

- 13.13%

- 5.23%

- 8.89%

Answer 1

Part 1)

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.

Year	Cash Flow	PVF/ PVAF @ 8 %	PV of Cash Flows	PVF/ PVAF @ 9 %	PV of Cash Flows
1-8	$                  95.00	5.7466	$      545.93	5.5348	$                     525.81
8	$             1,000.00	0.5403	$      540.27	0.5019	$                     501.87
PV of Cash Inflows			$ 1,086.20		$                 1,027.67
PV of Cash Oiutflows			$ 1,080.00		$                 1,080.00
NPV			$          6.20		$                     -52.33

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 8 % + [ 6.2 / 58.53 ] * 1%
= 8 % + [ 0.11 ] * 1%
= 8 % + [ 0.1059 % ]
= 8.11 %

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

Part 2)

Two Years ago Bond is issued at par,

Bond will be issued at par if coupon rate equal to yield.

Thus Yield (YTM ) is 9.5%

Part 3)

Year	Cash Flow	PVF/ PVAF @ 13 %	PV of Cash Flows	PVF/ PVAF @ 14 %	PV of Cash Flows
1-2	$                  95.00	1.6681	$      158.47	1.6467	$                     156.43
2	$             1,080.00	0.7831	$      845.80	0.7695	$                     831.02
PV of Cash Inflows			$ 1,004.27		$                     987.46
PV of Cash Oiutflows			$ 1,000.00		$                 1,000.00
NPV			$          4.27		$                     -12.54

Holding period Yield = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 13 % + [ 4.27 / 16.81 ] * 1%
= 13 % + [ 0.25 ] * 1%
= 13 % + [ 0.2539 % ]
= 13.25 %

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