Question

Assume you purchased a three-year, 9% coupon bond for $950. It pays annual coupon payment. Suppose interest rates have decreased 1.50% per year from you purchased the bond. Suppose that you sold the bond two years later right after receiving the second coupon payment. What was your rate of return from your investment over the holding period?

Note:

• Please clearly state your final answer.

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. 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 @ 11 %	PV of Cash Flows	PVF/ PVAF @ 12 %	PV of Cash Flows
1-3	$                  90.00	2.4437	$      219.93	2.4018	$                     216.16
3	$             1,000.00	0.7312	$      731.19	0.7118	$                     711.78
PV of Cash Inflows			$      951.13		$                     927.95
PV of Cash Oiutflows			$      950.00		$                     950.00
NPV			$          1.13		$                     -22.05

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 11 % + [ 1.13 / 23.18 ] * 1%
= 11 % + [ 0.05 ] * 1%
= 11 % + [ 0.0486 % ]
= 11.05 %

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

Now the require yield = 11.05% - 1.5% - 1.5%

= 8.05%

Price after 2 Years:

Balance leftover period is 1 Year

Price of bond is PV of Cash flows from it.

Year	Cash Flow	PVF @8.05 %	Disc CF
1	$      90.00	0.9255	$      83.29
1	$ 1,000.00	0.9255	$    925.50
Price of Bond	$ 1,008.79

Rate of ret from holding bond = The Rate at which PV of Cash inflows are equal to PV of cash Outflows.

Year	Cash Flow	PVF/ PVAF @ 12 %	PV of Cash Flows	PVF/ PVAF @ 13 %	PV of Cash Flows
1-2	$                  90.00	1.6901	$      152.10	1.6681	$                     150.13
2	$             1,008.79	0.7972	$      804.20	0.7831	$                     790.03
PV of Cash Inflows			$      956.31		$                     940.16
PV of Cash Oiutflows			$      950.00		$                     950.00
NPV			$          6.31		$                        -9.84

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 12 % + [ 6.31 / 16.15 ] * 1%
= 12 % + [ 0.39 ] * 1%
= 12 % + [ 0.3905 % ]
= 12.391 %

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

Realized ret during the holding period is 12.39%