Question

The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY).

a. Suppose that today you buy a bond with an annual coupon of 9 percent for $1,110. The bond has 16 years to maturity. What rate of return do you expect to earn on your investment? Assume a par value of $1,000. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected rate of return %

b1. Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What price will your bond sell for? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Bond price $

b2. What is the HPY on your investment? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

HPY %

Answer 1

Part A:

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%

Year	Cash Flow	PVF/ PVAF @ 7 %	PV of Cash Flows	PVF/ PVAF @ 8 %	PV of Cash Flows
1-16	$                  90.00	9.4466	$                        850.20	8.8514	$                     796.62
16	$             1,000.00	0.3387	$                        338.73	0.2919	$                     291.89
PV of Cash Inflows			$                    1,188.93		$                 1,088.51
PV of Cash Oiutflows			$                    1,110.00		$                 1,110.00
NPV			$                          78.93		$                     -21.49

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 7 % + [ 78.93 / 100.42 ] * 1%
= 7 % + [ 0.79 ] * 1%
= 7 % + [ 0.786 % ]
= 7.79 %

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 B1:

Price of Bond = PV of Cfs from it.

Year	Cash Flow	PVF/ PVAF @6.79 %	Disc CF
'1 - 14	$      90.00	8.8567	$    797.10
'14	$ 1,000.00	0.3986	$    398.63
Bond Price			$ 1,195.73

PVAF = Sum [ PVF(r%, n) ]
PVF = 1 / ( 1 + r)^n
Where r is int rate per Anum
Where n is No. of Years

PVAF using Excel:
+PV(Rate,NPER,-1)
Rate = Disc rate
Nper = No. of Periods

Part B2:

Particulars	Amount
Price at the End of Year2 (P2)	$ 1,195.73
Price at the begining of Year(P0)	$ 1,110.00
Coupon for Two years ($ 90 * 2)	$    180.00

HPY = [ P1 - P0 + D1 ] / P0
= [ 1195.73 - 1110 + 180 ] / 1110
= [ 265.73 ] / 1110
= 0.2394
I.e 23.94 %