Question

You buy a 20-year, 6.3% Treasury bond that is quoted at 101.19.

A. What is the yield to maturity on this bond?

B. If, 4 years later, the bond is selling to yield 5.6%, what would be your percentage return if you then sold the bond?

Answer 1

Assuming Face valueof bond is $ 100

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 @ 6 %	PV of Cash Flows	PVF/ PVAF @ 7 %	PV of Cash Flows
1-20	$                    6.30	11.4699	$        72.26	10.5940	$                       66.74
20	$                100.00	0.3118	$        31.18	0.2584	$                       25.84
PV of Cash Inflows			$      103.44		$                       92.58
PV of Cash Oiutflows			$      101.19		$                     101.19
NPV			$          2.25		$                        -8.61

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 6 % + [ 2.25 / 10.86 ] * 1%
= 6 % + [ 0.21 ] * 1%
= 6 % + [ 0.2073 % ]
= 6.21 %

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 B:

Price after 4 years:

Bond Price:
It refers to the sum of the present values of all likely coupon payments plus the present value of the par value at maturity. There is inverse relation between Bond price and YTM ( Discount rate ) and Direct relation between Cash flow ( Coupon/ maturity Value ) and bond Price.

Price of Bond = PV of CFs from it.

Year	Cash Flow	PVF/ PVAF @5.6 %	Disc CF
1 - 16	$           6.30	10.3894	$          65.45
16	$      100.00	0.4182	$          41.82
Bond Price			$        107.27

As Coupon Payments are paid periodically with regular intervals, PVAF is used.
Maturity Value is single payment. Hence PVF is used.

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

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

Yield for 4 Years:

Year	Cash Flow	PVF/ PVAF @ 7 %	PV of Cash Flows	PVF/ PVAF @ 8 %	PV of Cash Flows
1-4	$                    6.30	3.3872	$        21.34	3.3121	$                       20.87
4	$                107.27	0.7629	$        81.84	0.7350	$                       78.85
PV of Cash Inflows			$      103.18		$                       99.71
PV of Cash Oiutflows			$      101.19		$                     101.19
NPV			$          1.99		$                        -1.48

Yield for 4 Years = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 7 % + [ 1.99 / 3.46 ] * 1%
= 7 % + [ 0.57 ] * 1%
= 7 % + [ 0.5734 % ]
= 7.57 %

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

Yield for 4 years is 7.57%