Question

a. Consider a zero-coupon bond with a $100 face value maturing in 5 years. What is the yield to maturity of this bond if it is currently trading at $72? Answer in percent, rounded to one decimal place.

b. What is the value of a ten-year 6% annual coupon bond with face value of $1,000, assuming yield-to-maturity of 5%. Round to the nearest cent.

c. What is the value of a 20-year 4% coupon bond withsemi-annual coupons, $1,000 face value, and a yield-to-maturity of 3.6%? Round to the nearest penny.

d. A 7-year 5% annual coupon bond with face value of $1,000 is trading for $1,067. What is its yield to maturity? Round to the tenth of a percent (e.g., 5.24% = 5.2). [Use Excel or a financial calculator. Hint: Don't forget to enter the price of the bond (PV) as a negative number. Make sure to set Excel or your calculator to show sufficient decimal places.]

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. 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 @ 6 %	PV of Cash Flows	PVF/ PVAF @ 7 %	PV of Cash Flows
1-5	$                         -	4.2124	$                                 -	4.1002	$                              -
5	$                100.00	0.7473	$                          74.73	0.7130	$                       71.30
PV of Cash Inflows			$                          74.73		$                       71.30
PV of Cash Oiutflows			$                          72.00		$                       72.00
NPV			$                            2.73		$                        -0.70

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 6 % + [ 2.73 / 3.43 ] * 1%
= 6 % + [ 0.8 ] * 1%
= 6 % + [ 0.7953 % ]
= 6.8 %

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:

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 %	Disc CF
1 - 10	$      60.00	7.7217	$    463.30
10	$ 1,000.00	0.6139	$    613.91
Bond Price			$ 1,077.22

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

Part C:

Bond Price:

Period	Cash Flow	PVF/ PVAF @1.8 %	Disc CF
1 - 40	$      20.00	28.3401	$    566.80
40	$ 1,000.00	0.4899	$    489.88
Bond Price			$ 1,056.68

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

Periodic Cash Flow = Annual Coupon Amount / No. times coupon paid in a year
Disc Rate Used = Disc rate per anum / No. of times coupon paid in a Year

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

Part D: