Question

CSM Corporation has a bond issue outstanding at the end of the year. The bond has 15 years remaining to maturity and carries a coupon interest rate of 6%. Interest on the bond is compounded on a semiannual basis. The par value of the CSM bond is $1,000 and it is currently selling for $874.42. a. Solve for the yield to maturity. Show your work. b. Solve for the price of the bond if the yield to maturity is 2% higher. Show your work. c. Solve for the price of the bond if the yield to maturity is 2% lower. Show your work. d. What can you summarize about the relationship between the relationship between the price of the bond, the par value, the yield to maturity, and the coupon rate?

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.

Period	Cash Flow	PVF/PVAF @ 3.5 %	PV of Cash Flows	PVF/ PVAF @4 %	PV of Cash Flows
1-30	$                 30.00	18.3920	$               551.76	17.2920	$                   518.76
30	$           1,000.00	0.3563	$               356.28	0.3083	$                   308.32
PV of Cash Inflows			$               908.04		$                   827.08
PV of Cash Oiutflows			$               874.42		$                   874.42
NPV			$                  33.62		$                    -47.34

YTM per six months = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 0.5% in Int Rate ] * 0.5%
= 3.5 % + [33.62 / 80.96 ] * 0.5%
= 3.5 % + [0.42 * 0.5% ]
= 3.5 % + [0.2076 % ]
= 3.71 %

YTM Per anum = IRR per six months * 12 / 6
= 3.7076 % * 2
= 7.4153 %
i.e 7.42 %

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.

Period	Cash Flow	PVF/ PVAF @4.71 %	Disc CF
1 - 30	$      30.00	15.8940	$    476.82
30	$ 1,000.00	0.2514	$    251.39
Bond Price			$    728.21

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 C:

Period	Cash Flow	PVF/ PVAF @2.71 %	Disc CF
1 - 30	$      30.00	20.3561	$    610.68
30	$ 1,000.00	0.4484	$    448.35
Bond Price			$ 1,059.03

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:

There is inverse relation between Yiled and priceof the bond.

I.e If Yield increases,Price will decrease and vice versa.