Question

1.

What is the price of a bond with the following features?

• Face Value = $1,000
• Coupon Rate = 7% (stated as an ANNUAL rate)
• Semiannual coupon payments
• Maturity = 9 years
• YTM = 4.05% (Stated as an APR)

State your answer to the nearest penny (e.g., 984.25)

2.

You own a bond with the following features:

              Face value of $1000,

              Coupon rate of 3% (annual)

              11 years to maturity.

The bond is callable after 5 years with the call price of $1,069.

If the market interest rate is 4.57% in 5 years when the bond can be called, if the firm calls the bond, how much will it save or lose by calling the bond?

State your answer to the nearest penny (e.g., 84.25)

If there would be a loss, state your answer as a negative (e.g., -37.51)

Answer 1

Part1:

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 @2.03 %	Disc CF
1 - 18	$                   35.00	14.9591	$                 523.57
18	$             1,000.00	0.6971	$                 697.08
Bond Price			$             1,220.65

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 2:

Bond Price after 5 Years:

Year	Cash Flow	PVF/ PVAF @4.57 %	Disc CF
1 - 6	$                   30.00	5.1462	$                 154.39
6	$             1,000.00	0.7648	$                 764.82
Bond Price			$                 919.20

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
Amount can be saved = Bond Price - Call Price

= $ 919.20 - $ 1069

= -$ 149.80

Amount lost by calling bond is $ 149.80