Question

Bond prices and maturity dates. Les Company is about to issue a bond with quarterly coupon ​payments, an annual coupon rate of 11​%, and a par value of ​$5,000. The yield to maturity for this bond is 9​%.

a. What is the price of the bond if it matures in 15​, 20​, 25​, or 30 ​years?

b. What do you notice about the price of the bond in relationship to the maturity .of the​ bond?

Answer 1

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.

Part A:

1)

Period	Cash Flow	PVF/ PVAF @2.25 %	Disc CF
1 - 60	$      137.50	32.7490	$     4,502.98
60	$   5,000.00	0.2631	$     1,315.74
Bond Price			$     5,818.72

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

2)

Period	Cash Flow	PVF/ PVAF @2.25 %	Disc CF
1 - 80	$      137.50	36.9498	$     5,080.59
80	$   5,000.00	0.1686	$        843.15
Bond Price			$     5,923.74

3)

Period	Cash Flow	PVF/ PVAF @2.25 %	Disc CF
1 - 100	$      137.50	39.6417	$     5,450.74
100	$   5,000.00	0.1081	$        540.30
Bond Price			$     5,991.04

4)

Period	Cash Flow	PVF/ PVAF @2.25 %	Disc CF
1 - 120	$      137.50	41.3668	$     5,687.93
120	$   5,000.00	0.0692	$        346.24
Bond Price			$     6,034.17

Part B:

As Coupon Rate > YTM, As the maturityperiod increases, Bond price will increase.