Question

The Metchosin Corporation has two different bonds currently outstanding. Bond M has a face value of $30,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $1,400 every six months over the subsequent eight years, and finally pays $1,700 every six months over the last six years. Bond N also has a face value of $30,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. The required return on both these bonds is 10% compounded semiannually, what is the current price of bond M and bond N?

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.

Bond M:

Period	Cash Flow	PVAF @5%	PV of CFs
1-12	$             -	8.8633	$                -
13-28	$ 1,400.00	6.0349	$    8,448.83
29-40	$ 1,700.00	2.2610	$    3,843.63
Price Today			$ 12,292.46

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

Bond N:

Particulars	Amount
Maturity Price	$ 30,000.00
Maturity in Periods	40
Disc RatePer period	5.00%

Price of Zero coupon Bond is PV of Maturity Price.
Bond Price = Maturity Price * PVF(r%, n)
PVF(r% , n) = 1 / ( 1 + r)^n
r - Disc Rate Per Anum
n - No.of Years

Bond Price = Maturity Price * PVF(r%, n)
= $ 30000 * PVF( 5 % , 40 )
= $ 30000 * 0.142
= $ 4261.37

Bond Price is $ 4261.37