Question

You are considering buying a bond with a 10-year maturity. The bond’s coupon rate is 8% and the interest rate is paid semiannually. If youu want to earn an effective interest rate of 8.16%, how much should you be willing to pay for the bond? Where the value is 1.000.000.000.

Answer 1

Annual Int Rate or Nominal Rate = [ ( 1 + r )^ ( 1 / n ) - 1 ] * n
r = Effective Annual Rate
n = No. of times compounded per anum

Particulars	Amount
Effective Annual rate	8.1600%
No. of periods per anum	2.0000

APR = [ [ ( 1 + EAR )^( 1 / n ) ] - 1 ] * n
= [ [ ( 1 + 0.0816 )^( 1 / 2 ) ] - 1 ] * 2
= [ [ ( 1.0816 )^( 1 / 2 ) ] - 1 ] * 2
= [ [ 1.04 ] - 1 ] * 2
= [ 0.04 ] * 2
= 0.08
= 8.00 %

Annual int rate ( APR ) is 8.00 % per anum

Rate per Six months = 8% / 2

= 4%

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 %	Disc CF
1 - 20	$      40.00	13.5903	$    543.61
20	$ 1,000.00	0.4564	$    456.39
Bond Price			$ 1,000.00

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

Price of Bond = $ 1000