Question

Today's price for a 1-year, zero-coupon risk-free bond is $983.25, and the price of a 2-year, zero-coupon risk-free bond is $906.46. What should be the price of a risk-free, 2-year annual coupon bond with a coupon rate of 2.0%? Round your answer to the nearest penny (i.e., two decimal places).

Answer 1

YTM of Zero coupon Bond:

YTM is the Rate at which Maturity value of Zero coupon Bond shall be equal to Bond Price.

Particulars	Amount
Maturity price	$   1,000.00
Current Price	$      906.46
Maturity period	2

YTM = [ Maturity Value / Current Price ] ^ ( 1 / n ) - 1
= [ $ 1000 / $ 906.46 ] ^ ( 1 / 2) - 1
= [ 1.1032 ] ^ ( 1 / 2) - 1
= 1.0503 - 1
= 0.0503
I.e 5.03 %

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.

Year	Cash Flow	PVF/ PVAF @5.03 %	Disc CF
1 - 2	$                   20.00	1.8586	$                   37.17
2	$             1,000.00	0.9065	$                 906.51
Bond Price			$                 943.68

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