Question

Last year, the yield on AAA-rated corporate bonds averaged approximately 5 percent; one year later, the yield on these same bonds had climbed to about 6 percent because the Reserve Bank of Australia increased interest rates during the year. Assume that BHP Billiton Limited issued a 10-year, 5 percent coupon bond one year ago (on 1 January). On the same date, Rio Tinto Limited issued a 20-year, 5 percent coupon bond. Both bonds pay interest annually. Assume that the market rate on similar risk bonds was 5 percent at the time the bonds were issued.

1. Compute the market value of each bond at the time of the issue. (1.5 marks)
2. Compute the market value of each bond one year after issue if the market yield for similar risk bonds were 6 percent. (1.5 marks)

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.

Market Value of Bond at the time of Issue:

Bond issued by BHP Billiton Limited :

Year	Cash Flow	PVF/ PVAF @5 %	Disc CF
1 - 10	$                   50.00	7.7217	$                 386.09
10	$             1,000.00	0.6139	$                 613.91
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.

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

issued by Rio Tinto Limited:

Year	Cash Flow	PVF/ PVAF @5 %	Disc CF
1 - 20	$                   50.00	12.4622	$                 623.11
20	$             1,000.00	0.3769	$                 376.89
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.

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 after 1 Year:

Bond issued by BHP Billiton Limited :

Year	Cash Flow	PVF/ PVAF @6 %	Disc CF
1 - 9	$                   50.00	6.8017	$                 340.08
9	$             1,000.00	0.5919	$                 591.90
Bond Price			$                 931.98

issued by Rio Tinto Limited:

Year	Cash Flow	PVF/ PVAF @6 %	Disc CF
1 - 19	$                   50.00	11.1581	$                 557.91
19	$             1,000.00	0.3305	$                 330.51
Bond Price			$                 888.42