Question

a) A bond is offering 10 semi-annual payments of $50 until maturity in 2025, when the principal, $1000 will be paid.
What is the current value of the bond given that the yield of bonds with similar risk is 8% (annual effective yield- semi-annual yield is (1.08)1/2 -1 = 0.039)

b) How will this price change if the appropriate annual yield rises to 9%?

c) For which yield will the price be exactly $1000 (face or par value?).

Answer 1

Part A:

Value of Bond = PV of Cfs from it.

Particulars	Amount
Coupon Amount	$         50.00
Maturity Value	$    1,000.00
Disc Rate	3.900%
Starting	1
Ending on	10

Period	Cash Flow	PVF/ PVAF @3.9 %	Disc CF
'1 - 10	$      50.00	8.1514	$    407.57
'10	$ 1,000.00	0.6821	$    682.09
Bond Price			$ 1,089.67

PVAF = Sum [ PVF(r%, n) ]
PVF = 1 / ( 1 + r)^n
Where r is int rate per Period
Where n is No. of Periods

PVAF using Excel:
+PV(Rate,NPER,-1)
Rate = Disc rate
Nper = No. of Periods

Part B:

Annual Yield = 9%

Yield for 6 Months = [ 1.09 ^ ( 1 / 2 ) ] - 1

= 1.044 - 1

= 0.044 i.e 4.4%

Particulars	Amount
Coupon Amount	$         50.00
Maturity Value	$    1,000.00
Disc Rate	4.400%
Starting	1
Ending on	10

Period	Cash Flow	PVF/ PVAF @4.4 %	Disc CF
'1 - 10	$      50.00	7.9518	$    397.59
'10	$ 1,000.00	0.6501	$    650.12
Bond Price			$ 1,047.71

PVAF = Sum [ PVF(r%, n) ]
PVF = 1 / ( 1 + r)^n
Where r is int rate per Period
Where n is No. of Periods

PVAF using Excel:
+PV(Rate,NPER,-1)
Rate = Disc rate
Nper = No. of Periods

Part C:

Bond will trade at par, if the coupon rate & YTM are same.

Thus Yield for 6 Months is 5%

Annual Yield = ( 1 + 0.05 )^ 2 - 1

= [ 1.05^ 2 ] - 1

= 1.1025 - 1

= 0.1025 i.e 10.25%