Question

Microhard has issued a bond with the following characteristics:

Par: $1,000
Time to maturity: 16 years
Coupon rate: 12 percent
Semiannual payments

Calculate the price of this bond if the YTM is: (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

  Price of the Bond

a.12 percent$

b.15 percent$

c.9 percent$

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.

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

If YTM is 12%:

Period	Cash Flow	PVF/ PVAF @6 %	Disc CF
1 - 32	$      60.00	14.0840	$    845.04
32	$ 1,000.00	0.1550	$    154.96
Bond Price			$ 1,000.00

If YTM is 15%:

Period	Cash Flow	PVF/ PVAF @7.5 %	Disc CF
1 - 32	$      60.00	12.0155	$    720.93
32	$ 1,000.00	0.0988	$      98.84
Bond Price			$    819.77

If YTM is 9%:

Period	Cash Flow	PVF/ PVAF @4.5 %	Disc CF
1 - 32	$      60.00	16.7889	$ 1,007.33
32	$ 1,000.00	0.2445	$    244.50
Bond Price			$ 1,251.83