Question

Suppose that Ally Financial Inc. issued a bond with 10 years until maturity, a face value of $1,000, and a coupon rate of 11% (annual payments). The yield to maturity on this bond when it was issued was 9%.

a. What was the price of this bond when it was issued?

b. Assuming the yield to maturity remains constant, what is the price of the bond immediately before it makes its first coupon payment?

c. Assuming the yield to maturity remains constant, what is the price of the bond immediately after it makes its first coupon payment?

Answer 1

Part A:

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 @9 %	Disc CF
1 - 10	$    110.00	6.4177	$    705.94
10	$ 1,000.00	0.4224	$    422.41
Bond Price			$ 1,128.35

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

Part B:

Price Before Coupon Payment = Price after Coupon Paymnet + Coupon AMount

= $ 1119.90 ( from Part C) + $ 110

= $ 1229.90

Part C:

Price after Coupon Paymnet:

As already one coupon is received, there will be balance 9 coupons and maturity value. Bind Price is PV of those values.

Year	Cash Flow	PVF/ PVAF @9 %	Disc CF
1 - 9	$    110.00	5.9952	$    659.48
9	$ 1,000.00	0.4604	$    460.43
Bond Price			$ 1,119.90

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