Question

An investor has just purchased bonds for $35,000 that have a par value of $40,000, eight years remaining to maturity, and a coupon rate of 14 percent. It expects the required rate of return on these bonds to be 11 percent three years from now.

a. At what price could the investor sell these bonds three years from now?

b. What is the expected annualized yield on the bonds over the next three years, assuming they are to be sold in three years?

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.

Price after 3 Years:

Year	Cash Flow	PVF/ PVAF @11 %	Disc CF
1 - 5	$   5,600.00	3.6959	$   20,697.02
5	$ 40,000.00	0.5935	$   23,738.05
Bond Price			$ 44,435.08

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

PartB:

Year	Cash Flow	PVF/ PVAF @ 23 %	PV of Cash Flows	PVF/ PVAF @ 24 %	PV of Cash Flows
1-3	$             5,600.00	2.0114	$11,263.70	1.9813	$               11,095.30
3	$          44,435.08	0.5374	$23,878.70	0.5245	$               23,305.63
PV of Cash Inflows			$35,142.39		$               34,400.93
PV of Cash Oiutflows			$35,000.00		$               35,000.00
NPV			$      142.39		$                   -599.07

HPR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 23 % + [ 142.39 / 741.46 ] * 1%
= 23 % + [ 0.19 ] * 1%
= 23 % + [ 0.192 % ]
= 23.19 %

PVAF = Sum [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r )^n
r - Int Rate per period
n - No. of Periods

How to calculate PVAF using Excel?
+PV(Rate,NPER,-1)
Rate = Disc rate
NPER - No. of Periods

Holding Period Return is 23.19%