Question

You bought an 8% annual coupon, 10 year maturity bond ($1,000 par value) when the discount rate was 9%. A year later, the discount rate was 10%. What is your holding period rate of return over the year? Please also include financial calculator calculations.

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.

Bond Price Today:

Year	Cash Flow	PVF/ PVAF @9 %	Disc CF
1 - 10	$      80.00	6.4177	$    513.41
10	$ 1,000.00	0.4224	$    422.41
Bond Price			$    935.82

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

Bond Price after 1 Year:

Year	Cash Flow	PVF/ PVAF @10 %	Disc CF
1 - 9	$      80.00	5.7590	$    460.72
9	$ 1,000.00	0.4241	$    424.10
Bond Price			$    884.82

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

Holding period Ret = [ Price at end - Price at begining + Coupon Amount ] / Price at begining

= [ $ 884.82 - $ 935.82 + $ 80.00 ] / $ 935.82

= $ 29 / $ 935.82

= 0.0310 I.e 3.10%

Holding period Ret is 3.10%