Question

A bond has a 10 percent coupon rate, makes annual payments, matures in 12 years, and has a yield-to-maturity of 7 percent.

One year from now the bond will have 11 years until maturity. Assume market interest rates decrease to 5 percent. Given this: i. What will be the bond’s price one year from now? j. If you purchased the bond at the price in (a) and sold the bond at the price in (i) what would be your capital gain (or loss) once you sold? What would be your annualized holding period return?

Answer 1

Part I:

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 1 Year:

Year	Cash Flow	PVF/ PVAF @5 %	Disc CF
1 - 11	$      100.00	8.3064	$        830.64
11	$   1,000.00	0.5847	$        584.68
Bond Price			$     1,415.32

Price after 1 Year is $ 1415.32

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 J:

Price Today:

Year	Cash Flow	PVF/ PVAF @7 %	Disc CF
1 - 12	$      100.00	7.9427	$        794.27
12	$   1,000.00	0.4440	$        444.01
Bond Price			$     1,238.28

Capital Gain = Price after 1 Year - Price Today

= $ 1415.32 - $ 1238.28

= $ 177.04

Holding period Yielsd = [ Price after 1 Year - Price Today + Coupon ] / Price Today

= [ $ 1415.32 - $ 1238.28 + $ 100 ] / $ 1238.28

= $ 277.04 / $ 1238.28

= 0.2237 I.e 22.37%