Question

Susan bought a 15-year bond when it was issued by Octodan Corporation 3 years ago (NOTE: the bond was issued 3 years ago. In calculating price today, remember it has only 12 years remaining to maturity). The bond has a $1,000 face value, an annual coupon rate equal to 8 percent and the coupon is paid every six months. If the yield on similar-risk investments is 10 percent,

a. What is the current market value (price) of the bond?

b. Suppose interest rate levels rise to the point where such bonds now yield 12 percent. What would be the price of Octodan bond?

c. At what price would Octodan bonds sell if the yield on them was 7 percent?

d. What do you observe regarding the relationship between interest rate (YTM) bond’s price?

e. What do you observe regarding the relationship between coupon, YTM and the bond’s price?

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.

Period	Cash Flow	PVF/ PVAF @5 %	Disc CF
1 - 24	$                   40.00	13.7986	$                 551.95
24	$             1,000.00	0.3101	$                 310.07
Bond Price			$                 862.01

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

Part B:

Period	Cash Flow	PVF/ PVAF @6 %	Disc CF
1 - 24	$                   40.00	12.5504	$                 502.01
24	$             1,000.00	0.2470	$                 246.98
Bond Price			$                 748.99

Part C:

Period	Cash Flow	PVF/ PVAF @3.5 %	Disc CF
1 - 24	$                   40.00	16.0584	$                 642.33
24	$             1,000.00	0.4380	$                 437.96
Bond Price			$             1,080.29

Part D:

At YTM 10% - Price of bond is $ 862.01

At YTM 12% - Price of bond is $ 748.99

At YTM 7% - Price of bond is $ 1080.29

Thus There is invesrse relation between Yield and Price of Bond.

Part E:

Price of Bond = PV of Cash flows from it, discounted at Yield rate provided.

Cash flow = Coupon & Maturity amount

Thus There is inverse relation between Yield and Price of bond and direct relation between coupon and Price of bond.