Question

Question 1

The bonds for Gladstone Limited will mature in 10 years, with a face value of $1000, and semi-annual coupons. The coupon rate on these bonds is 7.5% per year.

Question 1(a)

The risk associated with Gladstone Limited bonds has increased dramatically, as investors now want a 12% return to hold the bonds. At what price should the bonds trade today?                            

Question 1(b)

Today, Gladstone Limited admitted to having some management problems with seven (7) years to go before maturity. The price of Gladstone Limited immediately tumbled to $810. What is the new yield to maturity on Gladstone Limited bonds?           

Answer 1

Part 1a)

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 @6 %	Disc CF
1 - 20	$      37.50	11.4699	$    430.12
20	$ 1,000.00	0.3118	$    311.80
Bond Price			$    741.93

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 1b)

YTM :

YTM is the rate at which PV of Cash inflows are equal to Bond price when the bond is held till maturity. Yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until it matures. Yield to maturity is considered a long-term bond yield but is expressed as an annual rate.

Period	Cash Flow	PVF/PVAF @ 5.5 %	PV of Cash Flows	PVF/ PVAF @6 %	PV of Cash Flows
1-14	$                 37.50	9.5896	$               359.61	9.2950	$                   348.56
14	$           1,000.00	0.4726	$               472.57	0.4423	$                   442.30
PV of Cash Inflows			$               832.18		$                   790.86
PV of Cash Oiutflows			$               810.00		$                   810.00
NPV			$                  22.18		$                    -19.14

YTM per six months = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 0.5% in Int Rate ] * 0.5%
= 5.5 % + [22.18 / 41.32 ] * 0.5%
= 5.5 % + [0.54 * 0.5% ]
= 5.5 % + [0.2684 % ]
= 5.77 %

YTM Per anum = IRR per six months * 12 / 6
= 5.7684 % * 2
= 11.5368 %
i.e 11.54 %

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