Exercise on Bond valuation

Gain Allah (Subhana wa ta ‘ala) pleasure, and worshiping is the utmost reason of existence of human being on earth, we shall continue glorifying him alone. May the peace and salutations of Allah subhana watala be upon the beloved prophet Muhammad (Salal Allahu Alahe wa salam)  his family and the righteous guided Sahabas.

1.      (A) SECTION  (i) Semiannual base

FV= 1000

PMT= 0.09*1OOO= 90/2= 45

N= 10*2= 20 Years

I= 10%=10%/2= 5% OR 0.05

PV= PMT/I*[ 1-1/ (1+I)^N] +FV/(1+I)^N

PV= 45/0.05*[1-1(1+0.05)^20]+1000/(1+0.05)^20

PV= 560.7995 + 376.8895

PV= 937.6890

The result are shown in the table below:

FV	1000
PMT	45
N	20 Years
I	5%
PV	937.6890

1.      (A) (ii) 

FV= 1000

PMT= 45

N= 20 Years

I= 7%  = 7%/2 = 3.5 Or 0.035

PV= 45/0.035*[1-1/C1+0.035)^20] +1000/(1+0.035)^20

PV= 639.5581 + 502.5659

PV= 1,142.1240

The results are as showed in the table below:

FV	1000
PMT	45
N	20 Years
I	0.035
PV	1,142.1240

1.      (A) (iii)

FV=100

N= Issue 8 Years

PMT= 100*0.19 =19

I= 18.77%

PV= 100.917

PV= PMT/I*[1-1/(1+I)^N]+FV/(I+I)^N

Note: I have made several trials but 18.77 is the closest to PV= 100.9159. Let i= 18.77%

PV= 19/0.1877*[1-1/(1+0.1877)^8]+ FV/(1+0.1877)^8

PV= 75.6610 +25.2549

PV= 100.9159

.

The results are summarizing in the table below.

FV	100
N	8 Years
PMT	19
I / YTM	18.77%
PV	100.917

(B)  SECTION (I ) What is a callable bond? These are bond that  give or allow the issuer the right to be pensioned off the debt, completely or incompletely, formerly the scheduled maturity date.

      (B) (ii) who gain from the call option..? the Bond with a call option is benefiting or  in other word is  good for the issuer in a condition that, the interest rates drop, and the bond with a call option must be  sell at a lesser price for the reason that the call provision is more appreciable to the firm, not for the holder of the bond.

       (B) (iii) The price and yield of the two identical bonds, the Investors pay a lesser amount for a callable bond as compared to the non-callable bond. As a result, the yield to maturity must be greater on the callable bond then non-callable bond.

(C)      SECTION

The Interest Rate= 12.95% = 0.1295

 Monthly =  [1+ i/12]^12 -1

                = [ 1+o.1295/12]^12 -1

                = 1.137470-1

                =0.13747 Or 13.747%

The result  is as shown in the below:

Interest (I)	12.95%
Monthly	12
Monthly Interest rate Charge	13.747%

The Interest Rate= 12.95% = 0.1295

Effective Annual Rate= [1+0.1295]-1

                                      = 1.1295-1

                                     = 0.1295

                                    = 12.95%

The result is shown in the table below:

Interest (I)	12.95%
Effective Annual Rate (EAR)	12.95%

(D)  SECTION

Decided to buy Sofa for=  $109

Sale person offer to divide payment over 12 months without interest= $170/12 +Admin fee ($5)

 If the alternative is to choose the credit card with APR of 12%

SOLUTION

(i)                 The amounts pay for sofa without interest. = $170/12 = 14.1667 +Admin Fee ($5)

                                                                               = $14.1667 +$5

                                                                               = $19.1667

The amount pays for sofa with interest = EAR =[1+ rNom/M]^m -1

                                                                       = [1+0.12/12]^12 -1

                                                                      = 1.126825-1

                                                                      = 0.126825 Or 12.6825

                                                                      = $12.6825

(ii)               If I am to choose the payment type I will choose, the Credit Card this is because the Credit Card has lesser cause As compared to the At the store the sales person offers .

The credit Card  causes this (12.6825%), and the store the sales person offers (19.17%).

The results are  summarized in the table below:

Payments methods A	Interest Rate	Payments methods B	Administrative fee Charge per month
Credit Card	12.00%	sales person offers	$170/12 + $5.00
Total amount Charge using Credit Card	$12.6825	Total amount Charge by sales person	$19.1667
Desirable	More Desirable	Not Desirable

(E)  Section

Bond                                               Coupon Rate (annual payments)   Maturity (Years)
A	0%	15
B	0%	10
C	4%	15
D	8%	10

(i)                 Which of the bond from A to D will be sensitive to  a 1% drop interest rate from 6% to 5% and why..?

(ii)               Which bond id least sensitive provide intuitive explanation..?

SOLUTION

(i)                 Which bond is more sensitive to drop TYM Or Interest from 6% to 5%

Less first and foremost take the bond of each TYM using the face value of 1.(A)(1) with 6% of TYP and the face value of  1000 in 1.(A) I will be using it throughout..

To find the price of a bond:

YTM =6%

We used the formula PV= PMT/I*[1-1/(1+I)^N]+FV/(1+I)^N

{Bond A, 6% YTM}= 0/*[1-1/(1+0.06)^15]+1000/(1+0.06)^15

                                = 0  + 417.2651    =417.2651

 {Bond B, 6% YTM}=0/0.06*[1-1/(1+0.06)^10]+1000/(1+0.06)^10

                                 =0+ 558.3948 = 558.3948

 {Bond C, 6% YTM}=4/0.06*[1-1/(1+0.06)^15]+1000/(1+0.06)^15

                                 = 38.8490+ 417.2650  =456.1141

{Bond D, 6% YTM}=8/0.06*[1-1/(1+0.06)^10]+1000/(1+0.06)^10

                                 =58.8810+558.3948

                                =617.27577   =617.2758

YTM =5%

{Bond A, 5% YTM}= 0/*[1-1/(1+0.05)^15]+1000/(1+0.05)^15

                                 = 0+ 481.0171  =481.0171

{Bond B, 5% YTM}=0/0.05*[1-1/(1+0.05)^10]+1000/(1+0.05)^10

                                = 0+ 613.9133      =613.9133

{Bond C, 5% YTM}=4/0.05*[1-1/(1+0.05)^15]+1000/(1+0.05)^15

                               =41.5186 + 481.0171   = 522.5357

 {Bond D, 5% YTM}=8/0.05*[1-1/(1+0.05)^10]+1000/(1+0.05)^10

                                 = 61.7739 + 613.9133     =675.6872

Now we can compute the price of each YTM, the percentage price change as:

Percentage change = (Price at 5% of YTM)- (Price at 6% of YTM)/ (Price at 6% of YTM)

{Percentage of bond A} =(481.0171-417.2651)/( 417.2651) = 15.2785%

{Percentage of bond B} =( 613.9133 -558.3948)/(558.3948) = 9.9425%

{Percentage of bond C} = (522.5357-456.1141)/( 456.1141)  = 14.5625%

{Percentage of bond D} = (675.6872 -617.2758)/( 617.2758) = 9.4628%

The results are shown in the table below:

Bond	Coupon Rate (Annual Payments)	Maturity (Years)	Price at 6% of YTM	Price at 5% of YTM	% Change
A	0%	15	417.2651	481.0171	15.2785%
B	0%	10	558.3948	613.9133	9.9425%
C	4%	15	456.1141	522.5357	14.5625%
D	8%	10	617.2758	675.6872	9.4628%

(i)                 Which of the bond from A to D will be sensitive to  a 1% drop interest rate from 6% to 5% and why..? Bond A is most sensitive, this is because it has the lengthiest or longest maturity and no coupons rate.

(ii)               The bond D is the lowest or least sensitive to drop the interest. Therefore Intuitively, the greater coupon rates and a smaller the maturity characteristically lowered a bond’s interest rate sensitivity.

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