Question

You are considering buying a bond that will be issued today. It will mature in m=9 years. The annual coupon rate is n=7%. Face value is $1,000. The annual market rate is (n+1)=7+1=8%.

a) What is the capital gains yield at exactly a year before the bond matures, when only one coupon and face value are left to be paid, if the market rate stays the same through the years? Show your work.

b) There is another bond that is being issued today, identical to the bond described above in every aspect, except, it matures in 2m years. Which bond would you buy today, if you knew that the market rate would go down to n% a year from today ? Support your decision with clearly calculated numbers. Show your work.

Answer 1

Part (a):

Capital gains yield= (P1-P0)/P0 Where P1= price on selling and P0= purchase price

Given that-

Term to maturity= m years and coupon rate=n%. Annual market rate (YTM) = (n+1)%

Also given that term to maturity (m) = 9 years and coupon rate (n)= 7%. YTM= 8%

Assumed that coupon is paid annually.

Price of the bond is calculated at P0= $ 937.53 and P1=$ 942.53 using PV function of Excel as follows:

D Bond 1 2 Ε After 8 years $1,000 7% Annual $1,000 7% Annual E12 do =PV(E11,58,59,63)*-1 A B C 1 Formula 3 Face Value (F) Given FV 4 Coupon rate (R) Given 5 Interest frequency Assumed 6 Number of coupon payments a year (t) 7 Time to maturity (no. of years) (N) Given 8 Number of future coupon payments (t) N*t Nper 9 Amount of coupon payment F*R/t PMT 10 YTM 11 Interest rate per period YTM/t Rate 12 Price PV 13 Capital gain yield= (P1-PO)/PO 1 COCO 9 9 $70.00 8% 8.00% 937.53 $70.00 8% 8.00% $ 942.53 0.533581% $ 14

Capital gain yield= (P1-P0)/P0 = [($942.53- $937.53)/$937.53]*100 = 0.533581%

Part (b):

Term to maturity of Bond 2= 2m=18 years. All other features similar to that of Bond 1.

After 1 year, when YTM gets reduced to n ie., 7%, which is equal to coupon rate, value of both the bonds will become equal to face value which is $1,000 as shown below:

D Bond 1 E Bond 2 $1,000 7% Annual $1,000 7% Annual E12 f =PV(E11,58,59,63)*-1 C 1 2 Formula 3 Face Value (F) Given FV 4 Coupon rate (R) Given 5 Interest frequency Assumed 6 Number of coupon payments a year (t) 7 Time to maturity (no. of years) (N) Given 8 Number of future coupon payments (t) N*t Nper 9 Amount of coupon payment F*R/t PMT 10 YTM 11 Interest rate per period YTM/t Rate 12 Price 0000 $70.00 7% $70.00 7% 7.00% $ 1,000.00 7.00% 1,000.00 PV $

Issue price of bond 1= $937.53 as in part (a)

Issue price of bond 2= $906.28 as follows:

Bond 2 $1,000 7% Annual E12 f =PV(E11, E8, E9,E3)*-1 A В с 1 2 Formula 3 Face Value (F) Given FV 4 Coupon rate (R) Given 5 Interest frequency Assumed 6 Number of coupon payments a year (t) 7 Time to maturity (no. of years) (N) Given 8 Number of future coupon payments (t) N*t Nper 9 Amount of coupon payment F*R/t PMT 10 YTM 11 Interest rate per period YTM/t Rate 12 Price 18 18 $70.00 8% 8.00% 906.28 PV $

Capital gain of bond 1 over one year= P1-P0 = $1,000 - $937.53 = $62.47

Capital gain of bond 2 over one year= $1,000- $906.28 = $93.72

Since capital gain over a period of one year is higher for Bond 2, the same will be preferred.