Question

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

where

m is 7

and n is 1

Answer 1

Part (a):

Capital gains yield= (P1-P0)/P0 Where P1= end price and P0= Beginning price

Given that-

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

Also given that m=7. Hence term to maturity= 7 years

n= 1. Hence coupon rate=1% and YTM=2%

Assumed that coupon is paid annually.

Price of the bond is calculated at P0= $935.28 and P1=$990.20 using PV function of Excel as follows:

E13 F =PV(E12,E9,E10,E2)*-1 A B D Function At the time One year 1 Formula arguments of issue before maturity 2 Face Value (FV) Given $1,000 $1,000 3 Coupon rate (R) Given 1.00% 1.00% 4 Interest frequency Given Annual Annual 5 Number of coupon payments a year (n) 6 Original term (T) Given 7 Priod expired (years) (t) Given 8 Time to maturity (no. of years) (N) T-t 9 Number of future coupon payments N*n Nper 10 Amount of coupon payment FV*R/n PMT $10.00 $10.00 11 Interest rate (YTM) Given 2.00% 2.00% 12 Interest rate per period YTM/N Rate 2.00% 2.00% 13 Price (Present value) PV $ 935.28 $ 990.20 14 Capital gain yield= (P1-PO)/PO = ($990.20-$935.28)/(35.28 5.871609% 15

Capital gain yield= (P1-P0)/P0 = ($990.20-$935.28)/$935.28 = 5.871609%

Part (b):

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

E13 А E 1 Bond 2 $1,000 1.00% Annual L =PV(E12,E9,510,E2)*-1 B C D Function Formula arguments Bond 1 2 Face Value (FV) Given $1,000 3 Coupon rate (R) Given 1.00% 4 Interest frequency Given Annual 5 Number of coupon payments a year (n) 6 Original term (T) Given 7 Priod expired (years) (t) Given 8 Time to maturity (no. of years) (N) T-t 9 Number of future coupon payments Nin Nper 10 Amount of coupon payment FV*R/n PMT $10.00 11 Interest rate (YTM) Given 1.00% 12 Interest rate per period YTM/N Rate 1.00% 13 Value after one year of issue PV $ 1,000.00 13 13 $10.00 1.00% 1.00% 1,000.00 $ 11

Term to maturity of Bond 2= 2m=14 years. All other features similar to that of Bond 1.

Issue price of bond 1= $935.28 as in part (a)

Issue price of bond 2= $878.94 as follows:

D13 f =PV(D12,09,010,D2)*-1 BC Function Formula arguments Bond 2 2 Face Value (FV) Given $1,000 3 Coupon rate (R) Given 1.00% 4 Interest frequency Given Annual 5 Number of coupon payments a year (n) 1 6 Original term (T) Given 14 7 Priod expired (years) (t) Given 8 Time to maturity (no. of years) (N) T-t 14 9 Number of future coupon payments Nin Nper 10 Amount of coupon payment FV*R/n PMT $10.00 11 Interest rate (YTM) Given 2.00% 12 Interest rate per period YTM/N Rate 2.00% 13 Issue price PV $ 878.94

Capital gain of bond 1 over one year= P1-P0 = $1,000 - $935.28 = $64.72

Capital gain of bond 2 over one year= $1,000- $878.94 = $121.06.

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