Question

What would happen to the value of the above 5-year bond over time if the required annual rate of return remained at 10 percent?

Answer 1

ALWAYS ASSUME IF THE QUESTION IS SILENT THAT THE COUPON RATE AND COST OF DEBT(BOND HERE) ARE EQUAL AND NO OTHER INFORMATION IS GIVEN IN THE QUESTION REGARDING THE SAME.

NOW AS PER THE QUESTION ONLY ONE RATE IS GIVEN HENCE WE ASSUME THAT KD=COUPON RATE.

ALSO COUPON RATE IS THE RATE AT WHICH ACTUAL AMOUNT OF INCOME IS EARNED IN THE FORM OF INTEREST WHEREAS KD ALSO KNOWN AS YIELD TO MATURITY IS JUST THE ESTIMATED RATE UNTIL MATURITY .

ALSO WHENEVER WE NEED TO CALCULATE THE FAIR VALUE OF BOND THAT IS VALUE OF BOND FOR SAY AFTER FOUR YEARS IN TERMS OF VALUE TODAY WE DISCOUNT IT BY KD.(MATURITY VALUE AFTER FOUR YEARS/(1+KD)^4)

NOW AS PER QUESTION :

WE WILL TAKE THE FOLLOWING EXAMPLE:

FACE VALUE =1000(ASSUMED)

KD=COUPON RATE =10%(GIVEN)

LETS ASSUME BOND WILL MATURE AFTER 6 YEARS.

ACTUAL INTEREST =FACE VALUE*INTEREST RATE(COUPON RATE)=1000*10%=100(FOR EVERY YEAR)

VALUE OF BOND =[INTEREST(YEAR1)/1+KD] + [INTEREST(YEAR2)/(1+KD)(1+KD)]+[INTEREST(YEAR3)/(1+KD)(1+KD)(1+KD)]+[INTEREST(YEAR4)/(1+KD)(1+KD)(1+KD)(1+KD)]+[INTEREST(YEAR5)/(1+KD)(1+KD)(1+KD)(1+KD)(1+KD)]+INTEREST(YEAR6)/(1+KD)(1+KD)(1+KD)(1+KD)(1+KD)(1+KD)]+[MATURITY VALUE/(1+KD)(1+KD)(1+KD)(1+KD)(1+KD)(1+KD)]

NOW FILLING THE VALUES ABOVE WE WILL GET THE ANSWER =RS.1000(FACE VALUE )

HENCE WE CAN ANALYSE THAT VALUE OF BOND AFTER 5 YEARS AND FURTHER YEARS WILL BE RS 1000 ONLY AS KD = COUPON RATE AND THE RATE IS CONSTANT WITHOUT ANY GROWTH .THUS IT IS A PAR VALUE BOND.

ALSO IF BOTH THE RATES ARE SEPARATELY GIVEN IN THE QUESTION , THE ANSWER WILL BE DIFFERENT:

IT WILL BE A PREMIUM BOND (VALUE WILL COME OUT TO BE >1000) IF CR>KD

IT WILL BE A DISCOUNT BOND(VALUE WILL COME OUT TO BE <1000) IF CR<KD