Question

A coupon bond of 7.6 percent with 10 years left to maturity is priced to offer a 6.30 percent yield to maturity. You believe that in one year, the yield to maturity will be 7.2 percent.

What would be the total return of the bond in dollars?

what would be the total return of the bond in percentage?

Answer 1

In this question we need to find the price of the bond after one year, then we will calculate the $ return and % return on the bond.

Price of the bond

Price of the bond could be calculated using below formula.

P = C* [{1 - (1 + YTM) ^ -n}/ (YTM)] + [F/ (1 + YTM) ^ -n]

Where,

                Face value = $1000

                Coupon rate = 0.076

                YTM or Required rate = 0.063

                Time to maturity (n) = 10 years

                Annual coupon C = $76

Let's put all the values in the formula to find the bond current value

P = 76* [{1 - (1 + 0.063) ^ -10}/ (0.063)] + [1000/ (1 + 0.063) ^10]

P = 76* [{1 - (1.063) ^ -10}/ (0.063)] + [1000/ (1.063) ^10]

P = 76* [{1 - 0.54283}/ 0.063] + [1000/ 1.84218]

P = 76* [0.45717/ 0.063] + [542.83512]

P = 76* 7.25667 + 542.83512

P = 551.50692 + 542.83512

P = 1094.34204

So price of the bond is $1094.34

After one year YTM has increased to 7.2%, so Price of the bond will be

                Face value = $1000

                Coupon rate = 0.076

                YTM or Required rate = 0.072

                Time to maturity (n) = 9 years

                Annual coupon C = $76

Let's put all the values in the formula to find the bond current value

P = 76* [{1 - (1 + 0.072) ^ -9}/ (0.072)] + [1000/ (1 + 0.072) ^9]

P = 76* [{1 - (1.072) ^ -9}/ (0.072)] + [1000/ (1.072) ^9]

P = 76* [{1 - 0.53487}/ 0.072] + [1000/ 1.86962]

P = 76* [0.46513/ 0.072] + [534.86805]

P = 76* 6.46014 + 534.86805

P = 490.97064 + 534.86805

P = 1025.83869

So price of the bond is $1025.84

Total return ($)=$1025.84 - $1094.34 = - 68.5

% return = (-68.5)/ $1094.34 = - 0.0626 or – 6.26%