Question

Suppose you purchase a​ 10-year bond with 6.5 % annual coupons. You hold the bond for four​ years, and sell it immediately after receiving the fourth coupon. If the​ bond's yield to maturity was 5.3 % when you purchased and sold the​ bond, a. What cash flows will you pay and receive from your investment in the bond per $ 100 face​ value? b. What is the annual rate of return of your​ investment?

Answer 1

Answer:

• a. What cash flows will you pay and receive from your investment in the bond per $ 100 face​ value?

Year 0   Year 1   Year 2   Year 3   Year 4  

-$109,13   $6,50   $6,50   $6,50   $112,53 (6,5+106,03)  

• b. What is the annual rate of return of your​ investment?

5,3%, the YTM of the bond.

Explanation:

If the YTM of the bond does not change during the year, it means that at the time the bond was sold, the total rate of return would be the same as was when the bonds were purchased, in this case 5,3%.  

• Bond Value

Principal Present Value  =  F /  (1 + r)^t  

Coupon Present Value   =  C x [1 - 1/(1 +r)^t] / r  

Price of the Bond at the moment it was purchased:  

The price of this bond it's $59,66 + $6,5 = $109,13  

Present Value of Bonds $59,66 = $100/(1+0,053)^10    

Present Value of Coupons $49,47 =  $6,5 (Coupon) x 7,61  

7,61 =   [1 - 1/(1+0,053)^10 ]/ 0,053  

Price of the Bond 4 years later:    

The price of this bond it's $73,66 + $32,68 = $106,03    

Present Value of Bonds $73,66 = $100/(1+0,053)^6      

Present Value of Coupons $32,68 =  $6,50 (Coupon) x 5,03    

5,03 =   [1 - 1/(1+0,053)^6 ]/ 0,053