Question

Essentials of Investments- Bodie, Kane and Marcus.

1. A bond that sells for $ 957 at three years make annual payments of coupons at 8%. The interest rate for the next three years is estimated at: 8%, 10% and 12%, respectively. Calculate:

a) The YIELD TO MATURITY of the bond
b) The effective return at the end of the period (remember that it is compound interest)

Answer 1

Interest rate = 8%

Next year = 10% & 12%

Face value = $1000

Coupon

!st year = $1000 * 8% = 80

next year = $1000 * 10% = $100

Next year = $1000 * 12% = $120

Average interest = (80 +100+ 120)/ 3 = $100

Yield to maturity = Interest + (F.V. - S.V.)/n / [ (F.V. + S.V.)/2]

= 120 + ( 1000 -957)/3 / [(1000+ 957)/2]

= (120 + 14.33) / 978.50

= 13.73 %

b)In case compounded anually

Effective return = [1 + (i/n)]ⁿ - 1

= ( 1 + (0.1373/3)]³ - 1

= 14.37 %

If compounded continuously

r = e^r -1

= 2.71828^13.73 - 1

= 1.1471721 - 1

= 14.72 %