Bond valuation Enterprise Inc bonds have an annual coupon ra

(Bond valuation) Enterprise, Inc. bonds have an annual coupon rate of 12 percent. The interest is paid semiannually and the bonds mature in 8 years. Their par value is $1,000. If the market\'s required yield to maturity on a comparable-risk bond is 15 percent, what is the value of the bond? What is its value if the interest is paid annually? a. The value of the Enterprise bonds if the interest is paid semiannually is $. (Round to the nearest cent.)

Solution

When Interest is paid Semi Annually

Value of Bond = Cupon Amount * Present Value of Annuity Factor (r,n) + Redemption Amount * Present Value of Interest Factor (r,n)

Where Cupon Amount = $1,000 * 12% * 1/2

= $60

Why did we multiply 1/2?

- Since compounding is Semi Annual

Redemption Amount = $1,000

r is the Yield to Maturity (YTM)

Yield for 6 months = 15/2

r = 7.5%

n is the remaining maturity

n = 8 * 2

n = 16

(Semi Annual Compounding)

Present Value of Annuity Factor (7.5% ,16) = 9.14150673897

Present Value of Interest Factor (4% ,30) = 0.31438699448

Therefore

Value of Bond =$60* 9.14150673897 + $1,000 * 0.31438699448

Value of Bond =$548.490404338 + $314.38699448

Value of Bond = $862.877398818

Rounding to nearest cent

Value of Bond = $862.88

Therefore Value of Bond is $862.88

When Interest is paid Annually

Value of Bond = Cupon Amount * Present Value of Annuity Factor (r,n) + Redemption Amount * Present Value of Interest Factor (r,n)

Where Cupon Amount = $1,000 * 12%

= $120

Redemption Amount = $1,000

r is the Yield to Maturity (YTM)

r = 15%

n is the remaining maturity

n = 8

Present Value of Annuity Factor (15% ,8) = 4.48732150757

Present Value of Interest Factor (15% ,8) = 0.32690177382

Therefore

Value of Bond =$120* 4.48732150757 + $1,000 * 0.32690177382

Value of Bond =$538.478580908 + $326.90177382

Value of Bond = $865.380354728

Rounding to nearest cent

Value of Bond = $865.38

Therefore Value of Bond is $865.38