Question

5. On September 1, 2008, Casper, Inc. sold a $500 million bond issue to finance the purchase of a new manufacturing facility. These bonds were issued in $1,000 denominations with a maturity date of September 1, 2038. The bonds have a coupon rate of 10.00% with interest paid semiannually.

Required: a) Determine the value today, September 1, 2018 of one of these bonds to an investor who requires a 4 percent return on these bonds. Why is the value today different from the par value?
b) Assume that the bonds are selling for $1,215. Determine the current yield and the yield-to-maturity. Explain what these terms mean.
c) Explain what layers or textures of risk play a role in the determination of the required rate of return on Casper’s bonds.

Answer 1

a) Present value of per bond = Face value /(1+ yield)^{number of payment} + interest [1-(1+ yiled)^{-number of payments}] / yield

= 1000/(1+ 0.02)^30*2 + ($1000*10%/2) [1-(1+ 0.02)^-30*2] / 0.02

= 1000/(1.02)⁶⁰ + 50 * [1-(1.02)^-60] / 0.02

= 1000/(1.02)⁶⁰ + 50 * [1-1/(1.02)⁶⁰] / 0.02

= 1000/3.281031 + 50 * [1-1/3.281031] / 0.02

= 304.78 + 1738.04

= 2042.82

Present value of bond = $2042.82 * 500000 bonds

= $1021410000

b) current yield = Annual coupon / market price

= ($1000 * 10%) /  $1,215

= $100 /  $1,215

= 8.23%