Present Value

Practice Exercise #1:

On January 1, 2010, Cobble Inc issued eight-year bonds with a face value of $800,000 and a stated rate of 6%, payable annually on December 31. The bonds were sold to yield 8%. Table values are:

Present value of 1 for 8 periods at 6% = .627

Present value of 1 for 8 periods at 8% = .540

Present value of 1 for 16 periods at 3% = .623

Present value of 1 for 16 periods at 4% = .534

Present value of annuity for 8 periods at 6% = 6.210

Present value of annuity for 8 periods at 8% = 5.747

Present value of annuity for 16 periods at 3% = 12.561

Present value of annuity for 16 periods at 4% = 11.652

a. The present value of the principal is how much?

b. The present value of the interest is how much?

c. What is the issuance price of the bond?

d. How would hte present value of the principal change if interest was paid semiannually?

1. Calculations with Annual Interest Payments:

Face value=$800,000

Stated rate=0.06

Market rate=0.08

Term=8 years (8 periods)

Factors:

PV $1 (n=8, r=8%); discount factor =0.54

PV Annuity (n=8,r=8%); discount factor =5.747

PV of principal [$800,000*0.54(PV of $1, 8 periods, 8%)]......... ........................$432,000

PV of interest [$800,000*0.06*(12/12)*5.747 (PV of annuity, 8 periods, 8%)] .....................$275,856

Selling Price of Bond ($432,000+$$275,856)..............$707,856

Discount ($800,000-selling price) ..........................$92,144

Hence answers are:

a. PV of principal......................$432,000

b. PV of interest........................$275,856

c. Issuance price of bond ..........$707,856

2. Calculations with Semi-annual Interest Payments:

Face value=$800,000

Stated rate=0.06

Market rate=0.08

Term=8 years