Question

You are called in as a financial analyst to appraise the bonds of Olsen's Clothing Stores. The $1,000 par value bonds have a quoted annual interest rate of 10 percent, which is paid semiannually. The yield to maturity on the bonds is 10 percent annual interest. There are 15 years to maturity. a. Compute the price of the bonds based on semiannual analysis. b. With 10 years to maturity, if yield to maturity goes down substantially to 8 percent, what will be the new price of the bonds? (Please show all steps and explain)

Answer 1

Solution:

a.

N I/Y PV PMT FV

10 × 2 10 / 2 CPT

PV −1,000.00 100 / 2 1,000

10%/2=5% *1000= 50

n=20

i=5%

pmt 50

fv 1000

Answer: $1,000.00

b.

N I/Y PV PMT FV

5 × 2 10 / 2 CPT

PV −1,000.00 100 / 2 1,000

n=8

pmt 50

i 5%

fv 1000

Answer: $1,000.00

a.

Appendix D

Present value of interest payments:

PVA = A × PVIFA (5%, 20)

= $50 × 12.462

= $623.10

Appendix B

Present value of principal payment at maturity:

PV = FV × PVIF (5%, 20)

= $1,000 × .377

= $377.00

Bond price = $623.10 + 377.00

= $1,000.10

b.

Appendix D

Present value of interest payments:

PVA = A × PVIFA (5%, 10)

= $50 × 7.722

= $386.10

Appendix B

Present value of principal payment at maturity:

PV = FV × PVIF (5%, 10)

= $1,000 × .614

= $614.00

Bond price = $386.10 + 614.00

= $1,000.10