Question

A $1,000 par value bond was issued 15 years ago at a 12 percent coupon rate. It currently has 15 years remaining to maturity. Interest rates on similar obligations are now 10 percent. Assume Ms. Bright bought the bond three years ago when it had a price of $1,010. Further assume Ms. Bright paid 30 percent of the purchase price in cash and borrowed the rest (known as buying on margin). She used the interest payments from the bond to cover the interest costs on the loan.

a. What is the current price of the bond? Use Table 16-2. (Input your answer to 2 decimal places.)
  

b. What is her dollar profit based on the bond’s current price? (Do not round intermediate calculations and round your answer to 2 decimal places.)
  

c. How much of the purchase price of $1,010 did Ms. Bright pay in cash? (Do not round intermediate calculations and round your answer to 2 decimal places.)
  

d. What is Ms. Bright’s percentage return on her cash investment? Divide the answer to part b by the answer to part c. (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
  

Answer 1

It is assumed that interest is paid annually.

Part (a):

Given, Face Value= $1000, Coupon rate= 12% and term to maturity= 15 years

Therefore, Interest per year= 1000*12%= $120

Also given, yield on similar bonds= 10%

Current price of the bond= 120*(PVIFA 15%, 15) + 1000*(PVIF 10%, 15)

= 120* 7.606080 + 1000* 0.239392

= $912.73 + $239.39 = $1,152.12

Part (b):

Given, purchase price= $1010

Therefore, dollar profit based on current price= 1152.12-1010= $142.12

Part (c ):

Purchase price paid in cash= 1010/3= $336.67

Part (d):

Ms. Bright’s percentage return on her cash investment= (142.12/336.67)*100 = 42.21%