Question

A $1,000 par value bond was issued 25 years ago at a 12 percent coupon rate. It currently has 15 years remaining to maturity. Interest rates on similar obligations are now 8 percent. Assume Ms. Bright bought the bond three years ago when it had a price of $1,050 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 162. (Input your answer to 2 decimal places.) Price of the bond 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 Dollar profn c. How much of the purchase price of $1,050 did Ms. Bright pay in cash? (Do answer to 2 decimal places) not round intermediate calculations and round your Purchase price paid in cash

Answer 1

(a) Current Interest Rate = 8 %, Coupon Rate = 12 %, Par Value of Bond = $ 1000, Time remaining to maturity = 15 years

Current Price = Sum of Present Value of all remaining bond cash flows (remaining coupons+par value to be redeemed at maturity)

Annual Coupon = 0.12 x 1000 = $ 120

Current Price = 120 x (1/0.08) x [1-{1/(1.08)^(15)}] + 1000 / (1.08)^(15) = $ 1342.38

(b) Original Purchase Price = $ 1050 and Current Price = $ 1342.38

The investor also earns three coupons, one each at the end of the 18th,17th and 16th year as the bond was purchased three years ago and still has 15 years to maturity.

Coupon Earnings = 3 x 120 = $ 360

Total $ Profit = 360 + 1342.38 - 1050 = $ 652.38

(c) Cash Payment = 30 % of Purchase Price = 0.3 x 1050 = $ 315

(d) % Return = [652.38 / 315] x 100 ~ 207.1 %