Question

Prob Set 1 #15 pt 2

background data

14. You have an opportunity to purchase a corporate bond issued by Ford Motor Company with a face value of $1,000. It has 6 years left to maturity and has an 8% coupon rate, with interest paid semi-annually. If the current market interest rate for bonds with equivalent risk is 7.25%, what should you pay for the Ford bond?  

Answer to Question 14:

Face Value = $1,000

Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4% * $1,000
Semiannual Coupon = $40

Time to Maturity = 6 years
Semiannual Period to Maturity = 12

Annual Interest Rate = 7.25%
Semiannual Interest Rate = 3.625%

Current Price = $40 * PVIFA(3.625%, 12) + $1,000 * PVIF(3.625%, 12)
Current Price = $40 * (1 - (1/1.03625)^12) / 0.03625 + $1,000 / 1.03625^12
Current Price = $40 * 9.59263 + $1,000 * 0.65227
Current Price = $1,035.98

So, maximum amount paid for Ford bond is $1,035.98

Question 15

15. Suppose that Ford’s credit rating has declined due to poor earnings and increased concerns among investors about Ford’s future profitability. The required return for bonds with Ford’s risk is now 19.5%. How much should you pay for the Ford bond?

Answer 1

(14) Par Value = $ 1000, Bond Interest Rate = 7.25 % per annum or 3.625 % per half-year, Coupon Rate = 8 % per annum or 4% per half-year, Time to Maturity = 6 years or 12 half-years

Let the market price be Pm

Semi-Annual Coupon = 0.08 x 0.5 x 1000 = $ 40

Pm = 40 x (1/0.03625) x [1-{1/(1.03625)^(12)}] + 1000 / (1.03625)^(12) = $ 1035.98

(15) In this scenario, everything about the Ford Bond remains the same except for its required rate of return (or market interest rate/yield to maturity) which becomes 19.5 % per annum from 7.25 %

Let the new bond price be K

Therefore, K = 40 x (1/0.0975) x [1-{1/(1.0975)^(12)}] + 1000/(1.0975)^(12) = $ 603.37