Question

Bonds of Francesca Corporation with a par value of $1,000 sell for $920, mature in four years, and have a 9% annual coupon rate paid semiannually. Do not round intermediate calculations. Round your answers to two decimal places. Calculate:

a. current yield: ____% annually

b. yield to maturity, to the nearest basis point: ____% annually

c. horizon yield (or realized return) for an investor with a two-year holding period and a reinvestment rate of 8% over the period. At the end of two years, the 9% coupon bonds with two years remaining will sell to yield 9%: ____% annually

Answer 1

Par value = $1000

Current Price = $920

Maturity = 4 years

Coupon = Semiannual

C =9%

a) Current Yield = Annual Coupon / Current Price

Annual Coupon = C%*Par = 9%*1000 = 90

Current Yield = 90/920 = 0.0978 = 9.78%

b) YTM is rate at which current price will be equal to payments from bond till maturity

920 = 45 / (1+r)ⁱ   + 1000 / (1+r)⁸

Using excel, rate(8,45,-920,1000,0) = 5.777% = 11.55%

c)

Holding Period of 2 years, there will be 4 coupon payments reinvested as 8% annual reinvestment rate (4% semiannual)

FV = (4%,4,-45,0,0) = 191.09

Two years from now, bond will be selling at 1000 since YTM is forecasted to be same as coupon (9%)

Price = 191.09 + 1000 = 1191.09

Realised return is given by  920*(1+r)⁴ = 1191.09  

r=7.37% semiannual =14.74% annual