Question

Financial analysts forecast L Brands (LB) growth for the future to be 13.4 percent. LB's most recent dividend was $2.20. What is the fair present value of L Brands’s stock if the required rate of return is 16.3 percent? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

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a. What is the duration of a two-year bond that pays an annual coupon of 10.7 percent and has a current yield to maturity of 13.1 percent? Use $1,000 as the face value. (Do not round intermediate calculations. Round your answer to 4 decimal places. (e.g., 32.1616))

b. What is the duration of a two-year zero-coupon bond that is yielding 11.5 percent? Use $1,000 as the face value.

Answer 1

Answer 1:

Growth for future = 13.4%

Most recent dividend = $2.20

Required rate of return is 16.3 percent

Fair present value of L Brands’s stock = {Dividend * ( 1 + Growth rate%)} / (Required rate of return % - Growth rate %)

= {$2.20 * (1+ 13.4%)} / (16.3% - 13.4%)

= $86.03

Fair present value of L Brands’s stock = $86.03

Answer a:

Year 1 Cash flow = annual coupon amount = $1,000 * 10.7% = $107

Present value of year 1 cash flow = PV₁ = $107 / (1 + 13.1%) = $94.60654

Year 2 cash flow = annual coupon amount + face value redeemed = $1,000 * 10.7% + $1,000 = $1,107

Present value of year 2 cash flow = PV₂=$1,107 / (1 + 13.1%) ² = $865.411

Duration = (PV₁ * 1 + PV₂* 2) / Price

Current price of the bond = PV of cash year 1 flow year 1 + PV of year 2 cash flow = $94.60654 + $865.411 = $960.01754

Duration = ($94.60654 + $865.411 * 2) / $960.01754 = 1.9015 years

Duration = 1.9015 years

Answer b:

Zero coupon bond is purely a discount bond and it does not pay annual coupons.

As such its duration = maturity tenure = 2 years

=