Question

A company has the following projected free cash flows:

C₁ = -$50,000,000   C₂ = -$40,000,000      C₃ = -30,000,000      C₄ = ????

(a) If you apply the growing perpetuity model with a growth rate of 6% and a discount rate of 10% beginning in time 4 and in perpetuity thereafter, what number do you need to insert for C₄ to have a market value of equity of 1 billion?

(b) If the company has $500,000,000 in semi-annual bonds outstanding with 7.5% coupon and 12 years to maturity remaining, what is the market value of the bonds if the yield to maturity is 6.25%?

(c) What is the market value of the assets of the company?

(d) If you valued the bonds using continuous compounding with the same yield to maturity, show the calculation and the results of the bond valuation. (Note: the payments on the bond are made in the usual timing and amount).

Answer 1

(a) target equity value = $ 1 billion or $ 1000 million, Discount Rate = 10%, Perpetual Growth Rate = 6 %

C1 = - $ 50000000, C2 = - $ 40000000 and C3 = - $ 30000000

Total Present Value of Negative Free Cash Flows (During first three years) = -50 / (1.1) + -40 / (1.1)^(2) + -30 / (1.1)^(3) = - $ 101.052 million

Now, Target Equity Value = PV of Negative Free Cash Flows + Total PV of Pertual Constant Growth Cash Flows

1000 + 101.052 = Total PV of Pertual Constant Growth Cash Flows

Let the required value of C4 be $ C

Therefore, 1101.052 = C / (Discount Rate - Growth Rate) = C/(0.1-0.06)

C = 1101.052 x (0.1-0.06) = $ 44.0421 million

(b) Face Value of Bond = $ 500 million, Compounding Frequency: Semi-Annual, Coupon Rate = 7.5 %, Tenure = 12 years and Yield = 6.25 %

Semi-Annual Coupon = 0.075 x 0.5 x 500 = $ 18.75 million

Therefore, Bond Price = Market Value of Bond = 18.75 x (1/0.03125) x [1-{1/(1.03125)^(24)}] + 500 / (1.03125)^(24) = $ 552.22 million

(c) Market Value of Assets = Market value of bonds + Market Value of Equity = 552.22 + 1000 = $ 1552.22 million

(d) If compounding is done continuously, with the coupon frequency remaining constant, one needs to determine the equivalent semi-annual yield

Nominal Rate = 6.25 % and Period Length (in years) for Semi-Annual Compounding = 0.5

Therefore, Equivalent Semi-Annual Rate = e^(0.0625 x 0.5) - 1 = 0.0317 or 3.17 %

Market Value of Bond = 18.75 x (1/0.0317) x [1-{1/(1.0317)^(24)}] + 500 / (1.0317)^(24) = $ 547.84 million