Question

1. KF Enterprises has 8 million shares outstanding at a current price of $45/share. KF just paid a dividend of $1.35 and dividends are expected to continue growing at 5%. It has two bond issues as follows:

• 10,000 bonds of Issue A: A 20 year, semiannual 4.5% bond was issued 7 years ago and is currently selling at 97.3% of par.
• 15,000 bonds of Issue B: A 15 year zero coupon bond was issued 3 years ago, and is currently selling at 38.1 percent of face value.
• no tax rate
  1. What is the cost of equity for KF Enterprises?
  2. What is the YTM of Bond Issue A?
  3. What is the YTM of Bond Issue B?
  4. What is the after tax cost of debt for KF Enterprises?
  5. What is the weight of equity in KF Enterprises’ capital structure?
  6. What is the cost of capital for KF Enterprises?

Answer 1

(a) Current Dividend = D0 = $ 1.35, Growth Rate = 5 %

Expected Dividend = D1 = 1.35 x 1.05 = $ 1.4175

Current Stock Price = P0 = $ 45

Cost of Equity = (D1/P0) + g = (1.4175/45) + 0.05 = 0.0815 or 8.15 %

(b) Tenure = 20 years or (20 x 2) = 40 half-years, Semi-Annual Coupon = 4.5 % or (4.5/2) = 2.25 %, Remaining Tenure = 20 - 7 = 13 years or 26 half-years, Current Price = 97.3 % of par, Par Value = $ 1000 (assumed)

Semi-Annual Coupon = 0.045 x 0.5 x 1000 = $ 22.5, Current Price = 0.973 x 1000 = $ 973

Let the YTM be 2r1 %

Therefore, 973 = 22.5 x (1/r) x [1-{1/(1+r1)^(26)}] + 1000 / (1+r1)^(26)

Using EXCEL's Goal Seek Function/ a financial calculator/ hit and trial method, we get:

r1 = 0.02391 or 2.391 %

YTM = 2 x r1 = 2 x 2.391 = 4.782 %

(c) Zero Coupon Bond, Original Tenure = 15 years, Remaining Tenure = 12 years, Current Price = 38.1 % of Par Value, Par Value = $ 1000 (assumed)

Current Price = 0.381 x 1000 = $ 381

Let the YTM be r2

Therefore, 381 = 1000 / (1+r2)^(12)

r2 = [(1000/381)^(1/12)] - 1 = 0.08373 or 8.373 %

(d) Number of Bonds in Issue A = 10000, Value of Issue A = 973 x 10000 = $ 9730000

Number of Bonds in Issue B = 15000, Value of Issue B = 381 x 15000 = $ 5715000

Before-Tax Cost of Debt = [9730000/(9730000+5715000)] x 4.782 + [5715000/(5715000+9730000)] x 8.373 = 6.11075 %

Tax Rate = 0 %

Therefore, After-Tax Cost of Debt = 6.11075 %

(e) Price per Share = $ 45 and Number of Shares = 8 million

Value of Equity = 8 x 45 = $ 360 million or $ 360000000

Weight of Equity in Capital Structure = [360000000/(360000000+5715000+9730000] = 0.9589 or 95.89 %

(f) Cost of Capital = 8.15 x 0.9589 + 6.11075 x 0.0411 = 8.066 % ~ 8.07 %