Since the instruction in the question indicates that the % symbol should not be used, the weighted average cost of capital (WACC) for Easy Car Corp is therefore 12.07.
Step-by-step explanation:
This can be calculated using the following steps:
Step 1: Calculation of the current bond price
Semiannual coupon amount = Bond face value * Semiannual coupon rate = $1000 * (10% / 2) = $50
Semiannual coupon discount factor = ((1 - (1 / (1 + r))^n) / r) (1)
Where;
r = Semiannual yield to maturity (YTM) = 8% / 2 = 0.08 / 2 = 0.04
n = number of semiannuals = 23 years * 2 = 46
Substituting the values into equation (1), we have:
Semiannual coupon discount factor = ((1-(1/(1 + 0.04))^46) / 0.04) = 20.8846535613106
Present value of coupon = (Semiannual coupon amount * Semiannual coupon discount factor) = $50 * 20.8846535613106 = $1,044.23
Present value of the face value of the bond = Face value / (1 + r)^n = $1,000 / (1 + 0.04)^46 = $164.61
Therefore, we have:
Current bond price = Present value coupon + Present value of the face value of the bond = $1,044.23 + $164.61 = $1,208.84
Step 2: Calculation of weights of each finance source
Market value of common shares outstanding = Number common shares outstanding * Current price per share = 2,000,000 * $13 = $26,000,000.
Market value of bond = Number of bonds * Current bond price = 30,000 * $1,208.84 = $36,265,200
Total financing market value = Market value of common shares outstanding + Market value of bond = $26,000,000 + $36,265,200 = $62,265,200
Weight of Market value of common shares outstanding = Market value of common shares outstanding / Total financing market value = $26,000,000 / $62,265,200 = 0.42
Weight of Market value of bond = Market value of bond / Total financing market value = $36,265,200 / $62,265,200 = 0.58
Step 3: Calculation of return on equity
Current year dividend = Last year dividend * (1 + Dividend growth rate) = $2 * (1 + 4.0%) = $2.08
Next year dividend = Current year dividend * (1 + Dividend growth rate) = $2.08 * (1 + 4.0%) = $2.1632
The return on equity can now be calculated using the following formula:
Current share price = Next year dividend / (Return on equity – Dividend growth rate) ………………….. (2)
Where;
Current share price = $13
Next year dividend = $2.1632
Return on equity = ?
Dividend growth rate = 4.0%, or 0.04
Substituting the values into equation (2) and solve for return on equity, we have:
13 = 2.1632 / (Return on equity - 0.04)
13 * (Return on equity - 0.04) = 2.1632
(13 * Return on equity) – (13 * 0.04) = 2.1632
(13 * Return on equity) – 0.52 = 2.1632
13 * Return on equity = 2.1632 + 0.52
Return on equity = 2.6832 / 13
Return on equity = 0.21
Step 4: Calculation of Weighted average cost of capital
Weighted average cost of capital = (WS * CE) + (WD * CD * (1 – T)) ………………… (4)
Where;
WS = Weight of Market value of common shares outstanding = 0.42
WD = Weight of debt = Weight of Market value of bond = 0.58
CE = Cost of equity = Return on equity = 0.21
CD = Cost of debt = YTM = 8%, or 0.08
T = Tax rate = 30%, or 0.30
Substituting the values into equation (3), we have:
Weighted average cost of capital = (0.42 * 0.21) + (0.58 * 0.08 * (1 - 0.30)) = 0.12068, or 12.068%
Rounding to two decimal places, we have:
Weighted average cost of capital = 12.07%
Since the instruction in the question indicates that the % symbol should not be used, the weighted average cost of capital (WACC) for Easy Car Corp is therefore 12.07.
