Question

Calculation of individual costs and WACC Dillon Labs has asked its financial manager to measure the cost of each specific type of capital as well as the weighted average cost of capital. The weighted average cost is to be measured by using the following weights: 45% long-term debt, 10% preferred stock, and 45% common stock equity (retained earnings, new common stock, or both). The firm's tax rate is 24% Debt The firm can sell for $1020 a 14-year, $1,000-par-value bond paying annual interest at a 12.00% coupon rate. Aflotation cost of 4% of the par value is required. Preferred stock 7.50% (annual dividend) preferred stock having a par value of $100 can be sold for $98. An additional fee of $6 per share must be paid to the underwriters. Common stock The firm's common stock is currently selling for $80 per share. The stock has paid a dividend that has gradually increased for many years, rising from $3.00 ten years ago to the $5.90 dividend payment, Do, that the company just recently made. If the company wants to issue new new common stock, it will sell them $2.00 below the current market price to attract investors, and the company will pay $3.50 per share in flotation costs a. Calculate the after-tax cost of debt. b. Calculate the cost of preferred stock. c. Calculate the cost of common stock (both retained earnings and new common stock) d. Calculate the WACC for Dillon Labs.

Answer 1

a.

Let us begin with pre-tax cost of debt.

We know that the value of a bond is NPV of all the coupons and principal payments on the instrument
Hence, NPV of all the coupons and principal repayment is equal to the cash proceeds the company will receive from the bond issuance.

NPV of all the coupons and principal repayment = cash proceeds from bond issuance

Which means NPV of all the cash flows is 0.

When the NPV is 0, the discounting rate used is equal to the IRR.

Hence the cost of issuing this bond will be equal to IRR.

The following table lists down all the cash flows and calculates IRR, which is also the cost of debt for the company

Bond valuation
Face value	$        1,000
Coupon	12%
Flotation costs	4%
Year	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Cash proceeds	$        1,020
Flotation costs	$           (40)
Coupon payment		$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)
Principal repayment															$ (1,000)
Net cash flow	$           980	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$      (120)	$ (1,120)
IRR	12.3%

Hence pre-tax cost of debt = 12.3%

After-tax cost of debt = pre-tax cost of debt x (1-tax rate)

Hence After tax cost of debt = 12.3% x (1 - 24%)

Hence after tax cost of debt = 9.4%

b.

Cost of preferred stock = Preferred dividend / (Cash proceeds from issuance - Issuing costs)

The following table shows calculations of cost of preferred equity

Preferred stock
Par value	$           100
Cash proceeds	$              98
underwriting fees	$              (6)
Preferred dividend rate	7.50%
Preferred dividend	$            7.5
Cost of preferred stock	8.2%

$Cost of preferred equity = \frac{Preferred dividend}{Cash proceeds from issuance - Issuance costs}$

$Cost of preferred equity = \frac{7.5}{98 - 6}$

Hence the cost of preferred equity = 8.2%

c.

Dividend 10 years ago (D_-10) = $3.00
Dividend paid recently (D₀) = $5.90

Hence,

$CAGR of dividend growth = \sqrt[10]{\frac{D_{0}}{D_{-10}}} - 1$

$CAGR of dividend growth = \sqrt[10]{\frac{5.9}{3}} - 1$

Hence dividend growth rate = 7.0%

Hence next year's dividend (D₁) = 5.9 x (1+7%)

Hence D₁ = 6.3

CMP of the common stock is $80,
If the company issues new stocks now, it would sell $2 below CMP and there will be a flotation cost of $3.5
Hence the company would receive 80 - 2 - 3.5 = $74.5

Using the Gordon Growth Model,

$Value of equity = \frac{D_{1}}{cost of equity - dividend growth rate}$

Here we consider proceeds the company would receive if it issues new stocks as the value of equity because we are trying to find out what is the costs of equity for the company. While doing so, we must take into consideration flotation costs as well.

Hence

$74.5 = \frac{6.3}{cost of equity - 0.07}$

Rearranging the terms,

$cost of equity = \frac{6.3}{74.5} + 0.07$

Hence cost of equity = 15.5%

d.

WACC = weight of debt x post-tax cost of debt
+ weight of preferred stock x cost of preferred stock
+ weight of common stock x cost of common stock

Hence WACC = 0.45 x 9.4% + 0.10 x 8.2% + 0.45 x 15.5%

Hence WACC = 12.03%