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Rob's e2700 Notes

✏️ Full Example: Watson Company

Watson Company

  • Watson Company’s equity has a total book value of $50.0 million\$50.0\ million. Its common stock share price is $25.00\$25.00 and it is expected to pay a $1.25\$1.25 dividend per share next year. After that, the firm’s dividends are expected to grow at a rate of 4.0%4.0\% per year. It has 4.0 million4.0\ million common shares outstanding.
  • Watson Company also has .5 million.5\ million preferred stock outstanding that pays a $2.00\$ 2.00 per share fixed dividend. Its preferred stock is currently priced at $24.00\$ 24.00.
  • Watson Company has existing debt issued three years ago with a coupon rate of 6.0%6.0\%. The firm just issued new debt at par with a coupon rate of 6.5%6.5\%. Its debt liabilities have a market value of $20.0 million\$ 20.0\ million.
  • Watson Company faces a 35%35\% tax rate.

What are Watson Company’s WACC?

Weights/Percents

✔ First, we need to calculate the weights.

  Market Value of Equity: Market Cap = $25 ×4=$100M\$25\ × 4 = \$100M
  Market Value of Debt: $20M\$20M
  Market Value of Preferred: $24 ×.5=$12M\$24\ × .5 = \$12M
  Total Financing: $100M+$20M+$12M=$132M\$100M + \$20M + \$12M = \$132M

Market ValueProportions/Weights
Equity$100M$100/$132 = 76% of financing is from equity
Debt$20M$20/$132=15%
Preferred$12M$12/132 = 9%
Total$132M100%

Cost of Debt

The firm just issued new debt at par with a coupon rate of 6.5%6.5\%. Because the debt was issued at par, Pb=FPb=F, which means that the YTM=c=6.5%YTM=c=6.5\%. Watson’s pre-tax cost of debt is 6.5%6.5\%. We can use this trick over and over.

The corporate tax rate is 35%35\%, so the after tax cost of debt (taking account of the tax shelter) is 6.5%×(1−35%)=4.23%6.5\% × (1-35\%) = 4.23\%

Cost of Preferred

Watson’s preferred stock is currently priced at $24.00\$ 24.00. It has a dividend of $2\$2. Therefore, it has a return of $2/$24=8%\$2/\$24=8\%.. Therefore, Watson’s cost of preferred equity is 8%8\%.

Cost of Common Equity

Watson’s common stock share price is $25.00\$25.00 and it is expected to pay a $1.25\$1.25 dividend per share next year. After that, the firm’s dividends are expected to grow at a rate of 4.0%4.0\% per year. Therefore, using the Constant Dividend Growth Model, the cost of equity is:

1.25/25+4%=9%1.25/25+4\%=9\%

Summary

Market ValueProportions/WeightsCost of Financing
Equity$100M$100/$132 = 76%1.25/25+4%=9%
Debt$20M$20/$132=15%6.5%*(1-35%) = 4.23%
Preferred$12M$12/132 = 9%$2/$24=8%
Total$132M100%

WACC

WACC=wE×rE+wD×rD+wP×rP=%E×rE+%D×rD×(1−TC)+%P×rP=76%×9%+15%×4.23%+9%×8%=8.1945%\begin{aligned} WACC &= w_E × r_E + w_D × r_D + w_P × r_P \\ &= \%E × rE + \%D × rD × (1-TC) + \%P × rP \\ &= 76\% × 9\% + 15\% × 4.23\% + 9\% × 8\% \\ &= 8.1945\% \end{aligned}
Microsoft Excel File
7 WACC (ch 13)

CAPM

✏️ Suppose that the return on T-Bills is 5%5\% and the average return on the market, historically, is 15%15\%. Watson company is very risk averse, so it’s beta is .4.4. What is Watson’s Cost of Equity Capital?

✔ Click here to view answer

The CAPM Equation is: E(ri)=rF+β(E(rM)−rF)E(r_i )=r_F+β(E(r_M )−r_F)

We use T-Bills as rFr_F and the average return on the market as our expected return for the market.

We just plug numbers in: E(ri)=5%+.4×(15%−5%)=9%E(r_i) = 5\% + .4 × (15\%-5\%) = 9\%

Note that this is the same return as we found with the Constant Dividend Growth Model, above. If both models are accurate, we would expect both approaches to yield the same cost of capital.

✔ ⚠️ Watch out! In the above example, the expected return on the market was 15%. The market risk premium is defined as the expected return minus the risk free rate. Therefore, it will be, E(rM)−rF=15%−5%=10%E(r_M)-r_F=15\%-5\%=10\%. A question might tell you the market risk premium instead of the risk free rate. If it does, you don’t need to subtract the risk free rate because it has already been subtracted! See below for an example:

✏️ Suppose that the return on T-Bills is 5%5\% and the average risk premium on the market, historically, is 15%15\%. Watson company is very risk averse, so it’s beta is .4.4. What is Watson’s Cost of Equity Capital?

✔ Click here to view answer

The CAPM Equation is: E(ri)=rF+β(E(rM)−rF)E(r_i )=r_F+β(E(r_M )−r_F)

We use the average historical risk premium of the market as the expected risk premium on the market on the market. The notation for risk premium of the market is E(rM)−rFE(r_M )−r_F, so we are given that E(rM)−rF=15%E(r_M )−r_F=15\%

We just plug numbers in: E(ri)=5%+.4×(15%−5%)=9%E(r_i) = 5\% + .4 × (15\%-5\%) = 9\%

Note that this is the same return as we found with the Constant Dividend Growth Model, above. If both models are accurate, we would expect both approaches to yield the same cost of capital.

Corporate Finance Perspective

Corporate Finance Perspective: Using the following market value balance sheet, we could argue that the market values the assets fo the firm at $132M\$132M (because assets = liabilities.)

Assets Liabilities

$132M Assets

$20M Debt

$12M Preferred
$100M Equity (SHE)

For example, if $10M\$10M of the assets were cash, then the

EnterpriseValue=MVDebt+MVEquity−Cash=Assets−Cash=$132M−$10M\begin{aligned} Enterprise Value &= MV Debt + MV Equity - Cash \\ &= Assets - Cash \\ &= \$132M-\$10M \end{aligned}

If we use this, approach, we can define the WACC weights as

MVEquity/MVAssets=$100/$132=76%MVEquity/MVAssets = \$100/\$132 = 76\% MVDebt/MVAssets=$20/$132=15%MVDebt/MVAssets = \$20/\$132=15\%