Requirement (a) – Firm’s Market Value Capital Structure
Capital Components |
Calculation |
Market Value Capital Structure Weights |
Debt |
[$381,600,000 / 868,710,000] |
0.4393 |
Preferred Stock |
[$28,910,000 / 868,710,000] |
0.0333 |
Equity |
[$458,200,000 / 868,710,000] |
0.5274 |
Calculations
Market Value of Debt = $381,600,000 [180,000 Bonds x ($2,000 x 106%)]
Market Value of Preferred Stock = $28,910,000 [295,000 shares x $98 per share]
Market Value of Equity = $458,200,000 [7,900,000 shares x $58 per share]
Total Market Value = $868,710,000
Requirement (b) – Discount Rate to be used by the firm to discount the project's cash flows
After-tax Cost of Debt
The After-Tax Cost of Debt is the After-Tax Yield to maturity of (YTM) of the Bond and is calculated using financial calculator as follows (Normally, the YTM is calculated either using EXCEL Functions or by using Financial Calculator)
Variables |
Financial Calculator Keys |
Figure |
Face Value [$2,000] |
FV |
2,000 |
Coupon Amount [$2,000 x 5.70%] |
PMT |
114 |
Yield to Maturity [YTM] |
1/Y |
? |
Time to Maturity [17 Years x 2] |
N |
34 |
Bond Price [-$2,000 x 106%] |
PV |
-2,120 |
We need to set the above figures into the financial calculator to find out the Yield to Maturity of the Bond. After entering the above keys in the financial calculator, we get the yield to maturity (YTM) on the bond = 10.63%
The After-tax Cost of Debt is the after-tax Yield to maturity of the Bond
After Tax Cost of Debt = Yield to maturity x (1 – Tax Rate)
= 10.63% x (1 – 0.23)
= 10.63% x 0.77
= 8.19%
Cost of Preferred Stock
Cost of Preferred Stock = [Annual Preferred Dividend / Selling Price] x 100
= [($100 x 4.20%) / $98] x 100
= [$4.20 / $98] x 100
= 4.29%
Cost of Equity
As per CAPM Approach, the Cost of Equity = Risk-free Rate + [Beta x Market Risk Premium]
= Rf + [B x Risk Premium]
= 3.40% + [1.10 x 6.70%]
= 3.40% + 7.37%
= 10.77%
Discount Rate to be used by the firm to discount the project's cash flows
Therefore, Discount Rate = [After Tax Cost of Debt x Weight of Debt] + [Cost of Preferred stock x Weight of preferred stock] + [Cost of equity x Weight of Equity
= [8.19% x 0.4393] + [4.29% x 0.0333] + [10.77% x 0.5274]
= 3.60% + 0.14% + 5.68%
= 9.42%
“Hence, the Discount Rate to be used by the firm to discount the project's cash flows will be 9.42%”
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