Answer:
a. 6.5%
b. 13.06%
c. 10.91%
Explanation:
a.
Cost of debt of a bond is yield to maturity. Yield to maturity is the rate of return that a investor actually receives or a borrows actually pays on a bond. It is long term return or payment which is expressed in annual term.
Formula for yield to maturity is as follow
Yield to maturity = [ C + ( F - P ) / n ] / [ (F + P ) / 2 ]
By placing values in the formula
Assuming the bond face value is $1,000
Yield to maturity = [ (1000x7.2) + ( 1,000 - $1,090 ) / 20 ] / [ ( 1,000 + $1,090 ) / 2 ]
Yield to maturity = [ $72 + ( 1,000 - $1,090 ) / 20 ] / $1,045
Yield to maturity = [ $72 - $4.5 ] / $1,045
Yield to maturity = $67.5 / $1,045
Yield to maturity = 6.5%
So, the cost of Debt is 6.5%
b.
As 0.9 is the unlevered beta, We need Levered beta due to restructuring of capital.
Beta Levered = Beta Unlevered x ( 1 + ( 1 - tax rate ) x Debt / Equity)
Beta Levered = 0.9 x ( 1 + ( 1 - 0.35 ) x 0.4 )
Beta Levered = 1.134
Cost of equity can be calculated using CAPM
CAPM calculated the expected return on an equity investment based on the risk free rate, market premium and risk beta of the investment.
Formula for CAPM is as follow
Expected return = Risk free Rate + Beta ( Market premium)
As we know the Risk premium is the difference of market return and risk free rate.
Expected return = Risk free Rate + Beta ( Market Return - Risk free Rate )
Ra = Rf + β ( Rm - Rf )
Ra = 4.1% + 1.134 ( 12% - 4.1% )
Ra = 13.06%
Cost of Equity is 13.06%
c.
WACC is the average cost of capital of the firm based on the weightage of the debt and weightage of the equity multiplied to their respective costs.
According to WACC formula
WACC = ( Cost of equity x Weightage of equity )+ ( Cost of debt ( 1- t) x Weightage of debt )
Placing the values in formula
If the debt to equity 0.4 the equity value should be 1 and total capital is 1.4 ( 1 + 0.4 )
WACC = ( 13.06% x 1 / 1.4 )+ ( 6.5% ( 1- 0.35) x 0.4 / 1.4 ) = 9.71% + 1.2% = 10.91%
WACC is 10.91%
