Question

Solve not in excel and provide all the formulas

You have been asked to evaluate the quality of investments at an some inc., a firm that open 2 business – books and pens. You have been provided the following information of the businesses:

	Market value of assets	Unlevered beta of business
books	100 000 000$	1.30
pens	100 000 000$	0.70
	200 000 000$

A firm has 100 million shares, trading at $10 a share and faces a marginal tax rate of 31% . Company`s bonds have an A rating and a dedefault spread ( over risk free rate) of 4%. The risk rate is 6% and the equity risk premium is 9%.

1) Market value of equity and market value of debt

2) Unlevered beta for the total firm ( can be found as a weighted average) and unlevered/levered beta for the firm

3) Cost of equity and debt

4) Cost of capital ( WACC)

Answer 1

1) Market value of equity and market value of debt

Market value of equity, E = Price x Number = 10 x 10 = $ 100 million (Please note that number has been given as 100 million, which when multiplied by price of $ 10 will result into an equity value of 1,000 million which is more than the total value of assets of 200 milion, hence there appears to be some typo error and hence I have used N = 10 million shares)

Market value of debt, D = Value of assets - E = 200 - 100 = $ 100 million

2) Unlevered beta for the total firm ( can be found as a weighted average) and unlevered/levered beta for the firm

Unlevered beta = Bu = Sum of weighted average beta = Books / (books + pen) x Beta of Books + Pen / (books + pen) x Beta of pens = 100 / (100 + 100) x 1.30 + 100 / (100 + 100) x 0.70 = 1.00

Levered beta = Bu x [1 + D / E x (1 - T)] = 1 x [1 + 100 / 100 x (1 - 31%)] = 1.69

3) Cost of equity and debt

Cost of equity, Ke = Rf + B x ERP = 6% + 1.69 x 9% = 21.21%

Cost of debt, Kd = Rf + spread = 6% + 4% = 10%

4) Cost of capital ( WACC)

Wd = proportion of debt = D / (D + E) = 100 / (100 + 100) = 0.5

We = 1- Wd = 1 - 0.5 = 0.5

WACC - Wd x Kd x (1 - T) + We x Ke = 0.5 x 10% x (1 - 31%) + 0.5 x 21.21% = 14.06%