# The market value of equity

a. The book value of equity is the book value per share times the number of shares, and the book value of debt is the face value of the company’s debt, so:

Equity = 8,300,000($4) = $33,200,000

Debt = $70,000,000 + 60,000,000 = $130,000,000

So, the total book value of the company is:

Book value = $33,200,000 + 130,000,000 = $163,200,000

And the book value weights of equity and debt are:

Equity/Value = $33,200,000/$163,200,000 = .2034

Debt/Value = 1 – Equity/Value = .7966

b. The market value of equity is the share price times the number of shares, so:

S = 8,300,000($53) = $439,900,000

Using the relationship that the total market value of debt is the price quote times the par value of the bond, we find the market value of debt is:

B = 1.083($70,000,000) + 1.089($60,000,000) = $141,150,000

This makes the total market value of the company:

V = $439,900,000 + 141,150,000 = $581,050,000

And the market value weights of equity and debt are:

S/V = $439,900,000/$581,050,000 = .7571

B/V = 1 – S/V = .2429

c. The market value weights are more relevant.

PART 2

First, we will find the cost of equity for the company. The information provided allows us to solve for the cost of equity using the CAPM, so:

RS = .031 + 1.2(.07) = .1150, or 11.50%

Next, we need to find the YTM on both bond issues. Doing so, we find:

P1 = $1,083 = $35(PVIFAR%,16) + $1,000(PVIFR%,16) R = 2.847% YTM = 2.847% × 2 = 5.69%

P2 = $1,089 = $37.50(PVIFAR%,54) + $1,000(PVIFR%,54) R = 3.389% YTM = 3.389% × 2 = 6.78%

To find the weighted average aftertax cost of debt, we need the weight of each bond as a percentage of the total debt. We find:

XB1 = 1.083($70,000,000)/$141,150,000 = .537

XB2 = 1.089($60,000,000)/$141,150,000 = .463

Now we can multiply the weighted average cost of debt times one minus the tax rate to find the weighted average aftertax cost of debt. This gives us:

RB = (1 – .35)[(.537)(.0569) + (.463)(.0678)] = .0403, or 4.03%

Using these costs and the weight of debt we calculated earlier, the WACC is:

RWACC = .7571(.1150) + .2429(.0403) = .0968, or 9.68%