Finance concepts and applications

Corporate Finance

WACC = ((E/V) * Re) + [((D/V) * Rd)*(1-T)]

where E = Market value of the company's equity

D = Market value of the company's debt

V = Total Market Value of the company (E + D)

Re = Cost of Equity

Rd = Cost of Debt

T= Tax Rate

In this case, we have the following values for these parameters:

E/V = percentage of equity to finance the project = 60%

D/V = percentage of debt to finance the project = 40%

Re = Cost of Equity = required return by stockholders = 18.36%

Rd = Cost of Debt = required return by debt holders = 10.68%

T= Tax Rate = 36% = 0.36

As such,

WACC = ((0.6) * 0.1836) + [((0.4) * 0.1068)*(1-0.36)] = 0.027 = 2.7%

The firm's weighted average cost of capital is 2.7%.

b. The Net Present Value is calculate according to the formula below.

Here, the discount rate (r) is equal to the weighted average cost of capital. So, r = 2.7% = 0.027

The initial investment (C0) is equal to the cost of the project, which is $45,000.

The cash flows C. are each equal to $13,000 for the next 20 years. So, T = 20. The formula now becomes

NPV = C x

(1 ? (1 + r)-T)

Initial Investment

NPV = $13,000 X (1-1.027-20) - $45,000 = -$35,851

The project should not be undertaken.

c.

, with the following explanations:

is the required rate of return on equity, or cost of levered equity is the company cost of equity capital with no leverage is the required rate of return on borrowings, or cost of debt.

is the debt-to-equity ratio.

is the tax rate

In this case, we have the following values:

D/E = 40/60=2/3

Rd = 10.68% = 0.1068

Re = 18.36% = 0.1836

Tc = 36% = 0.36

R0 = required return on unlevered equity

As such, R0 = 0.229

d. APV = NPV (Unlevered) + NPV (Financing effects)

We need to discount the cash flows from the case study ($13,000 a year) at a rate that would reflect an all-equity financed project. The discount rate is R0, calculated according to the M&M Proposition II at the previous point. The discount rate is 0.229

So, we can now calculate the NPV (Unlevered) as

$13,000 X (1-1.229-20) - $45,000 = -$32,210.

However, now we also need to calculate the debt tax shields.

The annual tax shield = 40% X 18,000 (40% of the total cost of the project) X 36% = $2,592

The present value of tax savings can be discounted with 10.68% = 0.1068. So, the total debt shield over two decades will be PV = 2592/0.106820 = $695

We add the NPV (Unlevered) to the tax shields and the result is the same: the APV is negative, the project is not worth doing

e. The cash flow is $13,000 annually. The interest expense is calculated as 10.68% X 40% X $45,000 = $1,922.4. This means that the annual cash flow before tax will be $13,000-$1,922.4 = $11,077.6

The tax bracket is 36%, which means that the shareholders are left with 64% X 11077.6 = $7,090

We discount this cash flow with the required rate of return for equity. So, the net present value is calculated according to the following formula: