Question

Consider a project with free cash flows in one year of $90,000 in a weak economy or $117,000 in a strong economy, with each outcome being equally likely. The initial investment required for the project is $80,000, and the project's cost of capital is 15%. The risk-free interest rate is 5% . The firm has only this project and $80,000 cash. (Assuming perfect capital market)

(For Q 1-3, please round your answer to the dollar, write as a number, e.g. write "$2,123.45" as "2123")

1. The NPV for this project is $_____;

2.  Suppose the firm does not have enough cash, to raise the funds for the initial investment the firm borrows $40,000 at the risk free rate, then the cash flow that equity holders will receive in one year in a weak economy is $_____;

3.  Under the same condition as question 2,  the initial value of the firm's levered equity is $______;

4.  Under the same condition as question 2,   the cost of capital for the firm's levered equity is ______%. (Please round to an integer, e.g., write "12.34%" as "12")

Answer 1

1. NPV of the project.

It is said that the outcomes are equally likely events. Hence the chance of occurring the event will be same.

therefore NPV under a weak economy = 90000 * (1/ 1.15^1) = 78,264

NPV = 80000 - 78264 = -1736 (WEAK ECONOMY)

117000 * (1/1.15^1) = 101743

NPV = 80000 -101743 = 21743 (STRONG ECONOMY)

2. Cash flow that the equity holders will receive in a weak economy will be:-

cash flow in weak economy - interest on borrowed fund

= 90000 - ( 40000 * 5%) 5% = risk free rate

=90000 - 2000

=88,000

3. Value of levered firm = market value of debt + market value of equity

inorder to find the value of levered firm first we have to find the value of unlevered firm.

value of unlevered firm Vu = EBIT (1 - T)/.R

earnings before interest and tax under weak economy = 90000

there is no information about tax so ignore 'T'

therefore Vu = 90000 / .15 = 600,000

Value of levered firm VL = Vu + T*B

Vu = value of levered firm

t = tax

B = borrowed fund.

therefore, Vl = 600000 + 40000

= 640,000

4.  Value of firm's levered equity

= .15 + 40000 / 600000 (.15 - .05)

= 15