Medical Research Corporation is expanding its research and production capacity to introduce a new line of products. Current plans call for the expenditure of \(100 million on four projects of equal size (\)25 million each), but different returns. Project A is in blood clotting proteins and has an expected return of 18 percent. Project B relates to a hepatitis vaccine and carries a potential return of 14 percent. Project C, dealing with a cardiovascular compound, is expected to earn 11.8 percent, and Project D, an investment in orthopedic implants, is expected to show a 10.9 percent return.

The firm has \(15 million in retained earnings. After a capital structure with \)15 million in retained earnings is reached (in which retained earnings represent 60 percent of the financing), all additional equity financing must come in the form of new common stock.

Common stock is selling for \(25 per share and underwriting costs are estimated at \)3 if new shares are issued. Dividends for the next year will be \(.90 per share (D1), and earnings and dividends have grown consistently at 11 percent per year.

The yield on comparative bonds has been hovering at 11 percent. The investment banker feels that the first \)20 million of bonds could be sold to yield 11 percent while additional debt might require a 2 percent premium and be sold to yield 13 percent. The corporate tax rate is 30 percent. Debt represents 40 percent of the capital structure.

a. Based on the two sources of financing, what is the initial weighted average cost of capital? (Use Kd and Ke.)

b. At what size capital structure will the firm run out of retained earnings?

c. What will the marginal cost of capital be immediately after that point?

d. At what size capital structure will there be a change in the cost of debt?

e. What will the marginal cost of capital be immediately after that point?

f. Based on the information about potential returns on investments in the first paragraph and information on marginal cost of capital (in parts a, c, and e), how large a capital investment budget should the firm use?

g. Graph the answer determined in part f

Step by step solution

01

Definition of capital Structure

Capital structure can be defined as the proportion of the debt and equity elements present in the capital of the business entity. The business entity uses the debt-to-equity ratio to determine the risk associated with capital borrowings.

02

Weighted average cost of capital

Particular	Cost of capital	Weight	Weighted average cost of capital
Debt	7.7%	40%	3.08%
Common equity	14.6%	60%	8.76%
Weighted average cost of capital			11.84%

Working note:

Calculation of cost of debt:

$\begin{array}{c}{\mathbf{K}}_{\mathbf{d}}\mathbf{=}\mathbf{Y}\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{T}\mathbf{)}\\ \mathbf{=}\mathbf{11}\mathbf{\%}\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{30}\mathbf{)}\\ \mathbf{=}\mathbf{7}\mathbf{.}\mathbf{7}\mathbf{\%}\end{array}$

Calculation of cost of equity:

$\begin{array}{c}{\mathbf{K}}_{\mathbf{e}}\mathbf{=}\frac{{\mathbf{D}}_{\mathbf{1}}}{{\mathbf{P}}_{\mathbf{0}}}\mathbf{+}\mathbf{g}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{0}\mathbf{.}\mathbf{90}}{\mathbf{\$}\mathbf{25}}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{11}\\ \mathbf{=}\mathbf{14}\mathbf{.}\mathbf{6}\mathbf{\%}\end{array}$

03

Size of capital structure at which the firm will run out of retained earnings

$\begin{array}{c}\mathbf{X}\mathbf{=}\frac{\mathbf{Retained}\mathbf{}\mathbf{earnings}}{\mathbf{Weight}\mathbf{}\mathbf{of}\mathbf{}\mathbf{retained}\mathbf{}\mathbf{earnings}\mathbf{}\mathbf{in}\mathbf{}\mathbf{the}\mathbf{}\mathbf{capital}\mathbf{}\mathbf{structure}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{15}\mathbf{million}}{\mathbf{0}\mathbf{.}\mathbf{60}}\\ \mathbf{=}\mathbf{\$}\mathbf{25}\mathbf{\text{\hspace{0.17em}}}\mathbf{million}\end{array}$

04

Marginal cost of capital

Particular	Cost of capital	Weight	Weighted average cost of capital
Debt	7.7%	40%	3.08%
Common equity	15.09%	60%	9.05%
The marginal cost of capital			12.13%

Working note:

Calculation of new cost of common equity:

$\begin{array}{c}{\mathbf{K}}_{\mathbf{e}}\mathbf{=}\frac{{\mathbf{D}}_{\mathbf{1}}}{{\mathbf{P}}_{\mathbf{0}}\mathbf{-}\mathbf{F}}\mathbf{+}\mathbf{g}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{0}\mathbf{.}\mathbf{90}}{\mathbf{\$}\mathbf{25}\mathbf{-}\mathbf{\$}\mathbf{3}}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{11}\\ \mathbf{=}\mathbf{15}\mathbf{.}\mathbf{09}\mathbf{\%}\end{array}$

05

Capital structure at which the cost of debt will change

$\begin{array}{c}\mathbf{Z}\mathbf{=}\frac{\mathbf{Debt}}{\mathbf{Weight}\mathbf{}\mathbf{of}\mathbf{}\mathbf{Debt}\mathbf{}\mathbf{in}\mathbf{}\mathbf{the}\mathbf{}\mathbf{capital}\mathbf{}\mathbf{structure}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{20}\mathbf{million}}{\mathbf{0}\mathbf{.}\mathbf{40}}\\ \mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{\text{\hspace{0.17em}}}\mathbf{million}\end{array}$

06

Marginal cost of capital

Particular	Cost of capital	Weight	Weighted average cost of capital
Debt	9.10%	40%	3.64%
Common equity	15.09	60%	9.05%
The marginal cost of capital			12.69%

Working note:

$\begin{array}{c}{\mathbf{K}}_{\mathbf{d}}\mathbf{=}\mathbf{Y}\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{T}\mathbf{)}\\ \mathbf{=}\mathbf{13}\mathbf{\%}\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{30}\mathbf{)}\\ \mathbf{=}\mathbf{9}\mathbf{.}\mathbf{1}\mathbf{\%}\end{array}$

07

Capital investment budget

Particular	Return on investment	Marginal cost of capital	Acceptable/Not-acceptable
$25 million	18%	11.84%	Acceptable
$25 million to $50 million	14%	12.13%	Acceptable
$50 million to $75 million	11.8%	12.69%	Not-Acceptable
$75 million to $100 million	10.9%	12.69%	Not-Acceptable

The firm can invest up to $50 million in the project because up to $50 million return on investment is higher than the marginal cost of capital.

08

Representation on Graph

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!