Principle of Finance 1 Week 8 Assignment

Principle of Finance 1 Week 8 Assignment






This is the deduction of money done from taxing the payments made in interest in the income taxes.

    • Define each of the following terms
    • Interest tax shields:

    It is the current value of the amount of money acquired from the payment of interests of the tax savings.

    • Value of tax shield

    This is a model that gives discount to the interest tax shields and expected free cash flows in order to acquire the operational value at unlevered cost.

    • Adjusted present value (APV) model

    In this model a discount is done on the tax savings at the unlevered equity cost.

    • Compressed adjusted present value (CAPV) model

    According to (Miller & Rock, 2015), Modigliani and Miller changes the value of the levered firm and its cost by showing that the levered firm’s value should be the same as the unlevered firm’s value. If that cannot be achieved then the investors who were interested in the levered firm are likely to sell their shares. If the investors owned a certain percentage, they would take a loan of money equal to that percentage in the levered firm and purchase the same amount of percentage of the stock in the unlevered firm.

      • Modigliani and Miller assumed that firms do not grow. How does positive growth change their conclusion about the value of the levered firm and it’s cost of capital

    The unlevered firm has the ability to give the same return as the levered firm thus leaves the investor with some extra to be put as an investment in another firm. The investment process is able to influence the stock price of the levered will go down and the stock price of the unlevered firm will be up. This will consistently take place till the levered firm and unlevered firm will become equal.

    The assumptions of Modigliani and Miller model include;

    Minicase Question

    • The firm’s risk in business should be uniform such that when the firm’s have different rates of risks, the market would prioritize the firms at a rate that is not similar. The income of the firms will be financed at varying capital costs.
      • The investors of the firms have the same aspirations about the expected future (EBIT). The investment process will seize to be effective when the investors of a firm have different aspirations concerning the future EBIT, because the investors will more likely give the firms different values.
      • Corporate taxes do not exist. The presence of corporate taxes equalizes the levered firm’s value, the unlevered firm and tax shield acquired from debt.
      • The stocks and bonds of the firm are sold in capital markets that are made to perfection. It limits brokerage of costs and loans can be given to individuals at an equal rate with corporations.
      • The investors of the firms are rational because they go through the investment process with the aim of getting more profits in return. They are not contented with the profits acquired from the levered firm.

    David Lyons, CEO of Lyons Solar Technologies

    Their assumptions are as follows;

    • Modigliani and Miller made their first paper known in 1958. The book was about Capital structure which acquired zero taxes. Later in 1963, their paper had an inclusion on corporate taxes. Modigliani was an award winning Nobel prize in economics because of the work from MM on Capital structure stems ( Tirole, 2010).


    • There first paper released in 1958 gave an assumption that there are no personal or corporate taxes.
      • An assumption was made concerning all debt having no risks. Thus individuals and corporations would get unlimited loans at an equal rate.
      • The individuals and corporations did not incur brokerage costs.
      • The investors of the firms expect equal goals from the firms income in future.
      • The firms and individuals give out perpetual debt. The income of the firm is given out as dividends thus the growth becomes zero. The expected EBIT will remain constant for a period of time. The EBIT that might be achieved later can vary from going up or down contrary to how it was expected.
      • The business risk of the firm can be calculated by future EBIT. (George & Hwang, 2010) shares that firms with the same rate of risks can be classified into a business risk class of homogeneous.

    (1) Find V, S, rs, and WACC fort Firms U and L.

    The first calculation is finding Vu and Vl

    Where Vu is equal to Vl

    Thus Vu= EBIT


    Vu = $500,000/14%



    Since Vu and Vl are equal therefore Vl will be equivalent to $3,571,429

    The market values for firms L’s debt are essential for finding rs

    Since D + Sl = Vl

    Therefore Sl = Vl – D

    =$3,571,429 – $1,000,000


    The cost of equity can be found form firm L.

    Which will be calculated as;

    rsl = rsu + ( rsu – rd )(D/S)

    = 14% + (14% – 8%)($1,000,000/$2,571,429)

    =14% + 2.33%


    WACC must be equal to rsU according to proposition I. This can be verified using the WCC formula

    WACC= (D/V)rd + (S/V)rs

    =($1,000/$3,571)(8%) + ($2571/$3,571)(16.33%)

    =(2.24% + 11.76%)


    (2) Graph (a) the relationships between capital costs and leverage as measured by

    D/V and (b) the rd relationship between V and D.

    The graph above graphs capital costs against leverage as measured by D/V. When MM assumed no tax, rd remains constant at 8% but the leverage of rs continues to increase. The increase in rs is thus enough to influence WACC to be constant. (Tirole, 2010), supports that when the firm adds more debt to finance its business, the equity of the firm becomes more risky and the cost becomes higher.

    The above graph plots the firm’s value against debt. When the firm assumes zero taxes, MM supports that the value of the firm will not affect the debt of the firm as shared by (Miller & Rock, 2015). Thus the plot gives out a horizontal line. However, the graph should not be extended to a certain level where the investors or debt holders become owners of the firm. This might cause a discontinuity of the firm.

    Proposition 1: Vl = Vu + TD

    • MM propositions with corporate taxes become;

    Proposition 2: rsl = rsU + (rsU – rd)(1-T)(D/S)

    The above propositions have two distinct differences with the zero tax propositions which are very important. Vl and Vu are not equivalent when corporate taxes are added because the Vl increases when debt accumulates in the capital structure. This encourages the debt to be used frequently

    The expected free cash flow is first calculated

    • According to (Hugonnier & Malamud, 2015), when a firm grows or is growing, the MM assumptions that were made will be violated. The MM model shows how growth influences the debt value, the tax shield and the capital used. One of the differences is that the rate of the discount that is required for the debt tax shield is usually not the unlevered cost of debt but the unlevered cost of equity. Another difference is that a debt tax shield that is constantly growing is considered more important than that which is constant.


    NOPAT = EBIT * (1-T)

    = $500,000 * (1-40%)

    =$500,000 * (1-0.4)


    Thus the investment in the net operating assets is;

    =0.10 * EBIT

    =0.10 * $500,000


    Free cash flow will be calculated as;

    =NOPAT – investment in net assets

    =$300,000 – $50,000


    The expected value since EBIT is for the coming year.

    Unlevered cost of equity is equal to WACC when there is no debt.

    Therefore; WACC = rsU = 14%

    The value of U is equal to the Expected FCF/ (WACC –g)

    = $250,000/(0.14-0.07)


    This is greater than part C because the firm is growing

    If a debt of $1,000,000 then;

    I = the value of U + value of debt tax shield

    The growing value of tax shield = rdTD/(rsU-g)



    Therefore , the value of the firm= $3,571,429+ $457,143

    Which is = $4,028,571

    Thus the value of the equity is;

    =$4,028,571 – $1,000,000


    The percentage of the increase in firm’s value due to debt tax shield is;

    =$400,000/2,142,857 *100%


    The new levered cost of equity will be calculated as;

    =14% + (14% -8%)($1,000,000/$3,028,571)


    The new levered WACC will be;

    WACCl = (D/V)rd(1-T)

    =($1,000,000/$4,028,571)8%(1-40%) + (($3,028,571/4,028,571)15.98%



    HVU3 = [(FCF3(1 + gL)]/(rsU – gL)



    The tax shields are found when the interest expenses are multiplied by the rate rate.

    Interest expense $80.00 $95.00 $120.00
    Tax rate 40% 40% 40%
    Tax savings $32 $38 $48

    The constant growth formula is used in order to calculate and find the horizon value

    HVTS = [TS3(1+gL)]

    =[$48(1.07)]/ (0.14-0.07)


    The unlevered value of operations is the current value of the free cash flows and the horizon value.

    =NPV(0.14,32,38,48 + 733.71)


    The value of operations is calculated by summing up the unlevered value of operations with the value of the tax shield.

    Vop = VU + VTS

    =$3,960.01 + $584.94



    J Tirole, (2010), The theory of corporate finance

    TJ George, CY Hwang, (2010), A resolution of the distress risk and leverage puzzles in the cross section of stock returns, journal of financial economics.

    J Hugonnier, S Malamud, (2015), Capital supply uncertainty, cash holdings, and investment.

    MH Miller, K Rock, (2015), Dividend policy under asymmetric information.