Business 1. risk is the risk a firms common stockholders would face if the firm has no debt. While analyzing Fit Trainer Company, 5 external business risk factors should be taken into account. The first significant external business risk is the demand instability, as well as the cyclical nature of the exercise industry. The foreseen variability in costs for labor and taxes should also be included as a risk factor, since for the taxes the direction and amount of change is still unknown and labor costs could increase by as little as 5 to as much as 20%. The final sales price of the shares will determine the total amount of equity. However, this price is subject to the interest of the investors, which is again uncertain. The last business risk that should be incorporated is the operating leverage, which is determined by the extend to which the costs are fixed. Of course, this is a greater risk for Plan B, because the fixed costs are higher compared to Plan A. 2. As stated in the book, a high degree of operating leverage, other factors held constant implies that a relatively small change in sales result in a large change in EBIT. In this case, Fit Trainer Company can choose between two plans. Plan A has fixed costs of $3.6 million and variable costs of $1150 per unit. Plan B will have fixed costs of $4.4 million and variable costs of $1110. Therefore, Plan B will have a higher operating leverage. It will depend on the companys forecast of amount of sales, whether they will choose Plan A or B. In case of high sales the higher operating will be beneficial and hence Plan B will generate more profit. In case of low expected sales, the company should choose Plan A, which has a lower operating leverage and consequently a lower risk in case of low sales.
3. As can be seen on the tables on the next page Plan A has a smaller expected EBIT than plan B ($3,612,500 to $3,966,500). However Plan A has a higher return on investment due to the lower start-up costs. In addition Plan A is less risky than Plan B which can be derived from the lower variation coefficient. (0.8563 to 0.9046). Since Fit Trainer Company is facing business risk, Plan A with its higher ROI and lower risk might be the best choice for the company.
Break-even points Break-even points are calculated with the following formula: QBE = F P V
The break-even points are 14,400 and 17,600 unit for Plan A and B, respectively which indicates that Plan B is riskier, since more units have to be sold before the break-even point will be reached.
Indifference point for EBIT The respective indifference points are calculated by setting the EBIT/ROI of Plan A equal to the EBIT/ROI of Plan B. S A X FA V A X = S B X FB V B X X = FA FB = 20,000 units VB V A
Sales price = S, fixed costs = F and variable costs = V, Quantity sold = X Indifference point for ROI S A X FA V A X S B X FB V B X FA I B FB I A = X= = 66,666.67 units IA IB S A I B V A I B S B I A + VB I A Sales price = S, fixed costs = F and variable costs = V, Quantity sold = X, Initial investment = I Based on the previous analysis it should be clear that Fit Trainer Company should invest in Plan A, because it yields a higher ROI and involves less risk, which can be derived from CV and the break-even points. 9. Fit Trainer Company faces many uncertainties like sales estimates, labor costs and taxes. Moreover, its debt is amortized over 30 years. All these factors can influence the cost of debt negatively and if these factors turn out to change negatively, the cost of debt could be understated. This would consequently negatively influence the estimated cost of equity, since risk by equity holders increases as the level of debt increases. Of course, this situation could also be turned around into a positive scenario in which cost of equity decreases due to the fact of lower taxes, lower labor costs and a higher sales price or higher demand than projected. In addition, the company assumes a no-growth situation which could to an understatement the of companys future opportunities. Overall, there are many assumptions that have to be made to estimate the opportunities and risks for Fit Trainer Company. There are many uncertainties in the companys operating activities. Therefore
it is very unlikely that the future will turn out differently than the expectations made by Frank.
Question 4a
Founder's Wealth @ 7.5 per share 675,000 4,886,364 6,062,500 4,484,375 4,150,000
Cost of Debt
Cost of Equity 10% 11% 12% 16% 20%
Debt 0 10,000,000 15,000,000 20,000,000 25,000,000
Firm Value 21,675,000 25,886,364 27,062,500 25,484,375 25,150,000
# of Founder's shares 54,656 395,657 490,891 363,107 336,032
7% 8% 10.75% 14.25% Table X
The calculations for the firm values can be found in the Appendix. It can be concluded from the table that the amount of debt which maximizes the firm value is equal to $ 15,000,000. Question 4b The Founders Wealth is determined by subtracting the firms capital requirement ($21,000,000) from the firms value. The number of founders shares can be calculated by dividing the founders wealth by expected issue price of $12.35. For the results, see Table X. Question 4c The investors paying $12.35 for the shares should not feel cheated. Issuing stock is a way of acquiring capital. If a share of stock has an (expected) fair value of $12.35, there is nothing wrong with the price. If, however, the founders of the company issue a large number of shares to themselves after they have issued the stocks to the public, the value of the stock, which has been issued before, will decrease. Therefore, the SEC should try to protect investors from founders issuing themselves excessive numbers of shares. Question 5
After Tax Cost of Debt *** 4.20% 4.80% Cost of Equity 10% 11% 12% Debt 0 10,000,000 15,000,000 Equity 21,675,000 15,886,364 12,062,500 Weight of Debt 0.00% 38.63% 55.43% Weight of Equity 100.00% 61.37% 44.57% Cost of Capital 10.0% 8.4% 8.0%
6.45% 8.55% Table XX the task. We
16% 20%
20,000,000 25,000,000
5,484,375 150,000
78.48% 99.40%
21.52% 0.60%
8.5% 8.6%
*** Please note that the values for after-tax cost of debt are different from those given in assume there is a printing error.
If it is assumed that there are no non-operating assets, the value of a company can be calculated with the help of the following formula: FCFn FCF1 FCF2 V= + + ...... + 2 (1 + WACC ) (1 + WACC ) (1 + WACC ) n Assuming, moreover, perpetuity of cash flows, the Value can be calculated even easier: FCF V= WACC From both formulas it becomes clear that a higher WACC decreases the value of a company and vice versa. This is in line with our results in Tables X and XX. When cost of capital is lowest (8%), firm value is maximized ($27,062,500).
The Effect of Leverage on the Cost of Capital
10.5% 10.0% 9.5% WACC 9.0% 8.5% 8.0% 7.5% 7.0% 0.00 0.63 1.24 Debt to Equity Ratio 3.65 166.67
Figure X Question 6
EBIT . The TIE Ratios for the Interest Ch arg es different capital structures can be found in the following table. The formula for the TIE Ratio is: TIE =
Debt 0 10000000 15000000 20000000 25000000 Table XXX Cost of Debt 7% 8% 10.75% 14.25% Interest 0 700000 1200000 2150000 3562500 E(EBIT) 3612500 3612500 3612500 3612500 3612500 TIE 5.160714 3.010417 1.680233 1.014035
The probability of TIE being less than 1 can be found in the following way: In a first step, the quantity of sales (Q) has to be calculated at which the Tie RATIO equals 1 and EBIT equals interest. TIE = 1 1 = 1,400 Q 1,150Q 3,600,000 EBIT QP QV F 1= 1= Q = 19,200 Interest Interest 1,200,000
At a Sales Quantity of 19,200 units, the TIE Ratio is equal to one. Consequently, the TIE Ratio is smaller than 1 for sales smaller than or equal to 19,199 units. The next step is to find the associated z-score:
Probability of TIE< 1
z=
X 19199 28850 = = 0.77986 12374
z=-0.78 19,199 TIE=1
z=0 =12,374 TIE=3.01
The probability of a TIE smaller than one, i.e. a z-value smaller than -0.78, is equal to 21.77%.