Homework #5: Leverage, Growth, Cost of Debt, and Risk Submit your step-by-step solutions in a Word document!! John is a Minnesotan arable farmer with 60 hectares of land. His main crop is consumption potatoes. His total assets are worth $3,600.000, and he has a loan outstanding of $750,000 over which he pays 6% interest. Their return on assets for this year was $150,000 and he had to pay $21,000 in taxes. Their family consumption rate is 30%. Assets = $3,600,000 Liabilities = $750,000 Equity = 3,600.000 - 750,000 - $2,850,000 Interest rate -6% Interest = $45,000 ROA = $150,000 Taxes = $21,000 Consumption rate = 30% 1. Determine the growth of equity for John's farm. Tip 1: B&E, page 107 footnote indicates that "The reference to returns on farm assets is generalized and slightly different from the accounting rate-of-return to farm assets (ROFA) and the rate-of-return on farm equity (ROFE) discussed in Chapter 3. The accounting rates of return included a deduction for operator labor, often proxied by family living withdrawals. The generalized measures here include returns before family withdrawals." Tip 2: The tax-rate can be calculated by dividing tax over taxable income. 2. Determine their weighted average cost of capital according to the Equilibrium Theory Tip 1: calculate first the ROE out of the (unweighted) ROA; then use this to calculate the WACC or I.. WACC = l. = L*(1 t).PULE Tip 2: The tax-rate can be calculated by dividing tax over taxable income. 2. Determine their weighted average cost of capital according to the Equilibrium Theory. Tip 1: calculate first The ROE out of the (unweighted) ROA; then use this to calculate the WACC or 1. WACC = la = Id * (1 t) + 1* Tip 2: WACC orla has to be calculated, all items known except le. Calculation of ROE (1.) can be derived from: ROA = la*+le 3. What happens to growth of equity and average cost of debt when John would only have $500,000 in liabilities? Explain. 4. Do the same for the hypothetical case that John would have $1,500,000 in liabilities, CUJUZUNellalle 2A John knows that there is some variability in the total production. This causes his retum on assets (ROA) to vary. In 10% of the years, his return on assets is $120,000, in 50% of the years it is $150,000 and the rest of the time the return on assets is $200,000. 5. How would you call this type of variation on return on assets? What other sources of variation cause ROA to vary? 6. Determine John's growth of equity under risk. Probability 0.1 0.5 ROA $120,000 $150,000 $200,000 ROA (%) 3.33% 4.17% 5.56% 0.4 7. Determine the standard deviation and coefficient of variation under risk of the growth of equity John also knows that the current interest rate of 6% may vary. He looked at the interest rates the past 15 years and discovered that in 6 out of 15 years the interest rate was 4%, in 3 out of 15 years 6% and in the remaining years the interest rate was 8%. 8. How would you call the variation in interest rate? What other sources of variation cause this kind of risk? 9. Determine John's growth of equity under risk. 10. Determine the standard deviation and coefficient of variation considering both types of risk. yuu van de variation in interest rate? What other sources of variation cause this kind of risk? I 9. Determine John's growth of equity under risk. 10. Determine the standard deviation and coefficient of variation considering both types of risk. 11. What would happen if variation in ROA and variation in interest rate were positively correlated? And in the case when they were negatively correlated? Homework #5: Leverage, Growth, Cost of Debt, and Risk Submit your step-by-step solutions in a Word document!! John is a Minnesotan arable farmer with 60 hectares of land. His main crop is consumption potatoes. His total assets are worth $3,600.000, and he has a loan outstanding of $750,000 over which he pays 6% interest. Their return on assets for this year was $150,000 and he had to pay $21,000 in taxes. Their family consumption rate is 30%. Assets = $3,600,000 Liabilities = $750,000 Equity = 3,600.000 - 750,000 - $2,850,000 Interest rate -6% Interest = $45,000 ROA = $150,000 Taxes = $21,000 Consumption rate = 30% 1. Determine the growth of equity for John's farm. Tip 1: B&E, page 107 footnote indicates that "The reference to returns on farm assets is generalized and slightly different from the accounting rate-of-return to farm assets (ROFA) and the rate-of-return on farm equity (ROFE) discussed in Chapter 3. The accounting rates of return included a deduction for operator labor, often proxied by family living withdrawals. The generalized measures here include returns before family withdrawals." Tip 2: The tax-rate can be calculated by dividing tax over taxable income. 2. Determine their weighted average cost of capital according to the Equilibrium Theory Tip 1: calculate first the ROE out of the (unweighted) ROA; then use this to calculate the WACC or I.. WACC = l. = L*(1 t).PULE Tip 2: The tax-rate can be calculated by dividing tax over taxable income. 2. Determine their weighted average cost of capital according to the Equilibrium Theory. Tip 1: calculate first The ROE out of the (unweighted) ROA; then use this to calculate the WACC or 1. WACC = la = Id * (1 t) + 1* Tip 2: WACC orla has to be calculated, all items known except le. Calculation of ROE (1.) can be derived from: ROA = la*+le 3. What happens to growth of equity and average cost of debt when John would only have $500,000 in liabilities? Explain. 4. Do the same for the hypothetical case that John would have $1,500,000 in liabilities, CUJUZUNellalle 2A John knows that there is some variability in the total production. This causes his retum on assets (ROA) to vary. In 10% of the years, his return on assets is $120,000, in 50% of the years it is $150,000 and the rest of the time the return on assets is $200,000. 5. How would you call this type of variation on return on assets? What other sources of variation cause ROA to vary? 6. Determine John's growth of equity under risk. Probability 0.1 0.5 ROA $120,000 $150,000 $200,000 ROA (%) 3.33% 4.17% 5.56% 0.4 7. Determine the standard deviation and coefficient of variation under risk of the growth of equity John also knows that the current interest rate of 6% may vary. He looked at the interest rates the past 15 years and discovered that in 6 out of 15 years the interest rate was 4%, in 3 out of 15 years 6% and in the remaining years the interest rate was 8%. 8. How would you call the variation in interest rate? What other sources of variation cause this kind of risk? 9. Determine John's growth of equity under risk. 10. Determine the standard deviation and coefficient of variation considering both types of risk. yuu van de variation in interest rate? What other sources of variation cause this kind of risk? I 9. Determine John's growth of equity under risk. 10. Determine the standard deviation and coefficient of variation considering both types of risk. 11. What would happen if variation in ROA and variation in interest rate were positively correlated? And in the case when they were negatively correlated