Key Concepts in Corporate Finance: A Comprehensive Review
Key Concepts in Corporate Finance
1. Primary financial goal of financial management: maximize market value of owners equity.
2. Characteristics of a corporation include: Limited owner’s liability, No operating control.
3. C corp pays income taxes at the business level, and then owners pay taxes on the same earnings when distributed.
4. Dividends are determined by the corporation’s board of directors.
5. Investor’s capital is best characterized as the: sum of the market value of debt and the market value of equity.
6. The rate of tax on the next dollar earned: marginal tax rate.
7. Bought equipment costing $100,000 4 years ago, sold this year for $10,000 when it had a book value of $4,000. If the marginal tax rate is 40%, then taxes: Capital gain = $10,000 – $4,000 = $6,000. Taxes = 40% * $6,000 = $2,400 (capital gains negative = tax refund).
8. Cash conversion cycle = days sales outstanding, plus the days in inventory, less the days payable outstanding.
9. Statement of cash flows reports a company’s capital expenditures during a particular period of time. Income statement summarizes revenues, expenses, and net income.
10. Dividends decrease shareholders’ equity on a corporation’s balance sheet.
11. As a company loosens its credit standards, the investment in accounts receivable is expected to increase.
12. If you decrease inventory turnover from 10 times to 4 times per year, the chance for spoilage will increase.
13. M has a current ratio of 0.5, and P has a current ratio of 2.0. If both firms increase current assets and current liabilities by the same dollar amount, we should see that: Only company M’s current ratio will increase. M: 2/4 = 0.5 (1+2/1+4) = 0.6.
14. Net profit margin of 4%, ROA of 20%, debt to total assets is 40%. TAT = 5.0. ROA = Net Income / Total Assets; Profit Margin = Net Income / Sales; TAT = Sales / Total Assets. So PM * TAT = ROA, ROA / NPM = TAT. 0.20 / 0.04 = 5.
15. Current annual credit sales of $36,500, current balance in AR of $1,000, projected annual credit sales of $43,800. Wants to reduce days customers are allowed to pay to 6 days. Its projected AR balance assuming 365 days a year = 720 (ACP = AR / Avg Days Sales on credit, ACP = 6 days = AR / ($43,800 / 365). AR = 6 x ($43,800 / 365)).
16. Revenues of $1,000,000, net profit after taxes of $30,000, total assets of $1,500,000, total liabilities of $500,000. ROE is closest to 3% (Total equity = total assets – total liabilities = $1,000,000. ROE = $30,000 / $1,000,000).
17. ROA of 10%, ROE of 20%, debt to equity ratio is closest to 1. ROA = Net Income / Total Assets = 10%. ROE = Net Income / Total Equity = 20%. So ROA / ROE = total equity / Total Assets = 10 / 20 = 50%. Given that total assets = total liabilities + total equity, then total liabilities should also be 50% of total assets.
18. Length of the cash cycle is closest to 62 days. ACP = 46 days, average payment period 22 days, days sales in inventory 38 days. (Cash cycle = DSI + ACP – APP = 84 – 22 = 62)
19. Today $1,000, Year 1 $1,000, Year 2 $1,000, Year 3 – (Annuity Due): payment at the beginning of the period. Ordinary annuity at the end.
20. A bond’s price converges to its face value as it approaches maturity.
21. Inherited $100,000 deposited on 15th birthday, earns interest at a fixed rate of 3%, compounded monthly. Can’t access until 40 years old, you can withdraw $211,502. PV = $100,000, N = (40 – 15) * 12 = 300, I/YR = 3% / 12 = 0.25%, FV = $211,502.
22. Buy $15,000 dining room set, 3-year loan with 10% APR (Annual Percentage Rate). Monthly payments = $484.01 (PV = $15,000, N = 3 * 12 = 36, I/YR = 10% / 12 = 0.833333%. Solve for PMT.
23. A loan is offered with monthly payments and an 8% APR. The loan’s effective annual rate (EAR) = (1 + 8% / 12)^12 – 1 = 8.3%.
24. Semi-annual bond with $1,000 par value and a coupon rate of 5%. If the bond has 30 years remaining and the YTM is 8%, the bond’s value is closest to $661 (FV = $1,000, PMT = 5% * $1,000 / 2 = $25, N = 30 * 2 = 60, I/YR = 8% / 2 = 4%. Solve for PV).
25. A 4.25% semi-annual coupon with 8 years left is offered for sale at 98.336. The YTM is closest to 4.5% (PMT = 4.25% * $1,000 / 2 = $21.25, N = 8 * 2 = 16, PV = -98.336% * $1,000 = $983.36, FV = $1,000. Solve for I/YR = 2.25 x 2 = 4.5).
26. Just paid $3.00 to stockholders as the annual dividend. Future dividends will be increasing 4% per year. If you require a 12% rate of return, the value of a share of stock = P0 = D0 * (1 + g) / (R – g) = 3 * (1 + 4%) / (12% – 4%) = $39.
27. The NPV assumes that cash flows are reinvested at the company’s cost of capital.
28. A decrease in a project’s cost of capital tends to cause NPV to increase.
29. When evaluating mutually exclusive projects, the recommended method of evaluation is the NPV.
30. Sunk costs are not negative cash flows.
31. Except the lowest WACC.
32. Mutually exclusive projects enter cash flows into CF register and choose the one with the higher NPV.
33. Initial -$15,000, yr 1 $2,000, yr 2 $2,000, yr 3 $2,000, yr 4 $2,000, yr 5 $15,000. The MIRR of this project based on a cost of capital of 12%, a reinvestment rate of 8%, and the 5-year planning horizon is closest to: PV of cash outflows = -$15,000; FV of cash inflows = $2,000 * 1.08^4 + $2,000 * 1.08^3 + $2,000 * 1.08^2 + $2,000 * 1.08^1 + $15,000 = $24,733. N = 5. Solve for I/YR = 10.5%.
34. Equipment costing $57,000 seven years ago. Depreciated as a 5-year asset using MACRS. The company’s marginal tax rate is 38%. If the equipment is sold for $3,000, the cash flow associated with the sale of the equipment is closest to: After 7 years, the BV should be 0, so the capital gain = $3,000 – 0; taxes on capital gain = 38% * $3,000 = $1,140; cash flow = $3,000 – $1,140 = $1,860.
35. Generate incremental revenues of $60,000 per year, but it won’t affect expenses other than depreciation. Depreciation from the project is $20,000 for the first year of operations. The tax rate is 30%. Operating cash flow for the first year = ($60,000 – 0 – $20,000) * (1 – 30%) + $20,000 = $48,000.
36. Initial cost of new equipment is $50,000, made at the end of 2012. At the end of 5 years (2017), intends to sell equipment for $6,000. The equipment will be depreciated using MACRS as a 5-year asset. The inventory of bulbs will increase by $5,000 before the project starts (and be maintained at that level). The project will produce additional revenues of $55,000 and operating expenses of $25,000 for each year. The corporate tax rate is 40%, and the cost of capital is 15%. Initial investment outlay is closest to: $55,000 ($50,000 + $5,000). Inventory will increase upfront and decrease at the end by the same amount.
37. The operating cash flow in the first year of operations (2013) is closest to: MACRS depreciation for year 1; $50,000 * 20% = $10,000. So, use the formula: operating cash flow = ($55,000 – $25,000 – $10,000) * (1 – 40%) + $10,000 = $22,000.
38. The cash flow for the fifth year, 2017, that we would use in calculating NPV or the IRR is closest to: BV at the end of year 5 = 5.76% * $50,000 = $2,880; so capital gain = $6,000 – $2,880 = $3,120. Taxes = 40% * $3,120 = $1,248; cash flow from the sale of equipment = $6,000 – $1,248 = $4,752. MACRS depreciation for year 5; $50,000 * 11.52% = $5,760. So, using the formula, operating cash flow = ($55,000 – $25,000 – $5,760) * (1 – 40%) + $5,760 = $20,304. Recovery of working capital = $5,000. So, total cash flow for year 5 = $4,752 + $20,304 + $5,000 = $30,056.
Capital Structure and Cost of Capital
39. Which of the following statements is correct: When calculating the cost of debt, a company needs to adjust for taxes because interest payments are tax deductible. (Preferred stock dividends aren’t tax deductible, the cost of debt financing is more than the cost of retained earnings).
40. As a general rule, at the optimal capital structure, the: weighted average cost of capital is minimized.
41. Which of the following would likely increase the risk to the bondholder? Inclusion of a call provision.
42. Bond ratings reflect which of the following? Default risk.
43. Madison Products is estimating its weighted average cost of capital. The company has collected the following information: the target capital structure consists of 30% debt and 70% common equity. The company can issue long-term debt at par with a YTM of 8%. The marginal tax rate is 35%. The risk-free rate is 3%, the market risk premium is 6%, and beta is 1.4. WACC is closest to 9.54%. YTM is the before-tax cost of debt. Using CAPM, and note that market risk premium = market return – risk-free rate, then the cost of equity = 3% + 1.4 * 6% = 11.4%. WACC = 30% * 8% * (1 – 35%) + 70% * 11.4% = 9.54%.
Risk and Return
44. Which form of efficient market asserts that asset prices fully reflect all information, which includes both public and private info: Strong-form efficient (Weak-form efficient: financial markets incorporate and reflect information efficiently. ALL past market prices and trading volume data are fully reflected in current stock prices).
45. Joe believes he can predict the market by trading based on how announced earnings differ from the expected earnings of a company. Joe is counting on the market not being: semi-strong efficient.
46. The risk that diminishes as a portfolio of assets becomes more diversified is best described as: unsystematic risk.
47. A dominated portfolio cannot be on the efficient frontier.
48. A negative correlation coefficient would provide more effective diversification.
49. If the risk-free rate is 1%, the Sharpe ratio for a security that has an expected return of 6% and a standard deviation of returns of 8% is closest to (6% – 1%) / 8% = 6.25%, and 6.3% is the closest.
50. The latest stock hit a beta of 1.8. If the returns on the market decline by 1.5%, you should expect the price of the latest hot stock to go down 2.7%. 1.5 * 1.8 = 2.7
47. A dominated portfolio cannot be on the efficient frontier.
48. A negative correlation coefficient would provide more effective diversification.
49. If the risk-free rate is 1%, the Sharpe ratio for a security that has an expected return of 6% and a standard deviation of returns of 8% is closest to (6% – 1%) / 8% = 6.25%, and 6.3% is the closest.
50. The latest stock hit a beta of 1.8. If the returns on the market decline by 1.5%, you should expect the price of the latest hot stock to go down 2.7%. 1.5 * 1.8 = 2.7
FV or PV? Present value = amount borrowed today or current value of a future stream of payments, discounted at a given interest rate. FV: future value, the total amount to be repaid at the end of the loan term, including principal and accrued interest.
How is a bond’s price valued? : determined by the PV of its future cash flows, which includes the coupon payments and principal repayment (face value) at maturity. Discounted to present using the bond’s YTM (or required rate of return). Coupon rate higher than YTM: Premium. Coupon rate lower than YTM: Discount. A longer maturity means more sensitive to interest rate changes. As maturity approaches, the price converges to its face value. When market interest rates rise, bond prices fall. Par bond: Price = Face value when YTM = coupon rate. AAA to BBB- High credit quality, lower default risk. Junk Bonds BB+ and below, Ba1 and below. Call Risk: the risk a bond issuer will redeem (call) the bond before its maturity date (when interest rates fall to refinance their debt at a lower interest rate to save on interest). Callable bond YTC is lower than YTM due to risk. Interest Rate risk: the risk that a bond’s price will fluctuate due to changes in the market interest rates: interest rates rise, bond prices fall. Longer maturities and lower coupon rates are more sensitive to interest rate changes. If rates rise, lower coupon rates become less attractive, decreasing the price.
NPV: difference between the present value of cash inflows and outflows: Accept the project if NPV > 0. IRR: discount rate at which NPV = 0. Accept the project if IRR > WACC (cost of capital). Reinvestment rate assumption: NPV assumes reinvestment of cash flows at the WACC, which is more realistic. IRR assumes at the IRR, which is optimistic. WACC increases, NPV decreases. A higher WACC makes it harder for projects to achieve a positive NPV. IRR: If WACC rises above IRR, a previously acceptable project is unviable. When the cost of capital is not equal to the reinvestment rate, the MIRR adjusts for this by: reinvesting cash inflows at the reinvestment rate and discounting cash outflows at the cost of capital.
Optimal capital structure is the mix of debt and equity financing that: Minimizes WACC (a lower WACC reduces the overall cost of financing). Maximizes Firm value by balancing the tax benefits of debt against the risks of financial distress. EPS)
Efficient frontier: the set of optimal investment portfolios offering the highest expected return for a given level of risk. X risk Y Expected return. Risk-averse lower left. After-tax salvage value: market value – tax rate * (market value – book value). Operating Cash Flow: EBIT x (1 – Tax rate) + Depreciation (no cash outflow)
Cost of debt (rd): interest paid on loans/bonds. After-tax cost adjusted for tax benefits from interest: rd * (1 – T). If a firm pays 6% on its debt and its corporate tax rate is 30%, the after-tax cost is 6% * (1 – 0.3) = 4.2%. Cost of preferred stock = preferred dividend / preferred stock price. Cost of common stock (not tax deductible). Cost of equity: re = rf + B (rm – rf). rf = risk-free rate (treasury bond yield). B: stock’s sensitivity to market movements (systematic risk). rm – rf: market risk premium. WACC: Debt = $500,000, cost of debt 6%, preferred stock = $100,000, cost of preferred stock 8%, equity = $400,000, cost of equity = 12%, tax rate = 30%. Total capital (V) = D + P + E = $1,000,000. D / V = 0.5, P / V = 0.1, E / V = 0.4. After-tax cost of debt for taxes: rd * (1 – t) = 6% * (1 – 0.3) = 4.2%. WACC = 0.5 * 4.2% + 0.1 * 8% + 0.4 * 12%. WACC = 2.1% + 0.8% + 4.8% = 7.7% (average cost to finance projects)
DOL: degree of Operating leverage (impact on fixed operating costs on profitability). DOL = % Change in EBIT / % Change in sales or DOL = Sales – Variable costs / EBIT. A higher DOL means higher fixed costs relative to variable costs, making the company more sensitive to changes in sales. If DOL = 2, a 10% increase in sales leads to a 20% increase in EBIT. DFL: degree of financial leverage. DFL = % change in EPS / % change in EBIT or EBIT / (EBIT – Interest expense). A higher DFL indicates greater use of debt or financial leverage. If DFL = 3, a 10% increase in EBIT leads to a 30% increase in EPS. Degree of total leverage DTL: measures the sensitivity of EPS (net income) to changes in sales. DTL = % Change in EPS / % Change in sales or DTL = DOL x DFL. A higher DTL indicates greater overall sensitivity to market changes. If DTL = 6, a 10% increase in sales leads to a 60% increase in EPS. DOL: operating costs. DFL: financial structure. DTL is both.
Revenue – COGS = Gross margin – SGA expense = EBIT – Interest expense = EBT – Taxes = EAT. Dividends are $1,000. The change in retained earnings is $21,000 – $1,000 = $20,000.
1. The primary goal of a publicly owned firm is best described as the maximization of: stock price.
2. The intrinsic value of a stock is best described as the: estimate of a stock’s true value, based on risk and return information about the corporation.
3. If the discount rate is the same for each of the following, which CF stream has the smallest present value? 2 years from today.
4. Which is not correct?: the cost of retained earnings is 0.
5. If a company estimates its WACC and uses the same cost of capital to evaluate all projects, the company will most likely: accept too many high-risk projects and too few low-risk projects.
7. $400,000 assets, no liabilities, sales of $600,000, net income of $25,000. Get ROE up to 15%, NPM = 10%, no liabilities, assets = equity, and EM = assets / equity = 1. TAT = Sales / Assets = $600,000 / $400,000 = 1.5. 15% = NPM * 1.5 * 1.0.
Variance = SD squared.
10. Bought equipment costing $100,000 4 years ago, depreciated based on MACRS 5-year asset. Just sold for $20,000. The tax rate is 40%. The company must pay $1,088 on the sale (the tax rate is the tax rate times the capital gain, and the capital gain is the difference between market value and book value. For 5 years, the first 4 percentages in the 5-year MACRS have been depreciated away, and the last two percentages are left. So, book value = (11.52% + 5.76%) * $100,000 = $17,280. Capital gain = market value – book value = $20,000 – $17,280 = $2,720. Tax = 40% * $2,720 = $1,088.
14. Price per unit: 4, 3. Variable price per unit: 1, 1. Fixed costs: $10,000, $5,000. Based on this information, which company is using the highest degree of operating leverage at 10,000 units produced and sold? The first one. DOL = Q(P – V) / (Q(P – V) – F). DOL = 1.5