FIN 480 Exam 3 - Modules 7,8,9

A project's NPV without flotation costs is $1,000,000 and its flotation costs are $50,000. What is the true NPV?

$1,000,000 - $50,000 = *$950,000*

A firm needs to raise $950,000 but will incur flotation costs of 5 percent. How much will it pay in flotation costs?

$950,000 = (1 - 0.05) x Amount Raised Amount Raised = $950,000/0.95 = $1,000,000 Flotation Costs = $1,000,000 - $950,000 = *$50,000*

Previously, a firm issued bonds at par with a 6 percent coupon. Today, similar bond yields are 8 percent and the risk-free rate is 3 percent. What is the embedded cost of the firm's debt?

*6%* The firm's embedded cost of debt is the coupon payment on previously issued debt. It is not related to the firm's cost of new debt.

Case Example: EVF Mowers vs. AEH Mowers Zoysia University must purchase mowers for its landscape department. The university can buy five EVF mowers that cost $6,800 each and have annual, year-end maintenance costs of $1,430 per mower. The EVF mowers will be replaced at the end of Year 4 and have no value at that time. Alternatively, Zoysia can buy six AEH mowers to accomplish the same work. The AEH mowers will be replaced after seven years. They cost $6,100 each and have annual, year-end maintenance costs of $1,570 per mower. Each AEH mower will have a resale value of $900 at the end of seven years. The university's opportunity cost of funds for this type of investment is 9 percent. Because the university is a nonprofit institution, it does not pay taxes. It is anticipated that whichever manufacturer is chosen now will be the supplier of future mowers. Would you recommend purchasing five EVF mowers or six AEH mowers?

*Equivalent Annual Cost (EAC) is also known as Equivalent Annual Annuity (EAA).* We will find the EAA of the EVF first. There are no taxes since the university is tax-exempt, so the maintenance costs are the operating cash flows. The PV of costs of the decision to buy one EVF is: CF0 = -6,800 C01 = -1,430 F01 = 4 I = 9% NPV = CPT = -11,432.80 In order to calculate the equivalent annual cost, set the PV of costs of the equipment equal to an annuity with the same economic life. Since the project has an economic life of four years and is discounted at 9 percent, set the PV of costs equal to a four-year annuity, discounted at 9 percent. So, the EAA per unit is: N = 4 I/Y = 9 PV = 11,432.80 PMT = CPT = -3,528.95 FV = 0 Since the university must buy five of the mowers, the total EAC of the decision to buy the EVF mower is: Total EAC = -$3,528.95(5 Mowers) = *-$17,644.75* Note, we could have found the total EAA for this decision by multiplying the initial cost by the number of mowers needed, and multiplying the annual maintenance cost of each by the same number. We would have arrived at the same EAA. We can find the EAA of the AEH mowers using the same method, but we need to include the salvage value as well. There are no taxes on the salvage value since the university is tax-exempt, so the PV of costs of buying one AEH will be: CF0 = -6,100 C01 = -1,570 F01 = 6 C02 = -1,570 + 900 = -670 I = 9% NPV = CPT = -13,509.41 So, the EAA per mower is: N = 7 I/Y = 9 PV = 13,509.41 PMT = CPT = -2,684.19 FV = 0 Since the university must buy six of the mowers, the total EAC of the decision to buy the AEH mowers is: Total EAC = -$3,424.43(6 Mowers) = *-$16,105.14* *The university should buy the AEH mowers since the EAC is less negative. This represents a lower annual cost.*

Zoysia University must purchase mowers for its landscape department. The university can buy six EVF mowers that cost $7,900 each and have annual, year-end maintenance costs of $1,775 per mower. The EVF mowers will be replaced at the end of Year 4 and have no value at that time. Alternatively, Zoysia can buy seven AEH mowers to accomplish the same work. The AEH mowers will be replaced after seven years. They each cost $6,900 and have annual, year-end maintenance costs of $2,225 per mower. Each AEH mower will have a resale value of $700 at the end of seven years. The university's opportunity cost of funds for this type of investment is 7 percent. Because the university is a nonprofit institution, it does not pay taxes. It is anticipated that whichever manufacturer is chosen now will be the supplier of future mowers. What is the EAC of each type of mower? EVF: -$24,643.81 AEH: -$23,971.01

*Equivalent Annual Cost (EAC) is also known as Equivalent Annual Annuity (EAA).* We will find the EAA of the EVF first. There are no taxes since the university is tax-exempt, so the maintenance costs are the operating cash flows. The PV of costs of the decision to buy one EVF is: CF0 = -7,900 C01 = -1,775 F01 = 4 I = 7% NPV = CPT = -13,912.30 In order to calculate the equivalent annual cost, set the PV of costs of the equipment equal to an annuity with the same economic life. Since the project has an economic life of four years and is discounted at 7 percent, set the PV of costs equal to a four-year annuity, discounted at 7 percent. So, the EAA per unit is: N = 4 I/Y = 7 PV = 13,912.30 PMT = CPT = -4,107.30 FV = 0 Since the university must buy six of the mowers, the total EAC of the decision to buy the EVF mower is: Total EAC = -$4,107.30(6 Mowers) = *-$24,643.81* Note, we could have found the total EAA for this decision by multiplying the initial cost by the number of mowers needed, and multiplying the annual maintenance cost of each by the same number. We would have arrived at the same EAA. We can find the EAA of the AEH mowers using the same method, but we need to include the salvage value as well. There are no taxes on the salvage value since the university is tax-exempt, so the PV of costs of buying one AEH will be: CF0 = -6,900 C01 = -2,225 F01 = 6 C02 = -2,225 + 700 = -1,525 I = 7% NPV = CPT = -18,455.24 So, the EAA per mower is: N = 7 I/Y = 7 PV = 18,455.24 PMT = CPT = -3,424.43 FV = 0 Since the university must buy seven of the mowers, the total EAC of the decision to buy the AEH mowers is: Total EAC = -$3,424.43(7 Mowers) = *-$23,971.01* *The university should buy the AEH mowers since the EAC is less negative.*

Case Example: The Cost of Capital for Swan Motors 1. Download Tesla's most recent 10-Q or 1o-K on the SEC website (www.sec.gov). Tesla's ticker symbol: TSLA. Find the book value of debt and the book value of equity. 2. To estimate the cost of equity for Tesla, go to finance.yahoo.com and enter the ticker symbol "TSLA." Follow the various links to find answers to the following questions: Answers will vary. a. What is the most recent stock price listed for Tesla? b. How many shares of stock does Tesla have outstanding? c. What is the market value of equity, or market capitalization? d. What is the beta for Tesla? e. Now go to https://home.treasury.gov/. What is the yield on a Treasury security? f. Using a 6% market risk premium, what is the cost of equity for Tesla using the CAPM? 3. Create a list of the top 5 competitors in the industry (you can use Competitors from Morningstar, Peers on Seeking Alpha, or People Also Watch on Yahoo Finance may have some competitors). a. Find the beta for each of these competitors: Ford Motor Co, Toyota Motor Corporation, General Motors Company, Honda Motor Co, NIO Inc. b. Then calculate the industry average beta. c. Using the industry average beta, what is the cost of equity? d. Does it matter if you use the beta for Tesla or the beta for the industry in this case? 4. You now need to calculate the cost of debt for Tesla. a. Go to http.//finra-markets.morningstar.com/BondCenter/Default.jsp, enter Tesla as the company, and find the yield to maturity for each of Tesla's bonds. b. What is the weighted average cost of debt for Tesla using the book value weights and the market value weights? c. Does it make a difference in this case if you use book value weights or market value weights? 5. You can now calculate the weighted average cost of capital for Tesla, assuming a 21% tax rate. a. Calculate the WACC for Tesla using book value weights and market value weights. b. Which cost of capital number is more relevant? 6. You used Tesla as a representative company to estimate the cost of capital for SMI. What are some of the potential problems with this approach in this situation? What improvements might you suggest?

1. Book Value of Debt = Current Portion of Debt and Finance Leases + Debt and Finance Leases, Net of Current Portion = 1,589 + 5,245 = 6,834 Book Value of Equity = Total Shareholders' Equity = 24,804 2-a. If we use December 31st, 2021: $1,056.78. 2-b. Per Document and Entity Information: 1,033,507,611 shares. 2-c. Market Capitalization = Shares Outstanding x Market Price = 1,033,507,611 x $1,056.78 = $1,092,190,173,152.58 2-d. Estimate with 60 monthly returns (for TSLA and SPY as S&P 500) Price data from end of November 2016 through end of December 2021. Beta = 1.95 2-e. If we use the 3-month Treasury, we have a risk-free rate of rRF = 0.06%. 2-f. If we use the Yahoo! Finance Beta of 2.05, we have a risk-free rate of: ri = rRF + (rM - rRF)bi = 0.06% + 6%(2.05) = 12.36% 3-a. Ford Motor Co - F: 1.12; Toyota Motor Corporation - TM: 0.63; General Motors Company - GM: 1.23; Honda Motor Co - HMC: 0.95; NIO Inc - NIO: 2.47 3-b. Industry Average Beta = (1.12 + 0.63 + 1.23 + 0.95 + 2.47)/5 = 6.40/5 = 1.28 3-c. ri = rRF + (rM - rRF)bi = 0.06% + 6%(1.28) = 7.74% 3-d. This estimate of the cost of equity using the industry beta is more than 4% lower than using Tesla's beta. We should also be careful of the industry comparison since the betas for the companies in this industry are so different. This may be the result of operational differences. 4-a. Notice, several of the bonds have a negative YTM. These bonds are convertible, and the conversion requirements have been met, so it is likely these bonds will be converted soon. Because of this, we will ignore these bond issues in our calculations. We will also ignore the 2019 bond since it has already matured. 4-b. Not Applicable - we only have one bond with a yield. Cost of debt = 3.885%. 4-c. Not Applicable - we only have one bond with a yield. 5-a. WACC = (Wd x Rd x (1 - T)) + (Wcs x Rcs) Book Value Weights = {[6,834/(6,834 + 30,189)] x 0.03885 x (1 - 0.21)} + {[30,189/(6,834 + 30,189)] x 0.1236] = 0.10645 = 10.645% Market Value Weights: Use the book value weights for debt since we did not find the market value. = {[6,834/(6,834 + 1,092,190)] x 0.03885 x (1 - 0.21)} + {[30,189/(6,834 + 1,092,190)] x 0.1236] = 0.123022 = 12.3022% 5-b. Market value weights are more appropriate than book value weights because the market values of the securities are closer to the actual dollars that would be received from their sale. In fact, it is better to think in terms of target market weights. These are the market weights expected to prevail over the life of the firm or project. 6. The biggest potential problem with SMI using Tesla's cost of capital is that SMI operates some dealerships that generate the company's sales. Tesla generates sales almost exclusively without dealers. Additionally, the difference in the type of vehicle, gas versus electric, could be a concern. Finally, another factor that could affect the cost of capital is Tesla's access to capital since it is a public company, while Swan Motors is private.

Case Example - Replacement Analysis: A firm is considering an investment in a new machine with a price of $9.26 million to replace its existing machine. The current machine has a book value of $2.48 million, and a market value of $4.16 million. The new machine is expected to have a four-year life, and the old machine has four years left in which it can be used. If the firm replaces the old machine with the new machine, it expects to save $2.1 million in operating costs each year over the next four years. Both machines will have no salvage value in four years and use straight line depreciation. If the firm purchases the new machine, it will also need an investment of $165,000 in net working capital. It will recover the investment in net working capital at project completion. The required return on the investment is 8 percent and the tax rate is 21 percent. 1. What are the NPV and IRR of the decision to replace the old machine? 2. Ignoring the time value of money, the new machine saves only $8.4 million over the next four years and has a cost of $9.26 million. How is it possible that the decision to replace the old machine has a positive NPV?

1. First, we need to find the After-Tax Net Cash Flow from Sale of Old Machine = Sales Price - Tax Effect. We know the sales price is the market value of $4,160,000. This would be a cash inflow. However, if the sales results in a book gain, we will pay taxes on the gain. Similarly, if the sales results in a book loss, the loss will lower our taxes paid. We can find the Tax Effect by finding the Book Gain (Loss) = Sales Price - Book Value = $4,160,000 - $2,480,000 = $1,680,000 Then multiply the book gain (loss) by the tax rate. Tax Effect = Book Gain (Loss) x T = $1,680,000 x 0.21 = $352,800 Therefore, the After-Tax Net Cash Flow from Sale of Old Machine = $4,160,000 - $352,800 = $3,807,200 Initial Investment Outlay at t=0: Purchase New Machine + After-Tax Net Cash Flow from Sale of Old Machine - Investment in NOWC = Initial Investment Outlay = -9,260,000 + $3,807,200 - $165,000 = -$5,617,800 Terminal Cash Flow at t=4: Recover Investment in NOWC = $165,000 Operating Cash Flows - Cash Flow Differentials at t=1 through t=4: With a replacement project, the focus is on cash flow differentials. "Which cash flows would change if we purchased and operated the new equipment versus the cash flows if we continue operating the old equipment?" We focus on Operating Cash Flows (OCF), where: OCF = EBIT(1 - T) + Depreciation - ∆NOWC - ∆Gross Fixed Assets When we think of cash flow differentials, we need to find the difference in OCF. ∆OCF = OCFnew - OCFold Therefore, we can find the differential for each component of OCF, starting with EBIT. EBIT = Sales - Costs {excluding depreciation} - Depreciation Sales will not change, but the firm will "save $2.1 million in operating costs each year over the next four years" and we can determine the change in depreciation expense: New Machine: Annual Depreciation Expense = Depreciable Basis/Useful Life = $9,260,000/4 = $2,315,000 per year for 4 years Old Machine: Annual Depreciation Expense = Depreciable Basis/Useful Life = $2,480,000/4 = $620,000 per year for 4 years ∆Depreciation = Annual Depreciation Expense.new - Annual Depreciation Expense.old = $2,315,000 - $620,000 = $1,695,000 Now we can find the change in recurring cash flows, which include the change in NOPAT and the change in depreciation in this particular problem: ∆EBIT x (1 - T) + ∆Depreciation = (∆Sales - ∆Costs {excluding depreciation} - ∆Depreciation) x (1 - T) + ∆Depreciation = ($0 - -$2,100,000 - $1,695,000) x (1 - 0.21) + $1,695,000 = $2,100,000 - $1,695,000 x 0.79 + $1,695,000 = $405,000 x 0.79 + $1,695,000 = $2,014,950 each year We can find the NPV and IRR as: CF0 = -5,617,800 C01 = 2,014,950 F01 = 3 C02 = 2,014,950 + 165,000 = 2,179,950 IRR = 16.97976 I = 8% NPV = CPT = 1,177,249.90 This analysis gives us the same result as subtracting the NPV of the decision to keep the old machine from the NPV of the decision to purchase the new machine. 2. Even though the saved expenses are less than the cost of the new machine, the cash flows are also increased because of the higher depreciation of the new machine. The depreciation tax shield increases the cash flows enough to help make the NPV positive. Additionally, the opportunity cost of selling the old machine helps to defray the cost of the new machine.

If 20-year Treasury-bonds yield 5 percent, and if the term premium is 2 percent what is the average one-year interest rate expected to be over the next 20 years?

3%

Compute the accounting break-even point for a firm reporting the following information: Fixed costs = $50,000; Depreciation = $10,000; Sale price per unit = $50; Variable cost per unit = $30.

Accounting Break-Even Point = [(Fixed Costs + Depreciation)/(Sales Price - Variable Costs)] = [($50,000 + $10,000)/($50 - $30)] = $60,000/$20 = *3,000 units*

Calculate the accounting break-even point for a firm that reports the following information: Sales per unit = $40,000; Variable cost per unit = $25,000; Fixed costs (excluding depreciation) = $960,000; Depreciation = $25,000.

Accounting Break-Even Point = [(Fixed Costs + Depreciation)/(Sales Price - Variable Costs)] = [($960,000 + $25,000)/($40,000 - $25,000)] = $985,000/$15,000 = *65.67 units*

A company has a borrowing rate of 15 percent and a tax rate of 30 percent. What is its aftertax cost of debt?

After-Tax Cost of Debt = (1 - T) x Borrowing Rate = (1 - 0.30) x 0.15 = 0.70 x 0.15 = 0.105 = *10.5%*

What are the after-tax earnings for HIJ Corporation if it reports $200 in revenue, $90 in operating expenses, has a tax rate of 30%, and pays $20 in interest on its bonds?

After-Tax Earnings for Unlevered Corporation = Revenue - Expenses = Pretax Earnings - Tax Rate After-Tax Earnings for Levered Corporation = $200 Revenue - $90 Expenses = $110 Earnings Before Interest and Taxes - $20 Interest Expense = $90 Pretax Earnings - $27 = ($90 x 0.30) Tax Rate = *$63*

ULC and LEV have earnings before interest and taxes of $110. LEV also has $20 of interest expense. Both companies are taxed at 30 percent, ULC's aftertax earnings are ___ , which is ___ than LEV's aftertax earnings.

After-Tax Earnings for Unlevered Corporation = Revenue - Expenses = Pretax Earnings - Tax Rate After-Tax Earnings for Levered Corporation = Revenue - Expenses = Earnings Before Interest and Taxes - Interest Expense = Pretax Earnings - Tax Rate LEV: EBIT = $110 - $20 Interest Expense Pretax Earnings = $90 - $27, ($90 x 0.30) Tax Rate After-Tax Earnings = $63 ULC: EBIT = $110 - $33, ($110 x 0.30) Tax Rate After-Tax Earnings = *$77* $77 - $63 = *$14* more than LEV's after-tax earnings.

A firm's capital structure consists of 25 percent debt and 75 percent equity. Its bonds yield 15 percent, pretax, its cost of equity is 22 percent, and the tax rate is 35 percent. What is its after-tax WACC?

After-Tax WACC = [(0.25 x 0.15) x (1 - 0.35)] + (0.75 x 0.22) = 0.0375 x 0.65 + 0.165 = 0.02438 + 0.165 = 0.1894 = *19%*

If a firm has $10 million of debt with a debt beta of .4 and $30 million of equity with equity beta of 2, then the firm's asset beta is ____.

Asset Beta = [Debt/(Debt + Equity) x ßDebt] + [Equity/(Debt + Equity) x ßEquity] = [$10,000,000/($10,000,000 + $30,000,000) x 0.40] + [$30,000,000/($10,000,000 + $30,000,000) x 2] = $10,000,000/$40,000,000 x 0.40 + $30,000,000/$40,000,000 x 2 = 0.25 x 0.40 + 0.75 x 2 = 0.10 + 1.5 = *1.6*

A project requires $240 of equipment that will be depreciated straight-line over the 3-year project life. What is the average investment for AAR purposes?

Average Accounting Return (AAR) = Average Net Income/Average Amount Invested Average Amount Invested = ($240 + $160 + $80 + $0)/4 = $480/4 = *$120*

A project is projected to have the following net income: Year 1 = $80,000; Year 2 = $40,000; Year 3 = -$30,000. The same project has an initial investment of $300,000 and will lose value at a rate of $100,000 per year. The numerator in the average accounting return method will be:

Average Accounting Return (AAR) = Average Net Income/Average Amount Invested Average Net Income = ($80,000 + $40,000 + -$30,000)/3 = $90,000/3 = *$30,000*

An increase in depreciation expense will increase cash flows from operations.

Because depreciation is not a cash expense, its only effect is to decrease taxes paid, thereby increasing cash flows from operations.

If a preferred stock pays a dividend of $5 per year and is selling for $40, its yield is:

Because preferred stocks are perpetuities, they should be priced using the perpetuity formula: PV = C/RP, where PV is the present value, or price; C is the cash to be received each year; and RP is the yield, or rate of return. Rearranging, we have: RP = C/PV = $5/$40 = 0.125 = *12.5%* We do not tax-adjust here because dividend payments on preferred stock are not tax deductible.

According to the bottom-up approach, what is the OCF if EBIT is $1,100, depreciation is $2,500, and the tax rate is 35 percent?

Because we are ignoring any financing expenses, such as interest, in our calculations of project OCF, we can write project net income as: Project Net Income = EBIT - Taxes = $1,100 - ($1,100 x 0.35) = $1,100 - $385 = $715 If we add the depreciation to both sides, we arrive at a slightly different and very common expression for OCF: OCF = Net Income + Depreciation = $715 + $2,500 = *$3,215* This is the bottom-up approach. Here, we start with the accountant's bottom line (net income) and add back any non-cash deductions such as depreciation. It is crucial to remember that this definition of operating cash flow as net income plus depreciation is correct only if there is no interest expense subtracted in the calculation of net income.

According to the bottom-up approach, what is the OCF if EBIT is $600, depreciation is $1,800, and the tax rate is 30 percent?

Because we are ignoring any financing expenses, such as interest, in our calculations of project OCF, we can write project net income as: Project Net Income = EBIT - Taxes = $600 - ($600 x 0.30) = $600 - $180 = $420 If we add the depreciation to both sides, we arrive at a slightly different and very common expression for OCF: OCF = Net Income + Depreciation = $420 + $1,800 = *$2,220* This is the bottom-up approach. Here, we start with the accountant's bottom line (net income) and add back any non-cash deductions such as depreciation. It is crucial to remember that this definition of operating cash flow as net income plus depreciation is correct only if there is no interest expense subtracted in the calculation of net income.

Pear Orchards is evaluating a new project that will require equipment of $249,000. The equipment will be depreciated on a 5-year MACRS schedule. The annual depreciation percentages are 20.00 percent, 32.00 percent, 19.20 percent, 11.52 percent, and 11.52 percent, respectively. The company plans to shut down the project after 4 years. At that time, the equipment could be sold for $67,100. However, the company plans to keep the equipment for a different project in another state. The tax rate is 40 percent. What aftertax salvage value should the company use when evaluating the current project?

Book Value = $249,000 - [$249,000(0.20 + 0.32 + 0.1920 + 0.1152)] $249,000 - ($249,000)(0.8272) = $249,000 - $205,972.80 = $43,027.20 Tax Refund (Due) = ($43,027.20 - $67,100)(0.40) = -$24,072.80(0.40) = -$9,629.12 Aftertax Salvage Value = $67,100 + -$9,629.12 = $57,470.88 = *$57,471*

Compute the NPV of a project that has the following end-of-year cash flow projections: Year 1 = $40,000; Year 2 = $50,000; Year 3 = -$22,000. The project requires an initial investment of $75,000 and has a discount rate of 10 percent.

CF0 = -75,000 C01 = 40,000 C02 = 50,000 C03 = -22,000 I = 10% NPV = CPT = *-13,842.98*

What is the PI for a project with an initial cash outflow of $30 and subsequent cash inflows of $80 in Year 1 and $20 in Year 2 if the discount rate is 12 percent?

CF0 = 0 C01 = 80 C02 = 20 I = 12% NPV = CPT = 87.37245 Profitability Index = Present Value of Cash Flows Subsequent to Initial Investment/Initial Investment = $87.37/$30 = *2.91*

What is the PI for a project with an initial cash outflow of $40 and subsequent cash inflows of $90 in Year 1 and $30 in Year 2 if the discount rate is 10 percent?

CF0 = 0 C01 = 90 C02 = 30 I = 10% NPV = CPT = 106.61157 Profitability Index = Present Value of Cash Flows Subsequent to Initial Investment/Initial Investment = $106.61/$40 = *2.67*

A project with a cash inflow of $200 followed by a cash outflow of -$250 one year later will have an IRR of ___ percent.

CF0 = 200 C01 =-250 IRR = CPT = *25.00*

A small project has cash flows of -$10 and $45, and a large project has cash flows of -$30 and $70. What is the incremental IRR?

Cash Flow at Year 0 = -$30 - -$10 = -$20 Cash Flow at Year 1 = $70 - $45 = $25 CF0 = -20 C01 = 25 IRR = CPT = *25.00*

Connect Homework: Module 7

Chapter 12

Connect Homework: Module 8

Chapter 7

Connect Homework: Module 9

Chapters 8-9

What is the contribution margin if the sales price per unit is $15,000, variable cost per unit is $10,000, and fixed costs are $2,000? Ignore taxes.

Contribution Margin = Sales Price - Variable Cost = $15,000 - $10,000 = *$5,000*

If an analyst's forecast for a firm's earnings growth is 6 percent, and its dividend yield is 3 percent, its cost of equity will be ___.

Cost of Equity = Earning Growth + Dividend Yield = 0.06 + 0.03 = 0.09 = *9%*

Case Example: Bullock Gold Mining Construct a spreadsheet to calculate the payback period, internal rate of return, modified internal rate of return, and the net present value of the proposed mine. Year - Cash Flow - Cumulative Cash Flow 0 → $(750,000,000) → $(750,000,000) 1 → 150,000,000 → (600,000,000) 2 → 180,000,000 → (420,000,000) 3 → 195,000,000 → (225,000,000) 4 → 235,000,000 → 10,000,000 5 → 220,000,000 → 230,000,000 6 → 185,000,000 → 415,000,000 7 → 165,000,000 → 580,000,000 8 → 145,000,000 → 725,000,000 9 → (105,000,000) → 620,000,000 Based on your analysis, should the company open the mine?

Cumulative Cash Flow Calculations: -$750,000,000 + 150,000,000 = -$600,000,000 -$600,000,000 + 180,000,000 = -$420,000,000 -$420,000,000 + 195,000,000 = -$225,000,000 -$225,000,000 + 235,000,000 = $10,000,000 $10,000,000 + 220,000,000 = $230,000,000 $230,000,000 + 185,000,000 = $415,000,000 $415,000,000 + 165,000,000 = $580,000,000 $580,000,000 + 145,000,000 = $725,000,000 $725,000,000 + -105,000,000 = $620,000,000 *Payback Period:* Regular Payback = Number of Years Prior to Full Recovery + (Unrecovered Cost at Start of Year/Cash Flow During Full Recovery Year) = 3 + ($225,000,000/$235,000,000) = 3 + 0.957447 = *3.95745 years* In Excel, you can use "IF" statements to calculate the Payback Period. *Internal Rate of Return (IRR):* CF0 = -750,000,000 C01 = 150,000,000 C02 = 180,000,000 C03 = 195,000,000 C04 = 235,000,000 C05 = 220,000,000 C06 = 185,000,000 C07 = 165,000,000 C08 = 145,000,000 C09 = -105,000,000 IRR = CPT = *17.00155%* We should note that this project has non-normal cash flows, and therefore, it may have multiple IRRs. We should not rely exclusively on IRR to make decisions when a project has non-normal cash flows. *Modified Internal Rate of Return (MIRR):* Find the Terminal Value: TV of CF t=1: N=8 I/Y=12 PV=-150,000,000 PMT=0 FV=CPT=371,394,476.44 TV of CF t=2: N=7 I/Y=12 PV=-180,000,000 PMT=0 FV=CPT=397,922,653.33 TV of CF t=3: N=6 I/Y=12 PV=-195,000,000 PMT=0 FV=CPT=384,895,423.61 TV of CF t=4: N=5 I/Y=12 PV=-235,000,000 PMT=0 FV=CPT=414,150,295.55 TV of CF t=5: N=4 I/Y=12 PV=-220,000,000 PMT=0 FV=CPT=346,174,259.20 TV of CF t=6: N=3 I/Y=12 PV=-185,000,000 PMT=0 FV=CPT=259,911,680.00 TV of CF t=7: N=2 I/Y=12 PV=-165,000,000 PMT=0 FV=CPT=206,976,000.00 TV of CF t=8: N=1 I/Y=12 PV=-145,000,000 PMT=0 FV=CPT=162,400,000.00 Add up the TVs: 371,394,476.44 + 397,922,653.33 + 384,895,423.61 + 414,150,295.55 + 346,174,259.20 + 259,911,680.00 + 206,976,000.00 + 162,400,000.00 = 2,543,824,788.14 PV of Costs: -$750,000,000 occurs at t=0 and -$105,000,000 occurs at t=9 PV of CF t=9: N=9 I/Y=12 PMT=0 FV=-105,000,000 PV=CPT=37,864,052.62 Add up the PVs: 750,000,000 + 37,864,052.62 = 787,864,052.62 Solve for MIRR: N=9 PV=-787,864,052.62 PMT=0 FV=2,543,824,788.14 I/Y=CPT=13.9094 MIRR = *13.91%* *Net Present Value:* CF0 = -750,000,000 C01 = 150,000,000 C02 = 180,000,000 C03 = 195,000,000 C04 = 235,000,000 C05 = 220,000,000 C06 = 185,000,000 C07 = 165,000,000 C08 = 145,000,000 C09 = -105,000,000 I = 12% NPV = CPT = *129,464,667.78* *Since the NPV of the mine is positive, the company should open the mine. We should note, it may be advantageous to delay the mine opening because of real options.*

Compute the depreciation tax shield based on the following information: EAC = $740,000; Fixed costs = $950,000; Depreciation expense = $475,000; Tax rate = 24 percent.

Depreciation Tax Shield = Depreciation x T = $475,000 x 0.24 = *$114,000*

What is next year's expected cash flow if there is a 30 percent probability that the cash flow will be $10 million and a 70 percent probability that the cash flow will be $1 million?

Expected Cash Flow = (0.30 x $10,000,000) + (0.70 x $1,000,000) = $3,000,000 + $700,000 = *$3,7000,000*

A project requires an initial investment of $250,000. There is a 30 percent probability of success with a $1.2 million cash flow next year. If the project fails, the project will not generate any cash flows. What is the NPV if the discount rate is 15 percent?

Expected Payoff = (Probability of Success x Payoff if Successful) + (Probability of Failure x Payoff if Failure) = ($1,200,000 x 0.30) + (0.70 x $0) = $360,000 + $0 = $360,000 NPV = -$250,000 + ($360,000/1 + 0.15) = -$250,000 + ($360,000/1.15) = -$250,000 + $313,043.48 = *$63,043.48*

Consider a project that will payoff $1.5 million if it is successful and nothing if it is not successful. If the probability of success is 30 percent, what is the project's expected payoff?

Expected Payoff = (Probability of Success x Payoff if Successful) + (Probability of Failure x Payoff if Failure) = ($1,500,000 x 0.30) + (0.70 x $0) = $450,000 + $0 = *$450,000*

A project requires an initial investment of $500,000. There is a 20 percent probability of success with a $2 million cash flow next year. If the project fails, the project will not generate any cash flows. What is the NPV if the discount rate is 10 percent?

Expected Payoff = (Probability of Success x Payoff if Successful) + (Probability of Failure x Payoff if Failure) = ($2,000,000 x 0.20) + (0.80 x $0) = $400,000 + $0 = $400,000 NPV = -$500,000 + ($400,000/1 + 0.10) = -$500,000 + ($400,000/1.10) = -$500,000 + $363,636.36 = *-$136,363.64*

Consider a project that will payoff $2 million if it is successful and nothing if it is not successful. If the probability of success is 20 percent, what is the project's expected payoff?

Expected Payoff = (Probability of Success x Payoff if Successful) + (Probability of Failure x Payoff if Failure) = ($2,000,000 x 0.20) + (0.80 x $0) = $400,000 + $0 = *$400,000*

Case Example - Decision Tree Problem: The manager for a growing firm is considering the launch of a new product. If the product goes directly to market, there is a 40 percent chance of success. For $60,000, the manager can conduct a focus group that will increase the product's chance of success to 60 percent. Alternatively, the manager has the option to pay a consulting firm $355,000 to research the market and refine the product. The consulting firm successfully launches new products 85 percent of the time. If the firm successfully launches the product, the payoff will be $1.23 million. If the product is a failure, the NPV is $0. Which action will result in the highest expected payoff to the firm?

Find the NPV of each option: NPV = -Investment + (Probability of Success x NPV Success + Probability of Failure x NPV Failure) Direct to Market: NPV = -0 + (0.40 x $1,230,000 + 0.60 x $0) = -0 + $492,000 + $0 = $492,000 Focus Group: NPV = -$60,000 + (0.60 x $1,230,000 + 0.40 x $0) = -$60,000 + $738,000 + $0 = $678,000 Consulting: NPV = -$355,000 + (0.85 x $1,230,000 + 0.12 x $0) = -$355,000 + $1,045,500 + $0 = $690,500 Decision: Hire the consulting firm - this has the highest NPV.

The Angelina Corporation's common stock has a beta of 1.6. If the risk-free rate is 4.1 percent and the expected return on the market is 11 percent, what is the company's cost of equity capital?

Here we have information to calculate the cost of equity using the CAPM. The cost of equity is: RS = 0.041 + 1.6(0.11 - 0.041) = 0.041 + 1.6(0.069) = 0.041 + 0.01104 = 0.1514 = *15.14%*

A firm has a target debt-equity ratio of .5, but it plans to finance a new project with all debt. What debt-equity ratio should be used when calculating the project's flotation costs?

If a firm has a target debt-equity ratio of 0.5, but chooses to finance a particular project with all debt, it will have to raise additional equity later on to maintain its target debt-equity ratio.

Case Example - Mutually Exclusive Project: Peyton Manufacturing is trying to decide between two different conveyor belt systems. System A costs $520,000, has a four-year life, and requires $145,000 in pretax annual operating costs. System B costs $695,000, has a six-year life, and requires $123,000 in pretax annual operating costs. Both systems are to be depreciated straight-line to zero over their lives and will have zero salvage value. Whichever system is chosen, it will not be replaced when it wears out. If the tax rate is 25 percent and the discount rate is 11 percent, which system should the firm choose if they want to pick the system with the lowest overall cost?

If we are trying to decide between two projects that will not be replaced when they wear out, the proper capital budgeting method to use is NPV. Both projects only have costs associated with them, no sales, so we will use these to calculate the NPV of each project. We know EBIT(1 - T) + Depreciation could also be expressed as: (Sales - Costs {excluding depreciation} x (1 - T) + Depreciation x T These projects will not result in an increase in sales, so we can remove the first term and we will focus on the pre-tax operating costs and depreciation expense. We can calculate the OCF of System A as: OCFA = -Costs {excluding depreciation} x (1 - T) + Depreciation x T = -$145,000 x (1 - 0.25) + ($520,000/4) x 0.25 = -$108,750 + $32,500 = -$76,250 We can find the NPV as: CF0 = -520,000 CO1 = -76,250 F01 = 4 I = 11% NPV = CPT = -756,561.48 We can calculate the OCF of System B as: OCFB = -Costs {excluding depreciation} x (1 - T) + Depreciation x T = -$123,000 x (1 - 0.25) + ($695,000/6) x 0.25 = -$92,250 + $28,958.33 = -$63,291.67 We can find the NPV as: CF0 = -695,000 C01 = -63,292 F01 = 6 I = 11% NPV = CPT = -962,759.20 If the system will not be replaced when it wears out, then System A should be chosen because it has the less negative NPV.

Compute net accounting profit based on the following information: Revenues = $4,000; Variable costs = $1,600; Fixed costs = $700; Depreciation = $300; Tax rate = 20 percent.

Net Accounting Profit = (Sales - Variable Costs - Fixed Costs - Depreciation) x (1 - T) = ($4,000 - $1,600 - $700 - $300) x (1 - 0.20) = $1,400 x 0.80 = *$1,120*

Compute net accounting profit based on the following information: sales revenue = $50,000; variable costs = $35,000; fixed costs = $5,000; depreciation expense = $1,000; and tax rate = 15%.

Net Accounting Profit = (Sales - Variable Costs - Fixed Costs - Depreciation) x (1 - T) = ($50,000 - $35,000 - $5,000 -$1,000) x (1 - 0.15) = $9,000 x 0.85 = *$7,650*

Compute the expected total revenues based on the following projections: Market size = 200,000 units; Market share = 7.5 percent; Price per unit = $75.

Number Sold = Market Size x Market Share = 200,000 units x 0.075 = 15,000 units sold Sales Revenue = Number Sold x Price Per Unit = 15,000 units sold x $75 = *$1,1250,000*

Compute the expected total revenues based on the following projections: Market size = 7,000 machines; Market share = 20 percent; Price per machine = $15,000.

Number Sold = Market Size x Market Share = 7,000 units x 0.20 = 1,400 units sold Sales Revenue = Number Sold x Price Per Unit = 1,400 units sold x $15,000 = *$21,000,000*

A company is considering a new 6-year project that will have annual sales of $222,000 and costs of $138,000. The project will require fixed assets of $257,000, which will be depreciated on a 5-year MACRS schedule. The annual depreciation percentages are 20.00 percent, 32.00 percent, 19.20 percent, 11.52 percent, 11.52 percent, and 5.76 percent, respectively. The company has a tax rate of 40 percent. What is the operating cash flow for Year 2?

OCF = ($222,000 - $138,000)(1 - 0.40) + 0.40(0.32)($257,000) =$84,000(0.60) + $32,896 = $50,400 + $32,896 = *$83,296*

According to the top-down approach, what is the operating cash flow if sales are $250,000, total cash costs are $206,514, and the tax bill is $1,638?

Perhaps the most obvious way to calculate OCF is: OCF = Sales - Costs - Taxes = $250,000 - $206,514 - $1,638 = *$41,848* This is the top-down approach, the second variation on the basic OCF definition. Here, we start at the top of the income statement with sales and work our way down to net cash flow by subtracting costs, taxes, and other expenses. Along the way, we leave out any strictly non-cash items such as depreciation.

Your manager has developed the following pricing equation: Price = Base price + $2 × Industry sales (in thousands) +/- $5 If the base price is $30 and industry sales are $2,000, the higher price, according to the model, would be:

Price = Base price + $2 × Industry sales (in thousands) +/- $5 Higher Price = $30 + ($2 × $2) + $5 = *$39* Lower Price = $30 + ($2 × $2) - $5 = $29

Your manager has developed the following pricing equation: Price = Base price + $3 × Industry sales (in thousands) +/- $7 If the base price is $45 and industry sales are $5,000, the lower price, according to the model, would be:

Price = Base price + $3 × Industry sales (in thousands) +/- $7 Higher Price = $45 + ($3 × $5) + $7 = $67 Lower Price = $45 + ($3 × $5) - $7 = *$53*

Countess Corp. is expected to pay an annual divided of $4.75 on its common stock in one year. The current stock price is $75.15 per share. The company announced that it will increase its dividend by 3.85 percent annually. What is the company's cost of equity?

RE = ($4.75/$75.15) + 0.0385 = 0.063207 + 0.0385 = 0.101707 = *10.17%*

If the nominal rate is 5 percent and the annual rate of inflation is 2 percent, what is the real rate of return?

REAL = [(1 + NOM)/(1 + i)] - 1 = [(1 + 0.05)/(1 + 0.02)] - 1 = (1.05/1.02) - 1 = 1.029412 - 1 = 0.029412 = *2.94%*

What is the real interest rate if the nominal annual interest rate is 10 percent and the annual inflation rate is 4 percent?

REAL = [(1 + NOM)/(1 + i)] - 1 = [(1 + 0.10)/(1 + 0.04)] - 1 = (1.10/1.04) - 1 = 1.057692 - 1 = 0.057692 = *5.77%*

Assume these market averages: dividend growth rate = 10 percent; average market dividend yield = 3 percent; average 1-year T-bill rate = 2 percent. What is the cost of equity capital for a firm with a beta of 2?

RM = Dividend Yield + Growth Rate in Dividends = 0.03 + 0.10 = 0.13 = 13% RS = Rf + ß(RM - Rf) = 0.02 + 2(0.13 - 0.02) = 0.02 + 2(0.11) = 0.02 + 0.22 = 0.24 = *24%*

Assume these market averages: dividend growth rate = 9 percent; average market dividend yield = 5 percent; average 1-year T-bill rate = 2.5 percent. What is the cost of equity capital for a firm with a beta of 1.5?

RM = Dividend Yield + Growth Rate in Dividends = 0.05 + 0.09 = 0.14 = 14% RS = Rf + ß(RM - Rf) = 0.025 + 1.5(0.14 - 0.025) = 0.025 + 1.5(0.115) = 0.025 + 0.1725 = 0.1975 = *19.75%*

MNO preferred stock pays a dividend of $2 per year and has a price of $20. If MNO's tax rate is 40 percent, the required rate of return on its preferred stock is ___ percent.

RP = C/PV = $2/$20 = 0.10 = *10%* We do not tax-adjust here because dividend payments on preferred stock are not tax deductible, so the 40% is NOT USED!

Suppose the risk-free rate is 5 percent, the market rate of return is 10 percent, and beta is 2. Find the required rate of return using the CAPM.

RS = Rf + ß(RM - Rf) = 0.05 + 2(0.10 - 0.05) = 0.05 + 2(0.05) = 0.05 + 0.10 = 0.15 = *15%*

Bethesda Water has an issue of preferred stock outstanding with a coupon rate of 5.80 percent that sells for $95.98 per share. If the par value is $100, what is the cost of the company's preferred stock?

Rp = (0.0580 x $100)/$95.98 = $5.80/$95.98 = 0.06043 = *6.04%*

A project has the following cash flows: Year - Cash Flows 0 → -$11,600 1 → $5,050 2 → $7,270 3 → $4,720 4 → -$1,660 Assuming the appropriate interest rate is 10 percent, what is the MIRR for this project using the discounting approach?

TV of CF t=1: N=3 I/Y=10 PV=-5,050 PMT=0 FV=CPT=6,721.55 TV of CF t=2: N=2 I/Y=10 PV=-7,270 PMT=0 FV=CPT=8,796.70 TV of CF t=3: N=1 I/Y=10 PV=-4,720 PMT=0 FV=CPT=5,192.00 Add up the TVs: 6,721.55 + 8,796.70 + 5,192.00 = 20,710.25 -11,600 occurs at t=0 and -1,660 occurs at t=4 PV of CF t=4: N=4 I/Y=10 PMT=0 FV=-1,660 PV=CPT=1,133.80 Add up the PVs: 11,600 + 1,133.80 = 12,733.80 Solving for MIRR: N = 4 PV = -12,733.80 PMT = 0 FV = 20,710.25 I/Y = CPT = 12.9293 = *12.93%*

A company has a project available with the following cash flows: Year - Cash Flows 0 → -$35,270 1 → $12,660 2 → $14,740 3 → $19,870 4 → $11,180 If the required return for the project is 8.2 percent, what is the project's NPV?

The NPV is the sum of the present value of all cash flows, so the NPV of the project if the required return is 8.2 percent will be: NPV = -$35,270 + $12,660/(1 + 0.082) + $14,740/(1 + 0.082)^2 + $19,870/(1 + 0.082)^3 + $11,180/(1 + 0.082)^4 = -$35,270 + $11,700.55 + $12,590.50 + $15,686.14 + $8,157.04 = *$12,864.24* When the required return is 8.2 percent, the NPV of the offer is $12,864.24. (You would accept this offer.) OR EASIEST: Using a financial calculator, we find that: CF0 = -35,270 C01 = 12,660 F01 = 1 C02 = 14,740 F02 = 1 C03 = 19,870 F03 = 1 C04 = 11,180 F04 = 1 I = 8.2% NPV = CPT = *$12,864.24*

Case Example Expansion at East Coast Yachts: Because East Coast Yachts is producing at full capacity, Larissa has decided to have Dan examine the feasibility of a new manufacturing plant. This expansion would represent a major capital outlay for the company. A preliminary analysis of the project has been conducted at a cost of $1.2 million. This analysis determined that the new plant will require an immediate outlay of $55 million and an additional outlay of $30 million in one year. The company has received a special tax dispensation that will allow the building and equipment to be depreciated on a 20-year MACRS schedule. Because of the time necessary to build the new plant, no sales will be possible for the next year. Two years from now, the company will have partial-year sales of $18 million. Sales in the following four years will be $27 million, $35 million, $39 million, and $43 million. Because the new plant will be more efficient than East Coast Yachts' current manufacturing facilities, variable costs are expected to be 60 percent of sales, and fixed costs will be $3.5 million per year. The new plant will also require net working capital amounting to 8 percent of sales for the next year. Dan realizes that sales from the new plant will continue into the indefinite future. Because of this, he believes the cash flows after Year 5 will continue to grow at 3 percent indefinitely. The company's tax rate is 21 percent and the required return is 11 percent. Larissa would like Dan to analyze the financial viability of the new plant and calculate the NPV. Also, Larissa has instructed Dan to disregard the value of the land that the new plant will require. East Coast Yachts already owns it, and, as a practical matter, it will go unused indefinitely. She has asked Dan to discuss this issue in his report.

The preliminary analysis of the project is a sunk cost and should be ignored. The cash flow to start the project is the $55 million and will occur immediately. The $30 million outlay will occur in one year. We need to be careful in depreciating the equipment. The $55 million expenditure will have depreciation in Year 1, while the depreciation for the Year 1 expenditure will not begin depreciating until Year 2. The depreciation for the next five years, according to the 20-year MACRS schedule, will be: Year 1: $55,000,000(0.03750) = $2,062,500 Year 2: $55,000,000(0.07219) + $30,000,000(0.03750) = $3,970,450 + $1,125,000 = $5,095,450 Year 3: $55,000,000(0.06677) + $30,000,000(0.07219) = $3,672,350 + $2,165,700 = $5,838,050 Year 4: $55,000,000(0.06177) + $30,000,000(0.06677) = $3,397,350 + $2,003,100 = $5,400,450 Year 5: $55,000,000(0.05713) + $30,000,000(0.06177) = $3,142,150 + $1,853,100 = $4,995,250 Since the NOWC is a percentage of sales (8 percent of sales for the next year), we need next year's sales to find this year's NOWC. Then, we need the beginning and ending NOWC requirements for each year, so we can find the Investment in NOWC. (Sales were provided in the problem). Year 1: Sales - N/A Required Working Capital - $18,000,000(0.08) = $1,440,000 Investment in NOWC - $1,440,000 Year 2: Sales - $18,000,000 Required Working Capital - $27,000,000(0.08) = $2,160,000 Investment in NOWC - $2,160,000 - $1,440,000 = $720,000 Year 3: Sales - $27,000,000 Required Working Capital - $35,000,000(0.08) = $2,800,000 Investment in NOWC - $2,800,000 - $2,160,000 = $640,000 Year 4: Sales - $35,000,000 Required Working Capital - $39,000,000(0.08) = $3,120,000 Investment in NOWC = $3,120,000 - $2,800,000 = $320,000 Year 5: Sales - $39,000,000 Required Working Capital - $43,000,000(0.08) = $3,440,000 Investment in NOWC - $3,440,000 - $3,120,000 = $320,000 Year 6: Sales - $43,000,000 Required Working Capital - N/A Investment in NOWC - N/A Now we can calculate the Operating Cash Flow (OCF) for each year. Since the cash flows will grow at 3 percent after five years, we only need to calculate the OCF for the next five years, so: OCF = Sales Revenue - Variable Costs (60% of Sales) - Fixed Costs - Depreciation = EBIT EBIT - Taxes (0.21) = NOPAT NOPAT + Depreciation - Investment in NOWC - Investment in Gross Fixed Assets = OCF Year 0 OCF: = $0 - $0 - $0 - $0 = $0 - $0 = $0 + $0 - $0 - $55,000,000 = -$55,000,000 Year 1 OCF: = $0 - $0 - $0 - $2,062,500 = -$2,062,500 - -$433,125 = $1,629,375 + $2,062,500 - $1,440,000- $30,000,000 = -$31,006,875 Year 2 OCF: = $18,000,000 - ($18,000,000 x 0.60) - $3,500,000 - $5,095,450 = $18,000,000 - $10,800,000 - $3,500,000 - $5,095,450 = -$1,395,450 - $293,045 = -$1,102,406 + $5,095,450 - $720,000 - $0 = $3,273,045 Year 3 OCF: = $27,000,000 - ($27,000,000 x 0.60) - $3,500,000 - $5,838,050 = $27,000,000 - $16,200,000 - $3,500,000 - $5,838,050 = $1,461,950 - $307,010 = $1,154,941 + $5,838,050 - $640,000 - $0 = $6,352,991 Year 4 OCF: = $35,000,000 - ($35,000,000 x 0.60) - $3,500,000 - $5,400,450 = $35,000,000 - $21,000,000 - $3,500,000 - $5,400,450 = $5,099,550 - $1,070,906 = $4,028,645 + $5,400,450 - $320,000 - $0 = $9,109,095 Year 5 OCF: = $39,000,000 - ($39,000,000 x 0.60) - $3,500,000 - $4,995,250 = $39,000,000 - $23,400,000 - $3,500,000 - $4,995,250 = $7,104,750 - $1,491,998 = $5,612,753 + $4,995,250 - $320,000 - $0 = $10,288,003 Next, we need to calculate the value of the perpetual cash flows (or the horizon value at year 5) since "the cash flows after Year 5 will continue to grow at 3 percent indefinitely." The total cash flow in Year 5 will be: HV Year 5 = OCF5 x (1 + g)/(WACC - g) = $10,288,003 x (1 + 0.03)/(0.11 - 0.03) = $10,596,643.09/0.08 = $132,458,032.19 (If we do not calculate this in Excel, and use the rounding in the above equation, we get $132,458,038.6) Therefore, the Year 5 cash flow = Year 5 OCF + HV Year 5 = $10,288,003 + $132,458,032.19 = $142,746,034.69 So, the cash flows for the project are: Year 0: -$55,000,000 Year 1: -$31,006,875 Year 2: $3,273,045 Year 3: $6,352,991 Year 4: $9,109,095 Year 5: $10,288,003 + $132,458,032 = $142,746,035 So, the NPV of the project will be: CF0 = -55,000,000 C01 = -31,006,875 C02 = 3,273,045 C03 = 6,352,991 C04 = 9,109,095 C04 = 142,746,035 I = 11% NPV = CPT = *15,080,874.46* Regarding the land, East Coast Yachts already owns it, and it will go unused indefinitely, meaning there is no loss of cash flows from the land as a result of accepting this project. However, Dan might bring up the opportunity cost associated with the land: if they don't accept this project, the firm could sell the land. This would be an incremental cash flow that the firm should include in the analysis.

A firm has a 50 percent probability of obtaining regulatory approval to enter an overseas market. If it enters that market, there is a 20 percent probability of successfully gaining significant market share. What is the probability of successfully entering the overseas market?

The probability of these two outcomes is: = 0.50 x 0.20 = 0.10 = *10%*

What is the key reason why a positive NPV project should be accepted? → The project is expected to increase shareholder value. → The present value of the expected cash flows equals the project's cost. → The project will produce positive cash flows in the future. → The project's payback will be positive. → The project's PI will be less than 1, which indicates acceptance.

The project is expected to increase shareholder value.

What is the depreciation tax shield if EBIT is $600, depreciation is $1,800, and the tax rate is 30 percent?

The third variation of on our basic definition of OCF is the tax shield approach. This approach will be very useful for some problems we consider in the next section. The tax shield definition of OCF is: OCF = (Sales - Costs) x (1 - T) + Depreciation x T This approach views OCF as having two components. The first part is what the project's cash flow would be if there was no depreciation expense. The second part of OCF in this approach is the depreciation deduction multiplied by the tax rate. This is called the depreciation tax shield. We know that depreciation is a non-cash expense. The only cash flow effect of deducting depreciation is to reduce our taxes, a benefit to us. Depreciation Tax Shield = Depreciation x T = $1,800 x 0.30 = *$540*

The NPV of a project is often referred to as an unlevered free cash flow.

The word "unlevered" mean that the cash flows are independent of any debt that may have been used to finance the project. The word "free" refers to the fact that these cash flows can be distributed to creditors and shareholders.

You are in the business of manufacturing watches. The estimated variable costs for each of these watches costs is $25. Fixed costs for the month are $8,000. What will be the total monthly costs if you manufacture 400 watches?

Variable Cost = Variable Cost Per Unit x Number Sold = $25 x 400 watches = $10,000 Total Cost Before Taxes = Variable Cost + Fixed Cost = $10,000 + $8,000 = *$18,000*

You are in the business of manufacturing dog collars. The estimated variable costs for each of the collars is $3.75. Fixed costs for the month are $3,000. What will be the total monthly costs if you manufacture 1,200 collars?

Variable Cost = Variable Cost Per Unit x Number Sold = $3.75 x 1,200 collars = $4,500 Total Cost Before Taxes = Variable Cost + Fixed Cost = $4,500 + $3,000 = *$7,500*

A firm's capital structure consists of 40 percent debt and 60 percent equity. The aftertax yield on debt is 2.5 percent and the cost of equity is 15 percent. The project is about as risky as the overall firm. What discount rate should be used to estimate the project's net present value?

WACC = (0.40 x 0.025) + (0.60 x 0.15) = 0.010 + 0.09 = 0.10 = *10%*

The manager for a growing firm is considering the launch of a new product. If the product goes directly to the market, there is a 40 percent chance of success. For $177,000, the manager can conduct a focus group that will increase the product's chance of success to 55 percent. Alternatively, the manager has the option to pay a consulting firm $392,000 to research the market and refine the product. The consulting firm successfully launches new products 70 percent of the time. If the firm successfully launches the product, the payoff will be $1.92 million. If the product is a failure, the NPV is $0. Calculate the NPV for each option available for the project. Which action should the firm undertake?

We need to calculate the NPV of each option, and choose the option with the highest NPV. So, the NPV of going directly to market is: NPV = Chance of Success(Probability of Success) = 0.40($1,920,000) = *$768,000* The NPV of the focus group is: NPV = C0 + Chance of Success(Probability of Success) = -$177,000 + 0.55($1,920,000) = -$177,000 + $1,056,000 = *$879,000* And the NPV of using the consulting firm is: NPV = C0 + Chance of Success(Probability of Success) = -$392,000 + 0.70($1,920,000) = -$392,000 + $1,344,000 = *$952,000* *The firm should hire the consulting firm since that option has the highest NPV.*

Hurzdan, Inc., is considering the purchase of a $367,000 computer with an economic life of five years. The computer will be fully depreciated over five years using the straight-line method. The market value of the computer will be $67,000 in five years. The computer will replace five office employees whose combined annual salaries are $112,000. The machine will also immediately lower the firm's required net working capital by $87,000. This amount of net working capital will need to be replaced once the machine is sold. The corporate tax rate is 22 percent. The appropriate discount rate is 15 percent. Calculate the NPV of this project.

We will calculate the aftertax salvage value first. The aftertax salvage value of the equipment will be: Taxes on Salvage Value = (Book Value - Market Value)(Corporate Tax Rate) = ($0 - $67,000)(0.22) = -$14,740 Aftertax Salvage Value = Market Price + Tax on Sale = $67,000 + -$14,740 = $52,260 Next, we will calculate the initial cash outlay, that is, the cash flow at Year 0. To undertake the project, we will have to purchase the equipment. The new project will decrease the net working capital, so this is a cash inflow at the beginning of the project. So, the cash outlay today for the project will be: Total Cash Outlay = Equipment + Net Working Capital = -$367,000 + $87,000 = -$280,000 Now we can calculate the operating cash flow each year for the project. Using the bottom up approach, the operating cash flow will be: Saved Salaries - Depreciation = EBT EBT - Taxes = Net Income $112,000 - $73,400 = $38,600 $38,600 - $8,492 = $30,108 And the OCF will be: OCF = Net Income + Depreciation = $30,108 + $73,400 = $103,508 Now we can find the NPV of the project. In Year 5, we must replace the saved NWC, so: CF0 = -367,000 + 87,000 = -280,000 C01 = (112,000 x 0.78) + [(367,000/5) x 0.22] = 103,508 F01 = 4 C02 = (112,000 x 0.78) + [(367,000/5) x 0.22] - 87,000 + (67,000 x 0.78) = 68,768 I = 15% NPV = CPT = *49,702.95*

Suppose the risk-free rate is 4 percent, the market rate of return is 9 percent, and beta is 0. Find the required rate of return using the CAPM.

When beta is zero, the required rate will equal the risk-free rate.

Suppose you are offered a project with the following payments: Year - Cash Flows 0 → $7,300 1 → -$4,000 2 → -$2,700 3 → -$1,800 4 → -$1,200 a. What is the IRR of this offer? IRR: 15.75% b. If the appropriate discount rate is 10 percent, should you accept this offer? c. If the appropriate discount rate is 22 percent, should you accept this offer? d-1. What is the NPV of the offer if the appropriate discount rate is 10 percent? NPV: -$739.75 d-2. What is the NPV of the offer if the appropriate discount rate is 22 percent? NPV: $674.33

a. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is: 0 = C0 + C1/(1 + IRR) + C2/(1 + IRR)^2 + C3/(1 + IRR)^3 + C4/(1 + IRR)^4 0 = $7,300 + -$4,000/(1 + IRR) + -$2,700/(1 + IRR)^2 + -$1,800/(1 + IRR)^3 + -$1,200/(1 + IRR)^3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation. EASIEST: Using a financial calculator, we find that: CF0 = 7,300 C01 = -4,000 F01 = 1 C02 = -2,700 F02 = 1 C03 = -1,800 F03 = 1 C04 = -1,200 F04 = 1 IRR = CPT = *15.75%* b. This problem differs from previous ones because the initial cash flow is positive and all future cash flows are negative. In other words, this is a financing-type project, while previous projects were investing-type projects. For financing situations, accept the project when the IRR is less than the discount rate. Reject the project when the IRR is greater than the discount rate. IRR = 15.75% Discount Rate = 10% 15.75% > 10% IRR > Discount Rate *Since this is a financing-type project, I will reject the project since the IRR is greater than the discount rate.* c. Use the same reasoning as part b. For financing situations, accept the project when the IRR is less than the discount rate. Reject the project when the IRR is greater than the discount rate. IRR = 15.75% Discount Rate = 22% 15.75% < 22% IRR < Discount Rate *Since this is a financing-type project, I will accept the project since the IRR is less than the discount rate.* d-1. The NPV is the sum of the present value of all cash flows, so the NPV of the project if the discount rate is 10 percent will be: NPV = $7,300 + -$4,000/(1 + 0.10) + -$2,700/(1 + 0.10)^2 + -$1,800/(1 + 0.10)^3 + -$1,200/(1 + 0.10)^4 = $7,300 + -$3,636.36 + -$2,231.40 + -$1,352.37 + -$819.62 = *-$739.75* When the discount rate is 10 percent, the NPV of the offer is -$739.75. Reject the offer. OR EASIEST: Using a financial calculator, we find that: CF0 = 7,300 C01 = -4,000 F01 = 1 C02 = -2,700 F02 = 1 C03 = -1,800 F03 = 1 C04 = -1,200 F04 = 1 I = 10% NPV = CPT = *-$739.75* d-2. The NPV is the sum of the present value of all cash flows, so the NPV of the project if the discount rate is 22 percent will be: NPV = $7,300 + -$4,000/(1 + 0.22) + -$2,700/(1 + 0.22)^2 + -$1,800/(1 + 0.22)^3 + -$1,200/(1 + 0.22)^4 = $7,300 + -$3,278.69 + -$1,814.03 + -$991.27 + -$541.68 = *$674.33* When the discount rate is 22 percent, the NPV of the offer is $674.33. Accept the offer. OR EASIEST: Using a financial calculator, we find that: CF0 = 7,300 C01 = -4,000 F01 = 1 C02 = -2,700 F02 = 1 C03 = -1,800 F03 = 1 C04 = -1,200 F04 = 1 I = 22% NPV = CPT = *$674.33*

Pandora Manufacturing has 9 million shares of common stock outstanding. The current share price is $75, and the book value per share is $6. The company also has two bond issues outstanding. The first bond issue has a face value of $85 million and a coupon rate of 10 percent and sells for 96 percent of par. The second issue has a face value of $65 million and a coupon rate of 11 percent and sells for 109 percent of par. The first issue matures in 25 years, the second in 9 years. a. What are the company's capital structure weights on a book value basis? Equity/Value: 0.2647 Debt/Value: 0.7353 b. What are the company's capital structure weights on a market value basis? Equity/Value: 0.8158 Debt/Value: 0.1842 c. Which are more relevant, the book or market value weights?

a. The book value of equity is the book value per share times the number of shares, and the book value of debt is the face value of the company's debt, so: BV/E = 9,000,000($6) = $54,000,000 BV/D = $85,000,000 + $65,000,000 = $150,000,000 So, the total book value of the company is: V = $54,000,000 + $150,000,000 = $204,000,000 And the book value weights of equity and debt are: E/V = $54,000,000/$204,000,000 = *0.2647* D/V = $150,000,000/$204,000,000 = *0.7353* OR D/V = 1 - E/V = 1 - 0.2647 = *0.7353* b. The market value of equity is the share price times the number of shares, so: MV/E = 9,000,000($75) = $675,000,000 Using the relationship that the total market value of debt is the price quote times the par value of the bond, we find the market value of debt is: MV/D = 0.96($85,000,000) + 1.09($65,000,000) = $81,600,000 + $70,850,000 = $152,450,000 This makes the total market value of the company: V = $675,000,000 + $152,450,000 = $827,450,000 And the market value weights of equity and debt are: E/V = $675,000,000/$827,450,000 = *0.8158* D/V = $152,450,000/$827,450,000 = *0.1842* OR D/V = 1 - S/V = 1 - 0.8158 = *0.1842* c. *The market value weights are more relevant.*

J&R Renovation, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 18 years to maturity that is quoted at 106 percent of face value. The issue makes semiannual payments and has a coupon rate of 10 percent annually. a. What is the company's pretax cost of debt? b. If the tax rate is 21 percent, what is the aftertax cost of debt?

a. The pretax cost of debt is the YTM of the company's bonds, so: N = 18 x 2 = 36 I/Y = CPT = 4.6534 PV = 1.06 x 1,000 = -1,060 PMT = (0.10 x 1,000)/2 = 50 FV = 1,000 I/Y = 4.6534 x 2 = *9.31%* b. And the aftertax cost of debt is: Aftertax cost of debt = 0.09307(1 - 0.21) = 0.09307(0.79) = 0.07352 = *7.35%*

Bill plans to open a self-serve grooming center in a storefront. The grooming equipment will cost $390,000. Bill expects aftertax cash inflows of $85,000 annually for six years, after which he plans to scrap the equipment and retire to the beaches of Nevis. The first cash inflow occurs at the end of the first year. Assume the required return is 10 percent. a. What is the project's profitability index (PI) PI: 0.949 b. Should the project be accepted?

a. The profitability index is defined as the PV of the cash inflows divided by the PV of the cash outflows. The cash flows from this project are an annuity, so the equation for the profitability index is: CF0 = 0 C01 = 85,000 F01 = 6 I = 10% NPV = CPT = $370,197.16 PI = $370,197.16/$390,000 = *0.949* b. *The project should not be accepted because the PI is less than 1.*

Brodsky Metals Corporation has 9.5 million shares of common stock outstanding and 390,000 5 percent semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $43 per share and has a beta of 1.25. The bonds have 15 years to maturity and sell for 114 percent of par. The market risk premium is 8.3 percent, T-bills are yielding 4 percent, and the company's tax rate is 25 percent. a. What is the firm's market value capital structure? Debt: 0.5212 Equity: 0.4788 b. If the company is evaluating a new investment project that has the same risk as the firm's typical project, what rate should the firm use to discount the project's cash flows? Discount Rate: 8.36%

a. We will begin by finding the market value of each type of financing. We find: Bonds = 390,000($1,000)(1.14) B = $444,600,000 Stock = 9,500,000($43) S = $408,500,000 And the total market value of the firm is: V = $444,600,000 + $408,500,000 = $853,100,000 So, the market value weights of the company's financing is: B/V = $444,600,000/$853,100,000 = *0.5212* S/V = $408,500,000/$853,100,000 = *0.4788* b. For projects equally as risky as the firm itself, the WACC should be used as the discount rate. First, we can find the cost of equity using the CAPM. The cost of equity is: RS = 0.04 + 1.25(0.083) = 0.04 + 0.10375 = 0.14375 The cost of debt is the YTM of the bonds, so: N = 15 x 2 = 30 I/Y = CPT = 1.8848 PV = 1.14 x 1,000 = -1,140 PMT = (0.05 x 1,000)/2 = 25 FV = 1,000 I/Y = 1.8848 x 2 = 3.7695% And the aftertax cost of debt is: RB = (1 - 0.25)(0.037695) = 0.75(0.037695) = 0.02827 = 2.83% Now, we can calculate the WACC as: WACC = 0.4788(0.14375) + 0.5212(0.02827) = 0.06883 + 0.014725 = 0.08356 = *8.36%*

The book value of an asset is primarily used to compute the: → annual depreciation tax shield. → amount of tax due on the sale of that asset. → amount of tax saved annually due to the depreciation expense. → amount of cash that can be received from the sale of that asset. → change in depreciation needed to reflect the market value of the asset.

amount of tax due on the sale of that asset.

If the option to abandon is ignored, the: → initial cash flow of a project may be overstated. → net present value of a project may be understated. → net present value of a project will be stated at a time other than Time 0. → net present value of a project will be overstated. → initial cash flow of a project will be understated.

net present value of a project may be understated.

The asset beta is defined as the beta of: → a fully diversified portfolio. → an undiversified portfolio. → the common stock of a levered firm. → a risk-free security. → the common stock of an unlevered firm.

the common stock of an unlevered firm.