application for finance

A project has the following cash flows. What is the internal rate of return?

8.57 percent Year 0 -$89,300 Year 1 $32,900 Year 2 $64,200 Year 3 $5,800 NPV = 0 = -$89,300 + $32,900 / (1 + IRR) + $64,200 / (1 + IRR)2 + $5,800 / (1 + IRR)3 IRR = 8.57%

Western Steer purchased some three-year MACRS property three years ago. What is the current book value of this equipment if the original cost was $94,250? The MACRS allowance percentages are as follows, commencing with Year 1: 33.33, 44.45, 14.81, and 7.41 percent.

Book value3 = $94,250 ×(1 - .3333 - .4445 - .1481) = $6,983.93

An investment has an installed cost of $566,382. The cash flows over the four-year life of the investment are projected to be $195,584, $239,318, $187,674, and $155,313. If the discount rate is zero, what is the NPV? If the discount rate is infinite, what is the NPV? At what discount rate is the NPV just equal to zero?

CFo -$566,382 CFo -$566,382 C01 $195,584 C01 $195,584 F01 1 F01 1 C02 $239,318 C02 $239,318 F02 1 F02 1 C03 $187,674 C03 $187,674 F03 1 F03 1 C04 $155,313 C04 $155,313 F04 1 F04 1 I = 0 IRR CPT NPV CPT 14.71% $211,507

Country Cook's cost of equity is 16.2 percent and its aftertax cost of debt is 5.8 percent. What is the firm's weighted average cost of capital if its debt-equity ratio is .42 and the tax rate is 34 percent?

WACC = (1/1.42)(.162) + [(.42 /1.42)(.058)] = .1312, or 13.12 percent

Suppose a stock had an initial price of $121 per share, paid a dividend of $3.30 per share during the year, and had an ending share price of $153. Compute the percentage total return. What was the dividend yield? What was the capital gains yield?

-The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. The return of this stock is: R = [($153 - 121) + 3.30] / $121 R = .2917, or 29.17% -The dividend yield is the dividend divided by the initial price, so: Dividend yield = $3.30 / $121 Dividend yield = .0273, or 2.73% -And the capital gains yield is the increase in price divided by the initial price, so: Capital gains yield = ($153 - 121) / $121 Capital gains yield = .2645, or 26.45%

An engineer is considering upgrading four production-lines. She has determined that upgrading all four lines is economically justifiable and proposes to invest the $64,000 necessary to make these improvements. Her boss declines her request for all of the funds and states she may spend only $40,000 for improvements this year. Given her discount rate of 8%, what is the highest NPV she can obtain from her total investment?

4792.50 As we are interested in creating the highest NPV given our limited funds, we will use PI to rank the projects by the wealth created per dollar invested. Begin by ranking the projects by their PI. While not given the present value of inflows, we know that as NPV = PVInflows - PVOutlflows, the present value of the inflows can be obtained as: PVInflows = NPV + PVOutlflows,. Using this trick we can calculate the PIs. Project PVInflows / PVOutlfows PI Rank A $13,250/$12,000 = 1.10 3 B $16,150/$15,000 = 1.08 4 C $13,640/$12,000 = 1.14 1 D $27,840/$25,000 = 1.11 2 As PI measures the NPV per dollar of investment and is a relative measure of wealth created, we would choose the the highest PI, then next highest, etc. This would result in the engineer fully investing in projects C and D. C + D $12,000 $25,000 = $37,000 This leaves $3,000 remaining for additional investment. $40,000 - $37,000 = $3,000 The engineer would invest this $3,000 in Project A, which would allow her to obtain 25% of A. $3,000/$12,000 = 0.25 or 25%. Investing in all of C and D and 25% of A would use up the total capital budget: $40,000 This would produce a total NPV: $4,792.50 $1,640 + $2,840 + $1,250(0.25) This is the maximum possible NPV for the $40,000 investment. The engineer has done the best she could do

Our engineer is now considering three new production lines. While each of these lines appear to have a positive NPV, their total cost would be $39 million. Her capital budget cannot exceed $30 million. The designs on each line have been optimally engineered, so no further design changes will be possible: these projects are not divisible. Given her discount rate of 8%, what projects should she invest in? Project Initial NPV Investment A $12 $1.250 B $15 $1.150 C $12 $1.640

A and C With a capital budget of $30 million she can't take on all projects. Additionally, each project must be accepted or rejected as a whole, so we cannot take part of a project. The engineer must therefore identify the portfolios of assets that are acceptable. This would produce the following alternatives. Project/Projects Initial NPV Investment A $12 $1.2 B $15 $1.1 C $12 $1.6 A+B $27 $2.3 A+C $24 $2.8 B+C $27 $2.7 A+B+C $39 $3.9 A+B+C is not on the table because it would exceed the capital budget. The optimal choice is A+C, which produces the highest NPV. She could invest more in A+B, but this produces a lower total NPV. The objective is to increase wealth, not spend money!

Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 -$ 421,000 -$ 38,000 1 46,000 20,000 2 60,000 13,700 3 77,000 16,600 4 536,000 13,400 The required return on these investments is 12 percent. a. What is the payback period for each project? b. What is the NPV for each project? c. What is the IRR for each project? d. What is the profitability index for each project? e. Based on your answers in (a) through (d), which project will you finally choose?

CF (A) CFo -$421,000 CFo -$421,000 CFo $0 C01 $46,000 C01 $46,000 C01 $46,000 F01 1 F01 1 F01 1 C02 $60,000 C02 $60,000 C02 $60,000 F02 1 F02 1 F02 1 C03 $77,000 C03 $77,000 C03 $77,000 F03 1 F03 1 F03 1 C04 $536,000 C04 $536,000 C04 $536,000 F04 1 F04 1 F04 1 I = 12 IRR CPT I = 12 NPV CPT 16.69% NPV CPT $63,347.83 $484,347.83 PI = $484,347.83 / $421,000 = 1.150 CF (B) CFo -$38,000 CFo -$38,000 CFo $0 C01 $20,000 C01 $20,000 C01 $20,000 F01 1 F01 1 F01 1 C02 $13,700 C02 $13,700 C02 $13,700 F02 1 F02 1 F02 1 C03 $16,600 C03 $16,600 C03 $16,600 F03 1 F03 1 F03 1 C04 $13,400 C04 $13,400 C04 $13,400 F04 1 F04 1 F04 1 I = 12 IRR CPT I = 12 NPV CPT 26.19% NPV CPT $11,110.19 $49,110.19 PI = $49,110.19 / $38,000 = 1.292 e. Project A

A new project is expected to generate an operating cash flow of $38,728 and will initially free up $11,610 in net working capital. Purchases of fixed assets costing $52,800 will be required to start up the project. What is the total cash flow for this project at Time zero?

CF0 = $11,610 - 52,800 = -$41,190

A firm evaluates all of its projects by applying the IRR rule. Year Cash Flow 0 -$ 146,000 1 70,000 2 69,000 3 53,000 What is the project's IRR?

CFo -$146,000 C01 $70,000 F01 1 C02 $69,000 F02 1 C03 $53,000 F03 1 IRR CPT 15.82%

Consider the following two mutually exclusive projects: Year Cash Flow (X) Cash Flow (Y) 0 −$ 16,100 −$ 16,100 1 6,690 7,250 2 7,270 7,750 3 4,790 3,590 What is the IRR of Project X? What is the IRR of Project Y? What is the crossover rate for these two projects?

CFo -$16,100 CFo -$16,100 C01 $6,690 C01 $7,250 F01 1 F01 1 C02 $7,270 C02 $7,750 F02 1 F02 1 C03 $4,790 C03 $3,590 F03 1 F03 1 CPT IRR CPT IRR 8.47% 8.41% CF (X) CFo -$16,100 CFo -$16,100 C01 $6,690 C01 $6,690 F01 1 F01 1 C02 $7,270 C02 $7,270 F02 1 F02 1 C03 $4,790 C03 $4,790 F03 1 F03 1 I = 0 I = 25 NPV CPT NPV CPT $2,650.00 -$3,642.72 CF (Y) CFo -$16,100 CFo -$16,100 C01 $7,250 C01 $7,250 F01 1 F01 1 C02 $7,750 C02 $7,750 F02 1 F02 1 C03 $3,590 C03 $3,590 F03 1 F03 1 I = 0 I = 25 NPV CPT NPV CPT $2,490.00 -$3,501.92 Crossover rate: CFo $0 C01 -$560 F01 1 C02 -$480 F02 1 C03 $1,200 F03 1 CPT IRR 9.67%

Hercules Movers pays a constant annual dividend of $1.48 per share on its stock. Last year at this time, the market rate of return on this stock was 15.7 percent. Today, the market rate has fallen to 13.3 percent. What would your capital gains yield have been if you had purchased this stock one year ago and then sold the stock today?

Capital gains yield = [($1.48 / .133) -($1.48 / .157)]/($1.48 / .157) = .1805, or 18.05 percent

NB's managers are concerned about their operating leverage. The forecast sales of 3,500 units and would like to know if they will be profitable at this sales level. The initial investment in the manufacturing facilities for the Ab Stretcher is $500,000, depreciated straight-line over the project's five-year economic life to a $0 salvage value. Sales price is $200 per unit and variable cost per unit is $30. Fixed operating costs are $100,000 per year and their tax rate is 20%. What is NB's break-even point?

Depreciation = ($500,000 - $0)/5 = $100,000 Total annual costs: TAC = (Fixed operating costs + Depreciation)(1 - TC) = ($100,000 + $100,000)(1 - .2) = $160,000 Contribution margin: CM = (Sales price - Variable cost per unit)(1 - TC) = ($200 - $30)(1 - .2) = $136 Accounting BE point: B-E = $160,000/$136 = 1,176.47 Ab Stretchers

Consider the following information: State of Economy Probability of State of Economy Rate of Return if State Occurs Recession .22 - .11 Normal .47 .13 Boom .31 .32 Calculate the expected return.

E(R) = .22(-.11) + .47(.13) + .31(.32) E(R) = .1361, or 13.61

The Wilson Bat Company has, at market value, $300,000 in bonds and $700,000 in stock outstanding. The coupon rate on the debt, which is currently selling at par, is 7%. The company's current stock price is $20, with an equity beta of 1.8 and an expected dividend next year of $1.40 which is expected to grow at 6% indefinitely. The company faces a corporate tax rate of 25%. Wilson is considering purchasing Harrison Balls, Inc. As part of its acquisition research, Wilson has determined that the average beta for ball manufacturers is 1.2. The current risk-free rate is 4%, and the current return on the S&P 500 is 8%. Calculate Wilson's WACC. The CFO directs that in calculating this WACC you are to calculate the equity return using the CAPM.

Equity return using CAPM: .04 + 1.8(.08 - .04) = .1120 The WACC is: $300,000/$1,000,000(.07)(1 - .25) + $700,000/$1,000,000(.1120) = .0942

The Oceanside Marina is considering the purchase of an excursion boat. Model SL would require an initial investment of $2.2 million and produce annual after-tax cash inflows of $1.2 million for each of three years. Model LL would require an initial investment of $5.5 million and produce annual after-tax cash inflows of $1.3 million for each of 7 years. Oceanside's discount rate is 8%. Which model should be chosen?

First step: find the NPV of each project NPVSL = -$2,200,000 + $1,200,000(PVFA.08, 3) = $892,516 NPVLL = -$5,500,000 + $1,300,000(PVFA.08, 7) = $1,268,281 Second step: find the EAS of each project NPVSL = EASSL(PVFA.08, 3) $892,516 = EASSL(2.5771) gives EASSL = $892,516/2.5771 = $346,326 NPVLL = EASLL(PVFA.08, 7) $1,268,281 = EASLL(5.2064) gives EASSL = $1,268,281/5.2064 = $243,600 Model SL has the highest EAS and should be selected.

H. Cochran, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of $2,550,000. The fixed asset falls into the three-year MACRS class (MACRS Table). The project is estimated to generate $2,300,000 in annual sales, with costs of $1,290,000. The project requires an initial investment in net working capital of $165,000, and the fixed asset will have a market value of $190,000 at the end of the project. Assume that the tax rate is 35 percent and the required return on the project is 7 percent. What is the net cash flow of the project each year? What is the NPV of the project?

First, we will calculate the annual depreciation for the equipment necessary for the project. The depreciation amount each year will be: Year 1 depreciation = $2,550,000(.3333) = $849,915 Year 2 depreciation = $2,550,000(.4445) = $1,133,475 Year 3 depreciation = $2,550,000(.1481) = $377,655 So, the book value of the equipment at the end of three years, which will be the initial investment minus the accumulated depreciation, is: Book value in 3 years = $2,550,000 - ($849,915 + 1,133,475 + 377,655) Book value in 3 years = $188,955 The asset is sold at a gain to book value, so this gain is taxable. Aftertax salvage value = $190,000 + ($188,955 - 190,000)(.35) Aftertax salvage value = $189,634.25 To calculate the OCF, we will use the tax shield approach, so the cash flow each year is: OCF = (Sales - Costs)(1 - TC) + Depreciation(TC) Year Cash Flow 0 -$2,715,000.00 = -$2,550,000 - 165,000 1 953,970.25 = ($1,010,000)(.65) + .35($849,915) 2 1,053,216.25 = ($1,010,000)(.65) + .35($1,133,475) 3 1,143,313.50 = ($1,010,000)(.65) + .35($377,655) + $189,634.25 + 165,000 Remember to include the NWC cost in Year 0, and the recovery of the NWC at the end of the project. The NPV of the project with these assumptions is: NPV = -$2,715,000 + ($953,970.25 / 1.07) + ($1,053,216.25 / 1.072) + ($1,143,313.50 / 1.073) NPV = $29,765.23

A stock has an expected return of 13.5 percent and a beta of 1.16, and the expected return on the market is 12.5 percent. What must the risk-free rate be?

Here, we need to find the risk-free rate, using the CAPM. Substituting the values given, and solving for the risk-free rate, we find: E(Ri) = Rf + [E(RM) - Rf] × βi .135 = Rf + (.125 - Rf)(1.16) .135 = Rf + .1450 - 1.16Rf Rf = .0625, or 6.25%

Please use this information on the following four questions. You are given the following transactions (in billions): •Intel (a US company) receives $4 in royalty payments from a Korean firm. •The US Federal Reserve sells $10 and purchases euros •US bondholders pay $12 in interest to Japanese investors •US imports $10 in consumer electronics •German investors buy $5 in Dell stock •US exports $8 in lumber •Indian investors buy $16 in US T-Bills Assume that these transactions are the only ones that occur during the reporting period. That is, do not worry about the offsetting credit/debit that would usually occur. Using these transactions, answer the following questions. Please enter only the numbers and do not enter a dollar sign. You should signify whether they are surpluses by using a "+' sign and deficits by entering a "-" sign. 1. What is the balance on current account?

In looking at the current account we must identify those transactions that cause an increase in the demand ofr US dollars in the foreign exchange market and those transactions that increase the supply of US dollars to the foreign exchange market. In this prolem there are three transactions that result in a demand for US dollars and two that produce a supply of US dollars. Credits Debits $4 Intel royalty payment $12 US pays interest $8 US exports of lumber $10 US electronics imports Given this information there is more supply than demand for the dollar, and we would see a $10 deficit. Credits - debits = $12 - $22 = $10 deficit in the current account

2. What is the balance on capital account?

In the capital account we see only two transactions. Both of these transactions require investors to obtain (demand) dollars to make investments, so we have a $21 surplus. Credits Debits $5 German investment in Dell $16 Indian investors buy T-Bill Credits - debits = $21 - $0 = $21 surplus in the capital account

There are three parts to this problem. This is part 3. Natural Bodyworks produces the popular Ab Stretcher that they sell for $200 per unit. NB's total fixed costs (fixed operating costs + depreciation) for the Ab Stretcher are $200,000.Their variable costs are $30 per unit. They are financed entirely by equity and face a 20% corporate tax rate. Did NB's NOI go up or down?

NOI went up. At a production level of 4,000 units, the NOI per unit is $480,000/4,000 = $120 At a production level of 5,000 units, the NOI per unit is $650,000/5,000 = $130 So, the NOI per unit increased by $130 - $120 = $10. This increase profit occurred because the fixed costs are fixed. If sales and production go up, the fixed cost per unit goes down. At a production of 40,000 units the fixed cost per unit is $200,000/4,000 = $50 If sales increase to 50,000 NB's the fixed cost per unit declines to: $200,000/5,000 = $40. With the operating leverage created by NB's use of fixed costs, the fixed cost per unit declines by $50 - $40 = -$10. This cost reduction nicely increases operating profit! On your own, show that if sales decline to 3,000 units, fixed costs per unit will increase, thus lowering operating profit.

Molly is considering a project with cash inflows of $811, $924, $638, and $510 over the next four years, respectively. The relevant discount rate is 11.2 percent. What is the net present value of this project if it the start-up cost is $2,700?

NPV = -$2,700 + $811 / 1.112 + $924 / 1.1122 + $638 / 1.1123 + $510 / 1.1124 NPV = -$425.91

What is the net present value of a project that has an initial cost of $42,700 and produces cash inflows of $9,250 a year for 9 years if the discount rate is 14.65 percent?

NPV = -$42,700 + $9,250 ×{1 - [1 / (1 + .1465)9]} / .1465 NPV = $1,992.43

A nine-year project is expected to generate annual revenues of $137,800, variable costs of $82,600, and fixed costs of $11,000. The annual depreciation is $23,500 and the tax rate is 34 percent. What is the annual operating cash flow?

Operating cash flow = ($137,800 -82,600 -11,000) ×(1 -.34) + ($23,500 ×.34) = $37,162

The Management of Premium Manufacturing Company is evaluating two forklift systems to use in its plant that produces the towers for a windmill power farm. The costs and the cash flows from these systems are shown below. If the company uses a 12 percent discount rate for all projects, determine which forklift system should be purchased using the net present value (NPV) approach.

Otis Forklifts NPV for Otis Forklifts: NPV = PVinflows - PVoutflows $337,075 = $979,225/(1.12) + $1,358,886/(1.12)^2 + $2,111,497/(1.12)^3 - $3,123,450 NPV for Craigmore Forklifts: $90,606 = $875/236/(1.12) + $1,765,225/(1.12)^2 + $2,865,110/(1.12)^3 - $4,137,410 As these are mutually-exclusive projects, Premium should purchase Otis forklift since it has a larger NPV.

Piedmont Hotels is an all-equity firm with 48,000 shares of stock outstanding. The stock has a beta of 1.19 and a standard deviation of 14.8 percent. The market risk premium is 7.8 percent and the risk-free rate of return is 4.1 percent. The company is considering a project that it considers riskier than its current operations so has assigned an adjustment of 1.35 percent to the project's discount rate. What should the firm set as the required rate of return for the project?

Project cost of capital = .041 + 1.19(.078) + .0135 = .1473, or 14.73 percent

Trendsetters has a cost of equity of 14.6 percent. The market risk premium is 8.4 percent and the risk-free rate is 3.9 percent. The company is acquiring a competitor, which will increase the company's beta to 1.4. What effect, if any, will the acquisition have on the firm's cost of equity capital?

RE= .039 + 1.4(.084) = .1566, or 15.66 percent Increase in cost of equity = 15.66 percent -14.6 percent = 1.06 percent

Assume that last year, Isaac earned 13.6 percent on his investments while U.S. Treasury bills yielded 2.7 percent, and the inflation rate was 2.2 percent. What real rate of return did he earn on his investments last year?

Real return = (1.136/1.022) - 1 = .1115, or 11.15 percent

There are three parts to this question. This is part 2. Natural Bodyworks produces the popular Ab Stretcher that they sell for $200 per unit. NB's total fixed costs (fixed operating costs + depreciation) for the Ab Stretcher are $200,000.Their variable costs are $30 per unit. They are financed entirely by equity and face a 20% corporate tax rate. If sales surge to 5,000 units, what is NB's new NOI?

Sales $1,000,000 $200 x 5,000 units VC $150,000 $30 x 5,000 units FC $200,000 NOI $650,000

There are three parts to this question. This is part 1. Natural Bodyworks produces the popular Ab Stretcher that they sell for $200 per unit. NB's total fixed costs (fixed operating costs + depreciation) for the Ab Stretcher are $200,000.Their variable costs are $30 per unit. They are financed entirely by equity and face a 20% corporate tax rate. Given their current production level of 4,000 units what is their Net Operating Income?

Sales $800,000 $200 x 4,000 units VC $120,000 $30 x 4,000 units FC $200,000 NOI $480,000

Green Woods sells specialty equipment for mountain climbers. Its sales for last year included $387,000 of tents and $718,000 of climbing gear. For next year, management has decided to sell specialty sleeping bags also. As a result of this change, sales projections for next year are $411,000 of tents, $806,000 of climbing gear, and $128,000 of sleeping bags. How much of next year's sales are derived from the side effects of adding the new product to its sales offerings?

Side effects = ($411,000 + 806,000) - ($387,000 + 718,000) = $112,000

Mittuch Corp. is evaluating a project with the following cash flows: Year Cash Flow 0 -$ 15,900 1 7,000 2 8,200 3 7,800 4 6,600 5 -4,000 The company uses an interest rate of 8 percent on all of its projects. Calculate the MIRR of the project using all three methods.

The MIRR for the project with all three approaches is: Discounting approach: In the discounting approach, we find the value of all cash outflows at Time 0, while any cash inflows remain at the time at which they occur. So, discounting the cash outflows at Time 0, we find: Time 0 cash flow = -$15,900 - $4,000 / 1.085 Time 0 cash flow = -$18,622.33 So, the MIRR using the discounting approach is: 0 = -$18,622.33 + $7,000 / (1 + MIRR) + $8,200 / (1 + MIRR)2 + $7,800 / (1 + MIRR)3 + $6,600 / (1 + MIRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: MIRR = 21.71% Reinvestment approach: In the reinvestment approach, we find the future value of all cash, except the initial cash flow, at the end of the project. So, reinvesting the cash flows to Time 5, we find: Time 5 cash flow = $7,000(1.084) + $8,200(1.083) + $7,800(1.082) + $6,600(1.08) - $4,000 Time 5 cash flow = $32,078.98 So, the MIRR using the reinvestment approach is: 0 = -$15,900 + $32,078.98 / (1 + MIRR)5 $32,078.98 / $15,900 = (1 + MIRR)5 MIRR = ($32,078.98 / $15,900)1/5 - 1 MIRR = .1507, or 15.07% Combination approach: In the combination approach, we find the value of all cash outflows at Time 0, and the value of all cash inflows at the end of the project. So, the value of the cash flows is: Time 0 cash flow = -$15,900 - $4,000 / 1.085 Time 0 cash flow = -$18,622.33 Time 5 cash flow = $7,000(1.084) + $8,200(1.083) + $7,800(1.082) + $6,600(1.08) Time 5 cash flow = $36,078.98 So, the MIRR using the discounting approach is: 0 = -$18,622.33 + $36,078.98 / (1 + MIRR)5 $36,078.98 / $18,622.33 = (1 + MIRR)5 MIRR = ($36,078.98 / $18,622.33)1/5 - 1 MIRR = .1414, or 14.14%

Sprigg Lane Manufacturing, Inc., needs to purchase a new central air-conditioning system for a plant. There are two choices. The first system costs $50,000 and is expected to last 10 years, and the second system costs $72,000 and is expected to last 15 years. Assume that the opportunity cost of capital is 10 percent. Which air-conditioning system should Sprigg Lane purchase?

The equivalent annual cost for each system is: EAC1 = (0.1)($50,000)[(1.1)10/{(1.1)10/[(1.1)10 - 1}] = 8,137.27 EAC2 = (0.1)($72,000)[(1.1)15/{(1.1)15/[(1.1)15 - 1}] = 9,466.11 Sprigg Lane should purchase the first one.

ICU Window, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with nine years to maturity that is quoted at 109 percent of face value. The issue makes semiannual payments and has an embedded cost of 7.8 percent annually. What is the company's pretax cost of debt? If the tax rate is 35 percent, what is the aftertax cost of debt?

The pretax cost of debt is the YTM of the company's bonds, so: P0 = $1,090 = $39(PVIFAR%,18) + $1,000(PVIFR%,18) R = 3.233% YTM = 2 × 3.233% YTM = 6.47% And the aftertax cost of debt is: RD = .0647(1 - .35) RD = .0420, or 4.20%

Six years ago, China Exporters paid cash for a new packaging machine that cost $347,000. Three years ago, the firm spent $14,300 on repairs and modifications to the machine. The machine is now fully depreciated and has just sat idly in a back corner of the shop for the past seven months. The estimated value of the machine today is $157,500. The firm is considering using this machine in a new project. If it does so, what value should be assigned to this machine and included in the initial costs of the new project?

The relevant cost is the opportunity cost of $157,500.

One year ago, you purchased a 6 percent coupon bond with a face value of $1,000 when it was selling for 98.6 percent of par. Today, you sold this bond for 101.2 percent of par. What is your total dollar return on this investment?

Total dollar return = (1.012 ×$1,000) - (.986 ×$1,000) + (.06 ×$1,000) = $86

If Wilson can expect a return of 9% on its investment in Harrison, should they complete the purchase?

Using the CAPM, we get a proper opportunity cost for the acquisition: .04 + 1.2(.08 - .04) = .0880 As the investment earns 9%, and the opportunity cost is 8.8%, this is an acceptable project. Because the risk of Wilson's existing operations differs from that of Harrison, the WACC is not an appropriate rate to use.

You own a portfolio of two stocks, A and B. Stock A is valued at $84,650 and has an expected return of 10.6 percent. Stock B has an expected return of 6.4 percent. What is the expected return on the portfolio if the portfolio value is $97,500?

ValueB = $97,500-84,650 = $12,850 Expected return = [($84,650/$97,500) × .106] + [($12,850/$97,500) × .064] = .1005 or 10.05 percent

The Five and Dime Store has a cost of equity of 14.8 percent, a pretax cost of debt of 6.7 percent, and a tax rate of 34 percent. What is the firm's weighted average cost of capital if the debt-equity ratio is .46?

WACC = (1/1.46)(.148) + (.46/1.46)(.067)(1 -.34) = .1153, or 11.53 percent

We are evaluating a project that costs $1,398,000, has a six-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 87,800 units per year. Price per unit is $34.65, variable cost per unit is $20.90, and fixed costs are $758,000 per year. The tax rate is 40 percent, and we require a return of 11 percent on this project. Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±10 percent. Calculate the best-case and worst-case NPV figures

We will use the tax shield approach to calculate the OCF for the best- and worst-case scenarios. For the best-case scenario, the price and quantity increase by 10 percent, so we will multiply the base case numbers by 1.1, a 10 percent increase. The variable and fixed costs both decrease by 10 percent, so we will multiply the base case numbers by .9, a 10 percent decrease. Doing so, we get: OCFbest = {[$34.65(1.1) - $20.90(.9)](87,800)(1.1) - $758,000(.9)}(.60) + .40($1,398,000 / 6) OCFbest = $802,566.14 The best-case NPV is: NPVbest = -$1,398,000 + $802,566.14(PVIFA11%,6) NPVbest = $1,997,286.44 For the worst-case scenario, the price and quantity decrease by 10 percent, so we will multiply the base case numbers by .9, a 10 percent decrease. The variable and fixed costs both increase by 10 percent, so we will multiply the base case numbers by 1.1, a 10 percent increase. Doing so, we get: OCFworst = {[$34.65(.9) - $20.90(1.1)](87,800)(.9) - $758,000(1.1)}(.60) + .40($1,398,000 / 6) OCFworst = -$18,538.66 The worst-case NPV is: NPVworst = -$1,398,000 - $18,538.66(PVIFA11%,6) NPVworst = -$1,476,428.50

What is the net present value of a project with the following cash flows if the discount rate is 13.6 percent?

Year 0 -$63,600 Year 1 $18,200 Year 2 $34,500 Year 3 $35,900 NPV = -$63,600 + $18,200 / 1.136 + $34,500 / 1.1362 + $35,900 / 1.1363 NPV = $3,643.38

A project has the following cash flows. What is the internal rate of return?

Year 0 -$68,700 Year 1 $19,600 Year 2 $22,300 Year 3 $27,500 Year 4 $15,300 NPV = 0 = -$68,700 + $19,600 / (1 + IRR) + $22,300 / (1 + IRR)2 + $27,500 / (1 + IRR)3 + $15,300 / (1 + IRR)4 IRR = 9.08 percent

Managers project sales of 3,500 units. Given your calculation of the break-even point in question 4, would you advise NB's to go ahead with the Ab Stretcher?

Yes, they should produce the Ab Stretcher. They project sales of 3,500 units, but would be profitable even if sales are disappointing, as they need sell only $1,177 units to have a positive Net Income.

Jiminy's Cricket Farm issued a 30-year, 8 percent semiannual bond 7 years ago. The bond currently sells for 91.5 percent of its face value. The company's tax rate is 35 percent. a. What is the pretax cost of debt? b. What is the aftertax cost of debt? c. Which is more relevant, the pretax or the aftertax cost of debt?

a. The pretax cost of debt is the YTM of the company's bonds, so: P0 = $915 = $40(PVIFAR%,46) + $1,000(PVIFR%,46) R = 4.436% YTM = 2 × 4.436% YTM = 8.87% b. The aftertax cost of debt is: RD = .0887(1 - .35) RD = .0577, or 5.77% c. The aftertax rate is more relevant because that is the actual cost to the company.