finance exam 2
74. What is the current market value of a bond that was issued 5 years ago if it had a maturity of 30 years on the issue date? The annual coupon rate is 18% with coupons paid semi-annually. Assume the bond has a $1,000 face value and a 14% per year yield to maturity (yield to maturity is expressed as an APR with semi-annual compounding). A) $734.86 B) $942.26 C) $1,135.90 D) $1,276.01 E) $1,545.62
D) $1,276.01 FV = 1,000; I/YR = 14/2 =7; PMT = 180/2 = 90; N = 25*2 =50; PV = ?
94. Luther Industries has a dividend yield of 4.5% and a cost of equity capital of 12%. Luther Industries' dividends are expected to grow at a constant rate indefinitely. The grow rate of Luther's dividends are closest to:
From the constant growth dividend model (Gordon Model): P0 = Div1/(rE - g), it follows that rE = Div1 / P0 + g 0.12 = 0.045 + g, so g = 0.075
93. NoGrowth Industries presently pays an annual dividend of $1.50 per share and it is expected that these dividend payments will continue indefinitely. If NoGrowth's equity cost of capital is 12%, what is the value of a share of NoGrowth's stock?
P0 = Div1 / (rE - g) = $1.50/(0.12 - 0) = $12.50
81. Solaris Energy Inc. has a new issue of preferred stock. The stock will pay a constant dividend of $10 per year, but the first dividend payment will be made 3 years from now. If you require a 10% return on this preferred stock, how much would you pay at most today?
Two years from today, the stock would be valued at (using Gordon's model) P2 = Div3/(r-g) = $10/(0.10 - 0) = $100 Thus, today, the stock price would be valued at P0 = $100/(1.10^2) = $82.64.
96. You expect KT industries (KTI) will have earnings per share of $3 at the end of this year and expect that they will pay out $1.50 of these earnings to shareholders in the form of a dividend. KTI's return on new investments is 15% and their equity cost of capital is 12%. a) What is the expected growth rate for KTI's dividends? b) What is the value of a share of KTI's stock?
a) What is the expected growth rate for KTI's dividends? g = retention rate × return on new investment g = ((3.00 - 1.50)/3.00) × 0.15 = 0.075 or 7.5% b) What is the value of a share of KTI's stock? P0 = Div1 / (rE - g) = 1.50/(0.12 - 0.075) = 33.33
7. Clarissa wants to fund a growing perpetuity that will pay $5000 per year to a local museum, starting next year. She wants the annual amount paid to the museum to grow by 5% per year. Given that the interest rate is 8%, how much does she need to fund this growing perpetuity?
𝑷𝑽 𝒐𝒇 𝒈𝒓𝒐𝒘𝒊𝒏𝒈 𝒑𝒆𝒓𝒑𝒆𝒕𝒖𝒊𝒕𝒚 = 𝟓𝟎𝟎𝟎 / (𝟎. 𝟎𝟖 − 𝟎. 𝟎𝟓) = $𝟏𝟔𝟔,𝟔𝟔𝟔.𝟔𝟕
125. CathFoods will release a new range of candies which contain anti-oxidants. New equipment to manufacture the candy will cost $2 million, which will be depreciated by straight-line depreciation over five years. It is expected that the range of candies will bring in revenues of $4 million per year for five years with production and support costs of $1.5 million per year. If CathFood's marginal tax rate is 35%, what are the incremental earnings in the second year of this project? A) $1.365 million B) $1.500 million C) $1.753 million D) $2.100 million
A) $1.365 million Depreciation = $2/5 = $0.4; Incremental EBIT = $4 - $1.5 - $0.4 = $2.1; Incremental Earnings after tax = $2.1 x 0.65 = $1.365 million
130. CathFoods will release a new range of candies which contain antioxidants. New equipment to manufacture the candy will cost $2 million, which will be depreciated by straight-line depreciation over five years. In addition, there will be $5 million spent on promoting the new candy line. It is expected that the range of candies will bring in revenues of $4 million per year for five years with production and support costs of $1.5 million per year. If CathFood's marginal tax rate is 35%, what are the incremental free cash flows in the second year of this project? A) $1.765 million B) $2.015 million C) $2.415 million D) $2.500 million
A) $1.765 million Depreciation = 2/5 = 0.4; Incremental EBIT = 4 - 1.5 - 0.4 = 2.1; Incremental Earnings after tax = 2.1 x 0.65 = 1.365; Add back depreciation = 1.365 + 0.4 = $1.765 million.
173. Your income statement shows sales of $1,000,000, cost of goods sold as $500,000, depreciation expense of $100,000 and a tax rate of 40%. What are the free cash flows generated this period? A) $340,000 B) $380,000 C) $400,000 D) $420,000
A) $340,000 (1,000,000 - 500,000 - 100,000)*(1 - 0.40) + 100,000 = 340,000
105. What is the value of a preferred stock that pays a constant and pre-determined dividend of $3.50 at the end of each year forever and has a required rate of return of 10% per year? (Round your answer to the nearest $1.) A) $35 B) $28 C) $24 D) $19
A) $35 𝑷𝟎 = 𝑫𝒊𝒗𝟏/(rE-g) = $𝟑.𝟓𝟎/(.10-0) =$𝟑𝟓
119. An auto-parts company is deciding whether to sponsor a racing team for a cost of $1 million. The sponsorship would last for three years and is expected to increase cash flows by $580,000 per year. If the discount rate is 7.5%, what will be the change in the value of the company if it chooses to go ahead with the sponsorship? A) $508,305 B) $740,000 C) $808,786 D) $863,000
A) $508,305 Financial Calculator Solution: CF0 = -1,000,000; CF1 = 580,000; CF2 = 580,000; CF3 = 580,000; I/YR = 7.5; Compute NPV = 508,305.
133. Your firm is considering building a new office complex. Your firm already owns land suitable for the new complex. The current book value of the land is $100,000; however, a commercial real estate agent has informed you that an outside buyer is interested in purchasing this land and would be willing to pay $650,000 for it. When calculating the net present value (NPV) of your new office complex, ignoring taxes, the appropriate incremental cash flow for the use of this land is: A) $650,000 B) $0 C) $100,000 D) $750,000
A) $650,000 The opportunity cost of using the land is equal to its market value.
100. Suppose a stock X has a required return of 15% per period. The stock's price is expected to increase to $75 per share by t=1 and it will pay a dividend of $8 on t=1. Compute the price of this stock at t=0. A) $72.17 B) $73.59 C) $74.34 D) $75.28
A) $72.17 𝑷𝟎 =𝑫𝒊𝒗𝟏 +𝑷𝟏/(rE-g) =($𝟖 + $𝟕𝟓)/𝟏.𝟏𝟓 = $𝟕𝟐.𝟏𝟕
104. Systems Inc. stock is currently selling for $66.67. The dividend one year from today is expected to be $6.00 and is expected to grow forever at 3%. The required rate on Systems' stock is 12%. Calculate the price of the stock after 3 years (at time 3)? Hint: recall the example in class where the capital gains yield of a stock with constant growth was equal to the growth rate in dividends. A) 72.85 B) 64.63 C) 56.90 D) 44.56
A) 72.85 In the constant dividend growth model: 𝑷𝒕 =𝑷𝟎 ×(𝟏+𝒈)^𝒕 =$𝟔𝟔.𝟔𝟕×𝟏.𝟎𝟑^𝟑 =$𝟕𝟐.𝟖𝟓
112. Which of the following best describes the Net Present Value rule? A) Take any investment opportunity where the net present value (NPV) is not negative; turn down any opportunity when it is negative. B) Take any investment opportunity where the net present value (NPV) exceeds the opportunity cost of capital; turn down any opportunity where the cost of capital exceeds the net present value (NPV) C) When choosing among any list of investment opportunities where resources are limited, always choose those projects with the highest net present value (NPV). D) If the payback period of the project is below a cut-off value, accept it. Otherwise, reject it.
A) Take any investment opportunity where the net present value (NPV) is not negative; turn down any opportunity when it is negative.
144. Which of the following statements is FALSE? A) To estimate a firm's enterprise value, we compute the present value (PV) of the free cash flows (FCF) that the firm has available to pay equity holders. B) The net present value (NPV) of any individual project represents its contribution to the firm's enterprise value. C) When using the total payout model, we discount total dividends and share repurchases, and use the growth rate in earnings when forecasting the growth of the firm's payout. D) In the total payout model, we first value the firm's equity, rather than just a single share
A) To estimate a firm's enterprise value, we compute the present value (PV) of the free cash flows (FCF) that the firm has available to pay equity holders. Explanation: FCF is available to pay both debt and equity holders.
181. When different investment rules give conflicting answers, then decisions should be based on the Net Present Value rule, as it is the most reliable and accurate decision rule. A) True B) False
A) True
188. To attract capital from outside investors, a firm must offer potential investors an expected return that is commensurate with the level of risk that they can bear. A) True B) False
A) True
191. The cash flow from a change in Net Working Capital is always equal in size and opposite in sign to the changes in Net Working Capital. A) True B) False
A) True
142. If you want to value the equity of a firm but do not want to explicitly forecast its dividends, share repurchases, or its use of debt, what is the simplest model for you to use? A) the discounted free cash flow model B) the dividend-discount model C) the enterprise value model D) the total payout model
A) the discounted free cash flow model
165. A firm is considering a new project that will generate cash revenue of $1,000,000 and cash expenses of $700,000 per year for five years. The equipment necessary for the project will cost $200,000 and will be depreciated straight line over four years. What is the expected free cash flow in the second year of the project if the firm's marginal tax rate is 35%?
Annual depreciation = $200,000/4 = $50,000. Free Cash Flow = ($1,000,000 - $700,000 - $50,000) × (1 - 0.35) + $50,000 = $212,500
164. A firm is considering investing in a new machine that will cost $600,000 and will be depreciated straight-line over five years. If the firm's marginal tax rate is 39%, what is the annual depreciation tax shield of purchasing the machine?
Annual depreciation expense = $600,000/5 = $120,000, Tax shield = $120,000 × 0.39 = $46,800
135. The Sisyphean Company is considering a new project that will have an annual depreciation expense of $2.5 million. If Sisyphean's marginal corporate tax rate is 40%, then what is the value of the depreciation tax shield on the company's new project?Hint: Depreciation tax shield: the amount of tax savings due to the depreciation expense of the project. A) $750,000 B) $1,000,000 C) $1,500,000 D) $1,750,000
B) $1,000,000 Depreciation tax shield = $2,500,000 × 0.40 = $1 million The depreciation expense of the project reduces the pre-tax income of the firm by $2,500,000. Therefore, the firm will pay $1,000,000 less in income taxes if it adopts this new project.
162. The Sisyphean Company is considering a new project that will have an annual depreciation expense of $2.5 million. If Sisyphean's marginal corporate tax rate is 40%, then what is the value of the depreciation tax shield on the company's new project? A) $750,000 B) $1,000,000 C) $1,500,000 D) $1,750,000
B) $1,000,000 Explanation: depreciation tax shield = $2,500,000 × 0.40 = $1 million
124. Cameron Industries is purchasing a new chemical vapor depositor in order to make silicon chips. It will cost $6 million to buy the machine and $10,000 to have it delivered and installed. Building a clean room in the plant for the machine will cost an additional $3 million. The machine is expected to have a working life of six years. If straight-line depreciation is used, what are the yearly depreciation expenses in this case? A) $1,000,000 B) $1,001,667 C) $1,500,000 D) $1,501,667
B) $1,001,667 Annual depreciation = (6,000,000 + 10,000) / 6 = 1,001,667
101. What is the price of a stock that just paid a dividend of $2 today (note this is D0) and has a required return of 10% per year? The dividends are expected to increase at an average rate of 4% per year from today. Hint: First compute dividend at t=1 before computing the price of the stock. A) $22.7 B) $34.7 C) $40.5 D) $41.6
B) $34.7 𝑷𝟎 = 𝑫𝒊𝒗𝟏/(rE-g) = ($𝟐×𝟏.𝟎𝟒)/(.10-.04) =$𝟑𝟒.𝟔𝟕
103. Shares of Books Inc. expect to pay annual dividends of $1.5 at t = 1, $2.5 at t = 2 and $4 at t = 5 (there are no dividends at time 3 and 4). After this period Books Inc. dividends will grow at 5% per year. The required rate of return on the stock of Books Inc. is 12% per year. Calculate the price of Books Inc. today. A) $36.3 B) $39.7 C) $41.4 D) $52.5
B) $39.7 first, P5 = Div6/(rE-g) = (4*1.05)/(.12-.05) = 60 then, cash flow c0=0; c1=1.50; c2=2.50; c3=0; c4=0; c5=4+60(64); I/YR=12; NPV=39.65
175. Books Inc. purchases a new machine for $100,000 that is to be depreciated on a straight line basis over 10 years. After 5 years, Books Inc. sells the machine for $90,000. If the capital gains tax rate is 40%, what is the cash inflow from this sale? A) $72,000 B) $74,000 C) $80,000 D) $70,000
B) $74,000 Depreciation per year = $100,000/10 = $10,000 Accumulated Depreciation after 5 years = 5*$10,000 = $50,000 Book value of the machine after 5 years = $100,000 - $50,000 = $50,000 Capital gain on sale = $90,000 - $50,000 = $40,000 Tax = 0.40*$40,000 = $16,000 Cash inflows from sale = $90,000 - $16,000 = $74,000
107. Which of the following statements is FALSE? A) The total payout model allows us to ignore the firm's choice between dividends and share repurchases. B) By repurchasing shares, the firm increases its share count, which decreases its earnings and dividends on a per-share basis. C) The total payout model discounts the total payouts that the firm makes to shareholders, which is the total amount spent on both dividends and share repurchases. D) In the dividend-discount model we implicitly assume that any cash paid out to the shareholders takes the form of a dividend.
B) By repurchasing shares, the firm increases its share count, which decreases its earnings and dividends on a per-share basis. Explanation: By repurchasing shares, the firm decreases its share count, which increases its earnings and dividends on a per-share basis.
129. Which of the following formulas will correctly calculate Net Working Capital? A) Cash + Inventory + Receivables + Payables B) Cash + Inventory + Receivables - Payables C) Cash + Inventory - Receivables + Payables D) Cash - Inventory + Receivables + Payables
B) Cash + Inventory + Receivables - Payables
145. Which of the following statements is FALSE? A) The more cash the firm uses to repurchase shares, the less it has available to pay dividends. B) Free cash flow measures the cash generated by the firm after payments to debt or equity holders are considered. C) We estimate a firm's current enterprise value by computing the present value (PV) of the firm's free cash flow. D) We can interpret the enterprise value as the net cost of acquiring the firm's equity, taking its cash, and paying off all debts.
B) Free cash flow measures the cash generated by the firm after payments to debt or equity holders are considered. Explanation: FCF is cash generated by the firm before payments to debt and equity holders, not after.
114. Which of the following is NOT a limitation of the payback period rule? A) It does not account for time value of money. B) It is difficult to calculate. C) It ignores cash flows after payback. D) The cut-off payback period is determined arbitrarily.
B) It is difficult to calculate.
186. Which of the following would you NOT consider when making a capital budgeting decision? A) The additional taxes a firm would have to pay in the next year B) The cost of marketing study completed last year C) The change in direct labor expense due to the purchase of a new machine D) The opportunity to lease out a warehouse instead of using it to house a new production line
B) The cost of marketing study completed last year Sunk costs are not incremental.
143. Which of the following statements is FALSE? A) In a share repurchase, the firm uses excess cash to buy back its own stock. B) The discounted free cash flow model begins by determining the value of the firm's equity. C) The discounted free cash flow model focuses on the cash flows to all of the firm's investors, both debt and equity holders, and allows us to avoid estimating the impact of the firm's borrowing decisions on earnings. D) In recent years, an increasing number of firms have replaced dividend payouts with share repurchases.
B) The discounted free cash flow model begins by determining the value of the firm's equity. Explanation: The discounted free cash flow model begins by determining the value of the entire firm (the enterprise value) first. Only in the second step, it subtracts the value of the firm's net debt from the enterprise value of the firm to finally find the value of the firm's equity.
126. Which of the following costs would you consider when making a capital budgeting decision? A) sunk cost B) opportunity cost C) interest expense D) fixed overhead cost
B) opportunity cost Note that sunk costs have been incurred in the past. They are not incremental. Interest expenses are a result of financial policy decisions, and they are ignored when making investment decisions. Fixed overhead costs of a firm are incurred no matter whether a new project is accepted or not. Therefore, they are not incremental. Opportunity costs are incremental. They are incurred when you accept a new project. Therefore, they must be considered when making a capital budgeting decision as to invest in a new project (or not).
122. Which of the following best defines incremental earnings? A) cash flows arising from a particular investment decision B) the amount by which a firm's earnings are expected to change as the result of an investment decision C) the earnings arising from all projects that a company plans to undertake in a fixed timespan D) the net present value (NPV) of earnings that a firm is expected to receive as the result of an investment decision
B) the amount by which a firm's earnings are expected to change as the result of an investment decision
182. The Sisyphean Company is planning on investing in a new project. This will involve an initial investment of $200,000. The Sisyphean Company expects cash inflows from this project as detailed below: Year1 Year2 Year3 Year4 $86,200 $86,200 $86,200 $86,200 The appropriate discount rate for this project is 20%. The internal rate of return (IRR) for this project is closest to: A) 20% B) 16% C) 26% D) 30%
C) 26%
128. Cameron Industries is purchasing a new chemical vapor depositor in order to make silicon chips. It will cost $6 million to buy the machine and $10,000 to have it delivered and installed. Building a clean room in the plant for the machine will cost an additional $3 million. The machine is expected to raise gross profits by $4 million per year, starting at the end of the first year, with associated costs of $1 million for each of those years. The machine is expected to have a working life of six years and will be depreciated over those six years. The marginal tax rate is 40%. What are the incremental free cash flows associated with the new machine in year 2? A) $1,001,667 B) $1,298,917 C) $2,200,667 D) $3,247,834
C) $2,200,667 Depreciation = (6,000,000 + 10,000) / 6 = 1,001,667; EBIT in year 2 = 4,000,000 - 1,000,000 - 1,001,667 = 1,998,333; Incremental Earnings = 1,998,333 x (0.6) = 1,199,000; Add back depreciation to incremental earnings to get $2,200,667.
99. Sunnyfax Publishing pays out all its earnings and has a share price of $37. In order to expand, Sunnyfax Publishing decides to cut its dividend from $3.00 to $2.00 per share and reinvest the retained funds. The return on reinvested funds is expected to be 13%. If the reinvestment does not affect Sunnyfax's equity cost of capital, what is the expected share price as a consequence of this decision? A) $36.67 B) $41.90 C) $52.38 D) $62.86
C) $52.38 check solutions sheet
111. What is the price of a stock that will pay a dividend of $3 in one year and has a required return of 9% per year? The dividends are expected to increase at an average rate of 4% per year from one year onwards. A) $52 B) $53 C) $60 D) $61
C) $60 𝑷𝟎 = 𝑫𝒊𝒗𝟏/(rE-g) =𝟑/(𝟎.𝟎𝟗−𝟎.𝟎𝟒) = 𝟔𝟎
102. Find the required return for a stock whose dividends are expected to grow at a constant rate forever, given the following information: - Current stock price P0 = $15.00, expected dividend after one year D1 = $1.04 and the dividend growth rate is 4% per year forever. Hint: This is a constant dividend growth stock where rate is unknown. A) Not enough information given B) 8.0% C) 11.0% D) 13.0%
C) 11.0% From 𝑷𝟎 = 𝑫𝒊𝒗𝟏/(rE-g) , it follows that 𝒓𝑬 = (𝑫𝒊𝒗𝟏/P0)+g= ($𝟏.𝟎𝟒/$15) + 𝟎. 𝟎𝟒 = (𝟎. 𝟎𝟕 + 𝟎. 𝟎𝟒) = 𝟎. 𝟏𝟏
189. A firm has outstanding debt with a coupon rate of 9%, seven years maturity, and a price of $1,000 per $1,000 face value. What is the after-tax cost of debt if the marginal tax rate of the firm is 40%? A) 5.9% B) 5.7% C) 5.4% D) 6.2%
C) 5.4% Recall that a coupon bond sells at face (par) value if and only if its YTM is equal to its coupon rate. So, yield to maturity (YTM) = 9% Verify: FV = 1,000; PV =-1,000; PMT = 90; N = 7; I/YR = ? (9) After-tax cost of debt = 9%*(1 - 0.40) = 5.4%
161. Time: 0. 1 2 3 Investment A: -$1 million. $300,000. 400,000. 500,000 Investment B: -$1 million $500,000 400,000. 500,000 An investor is considering the two investments shown above. Her cost of capital is 8%. Which of the following statements about these investments is true? A) The investor should take investment A since it has a greater net present value (NPV). B) The investor should take investment A since it has a greater internal rate of return (IRR). C) The investor should take investment B since it has a greater net present value (NPV). D) The investor should take investment B since it has a greater internal rate of return (IRR).
C) The investor should take investment B since it has a greater net present value (NPV). cash flows
108. If you want to value the equity of a firm's equity that consistently pays out its earnings as dividends, the simplest model for you to use is the A) enterprise value model. B) total payout model. C) dividend-discount model. D) discounted free cash flow model.
C) dividend-discount model.
140. If you want to value the equity of a firm's equity that consistently pays out its earnings as dividends, the simplest model for you to use is the A) enterprise value model. B) total payout model. C) dividend-discount model. D) discounted free cash flow model.
C) dividend-discount model.
123. Cameron Industries is purchasing a new chemical vapor depositor in order to make silicon chips. It will cost $6 million to buy the machine and $10,000 to have it delivered and installed. Building a clean room in the plant for the machine will cost an additional $3 million. The machine is expected to have a working life of six years. Which of these activities will be reported as an operating expense? A) the delivery and install cost only B) the cost of the depositor only C) the redesign of the plant only D) the delivery and install cost and the cost of the depositor
C) the redesign of the plant only
109. If you want to value the equity of a firm that has consistent earnings growth, but varies how it pays out these earnings to shareholders between dividends and repurchases, the simplest model for you to use is the A) enterprise value model. B) dividend-discount model. C) total payout model. D) discounted free cash flow model.
C) total payout model.
141. If you want to value the equity of a firm that has consistent earnings growth, but varies how it pays out these earnings to shareholders between dividends and repurchases, the simplest model for you to use is the A) enterprise value model. B) dividend-discount model. C) total payout model. D) discounted free cash flow model.
C) total payout model.
118. The Sisyphean Company is planning on investing in a new project. This will involve the purchase of some new machinery costing $450,000. The Sisyphean Company expects cash inflows from this project as detailed below: Year 1 Year 2 Year 3 Year 4 $200,000 $225,000 $275,000 $200,000 The appropriate discount rate for this project is 16%. What is the internal rate of return (IRR) for this project? Should the company invest in this project using the IRR rule?
CF0 = -450,000 CF1 = 200,000 CF2 = 225,000 CF3 = 275,000 CF4 = 200,000; Compute IRR = 34.12%. Applying the IRR rule: IRR = 34.12% > Cost of Capital = 16%. Accept the project.
113. Which of the following investment decision measures is best defined as the amount of time it takes to pay back the initial investment? A) internal rate of return (IRR) B) profitability index C) net present value (NPV) D) payback period
D) payback period
127. Which of the following adjustments should NOT be made when computing free cash flow from incremental earnings? A) adding back depreciation expenses B) subtracting capital expenditures C) subtracting increases in Net Working Capital D) subtracting depreciation expenses
D) subtracting depreciation expenses
174. The current sales of a company are $500,000 and the current working capital is $50,000 (10% of sales). Sales are expected to increase by 20% next year. What is the change in net working capital from this increase in sales assuming that net working capital as a percent of sales remains unchanged? A) $4,000 B) $6,000 C) $8,000 D) $10,000
D) $10,000 NWC will also increase by 20%. 0.20*$50,000 = $10,000.
171. Daily Enterprises purchases a $10 million machine to be depreciated on a straight line basis over 5 years. The machine generates incremental revenues of $4 million per year, along with incremental costs of $1 million per year. If the marginal tax rate is 30%, compute the incremental free cash flows generated from the new machine. Assume any replaced machine is fully depreciated and has no salvage value. A) $1.5 million B) $2 million C) $2.4 million D) $2.7 million
D) $2.7 million Depreciation per year = $10,000,000/5 = $2 million FCF = ($4 - $1 - $2)*(1 - 0.30) + $2 = $0.7 + $2 = $2.7
187. Ford Motors Company is considering launching a new line of hybrid diesel-electric SUVs. The heavy advertising expenses associated with the new SUV launch would generate operating losses of $30 million next year. Without the new SUV, Ford expects to earn pretax income of $80 million from operations next year. Ford pays a 40% tax rate on its pretax income. The amount that Ford Motors Company owes in taxes next year with the launch of the new SUV is closest to: A) $12.0 million B) $44.0 million C) $32.0 million D) $20.0 million
D) $20.0 million (80-30)*0.40 = 20
172. Heinz markets a new test product where the marketing will cost $600,000. If the tax rate for Heinz is 40%, what is the actual cost of marketing assuming Heinz is a profitable company (that is, Heinz earns sufficient taxable income from operations against which it can offset this cost)? A) $100,000 B) $150,000 C) $200,000 D) $360,000
D) $360,000 $600,000 - 0.40*$600,000 = $360,000. Note that the firm can use this $600,000 marketing cost to offset taxable income from other operations, which reduces the firm's taxes by $240,000. So, the net cost of marketing is $360,000.
134. You are considering adding a microbrewery onto one of your firm's existing restaurants. This will entail an increase in inventory of $8000, an increase in accounts payables of $2500, and an increase in property, plant, and equipment of $40,000. All other accounts will remain unchanged. The change in net working capital resulting from the addition of the microbrewery is: A) $45,500 B) $10,500 C) $6,500 D) $5,500
D) $5,500 Increase in NWC = Increase in minimum required level of cash + increase in accounts receivables + Increase in inventory - Increase in accounts payables Here, it is $8,000 - $2,500 = $5,500
190. A firm is considering investing in a new project with an upfront cost of $500 million. The project will generate an incremental free cash flow of $50 million at the end of the first year and this cash flow is expected to grow at an annual rate of 4% forever. If the firm's WACC is 13%, what is the value of this project? A) -$500 million B) -$115.38 million C) $3.3 million D) $55.56 million
D) $55.56 million NPV = -500 + 50/(0.13 - 0.04) = 55.56
106. With reference to question 105 above, what is the capital gains yield and dividend yield on the preferred stock? A) 1%, 9% B) 0%, 11% C) 1%, 8% D) 0%, 10% 105. What is the value of a preferred stock that pays a constant and pre-determined dividend of $3.50 at the end of each year forever and has a required rate of return of 10% per year? (Round your answer to the nearest $1.) stock value = $35
D) 0%, 10% 𝑫𝒊𝒗𝒊𝒅𝒆𝒏𝒅 𝒚𝒊𝒆𝒍𝒅 = 𝑫𝒊𝒗𝟏/P0 = $𝟑.𝟓𝟎/$35 = 𝟎. 𝟏𝟎 = 𝟏𝟎% 𝑪𝒂𝒑𝒊𝒕𝒂𝒍 𝒈𝒂𝒊𝒏𝒔 𝒚𝒊𝒆𝒍𝒅 = 𝑷𝟏 − 𝑷𝟎/P0 𝑷𝟏 = 𝑫𝒊𝒗𝟐/(rE-g) = $𝟑.𝟓𝟎/(.10-0) =$𝟑𝟓 𝑷𝟏 −𝑷𝟎/P0 =$𝟑𝟓−$𝟑𝟓/35=𝟎%
139. Luther Industries has outstanding tax loss carry-forwards of $70 million from losses over the past four years. If Luther earns $15 million per year in pretax income from now on, in how many years will Luther first pay taxes? A) 7 years B) 2 years C) 4 years D) 5 years
D) 5 years The number of years the tax loss carry-forwards will last can be calculated as the tax loss carry-forward divided by the annual pretax income or: years with no tax = 70/15 4.67 years, so Luther won't have to pay taxes for the next four years, but will have to start paying some taxes five years from now.
155. Which of the following situations can lead to IRR giving a different decision than NPV? A) Delayed investment B) Multiple IRRs C) Differences in project scale D) All of the above can lead to IRR giving a different decision than NPV
D) All of the above can lead to IRR giving a different decision than NPV
183. A security firm is offered $80,000 in one year for providing CCTV coverage of a property. The cost of providing this coverage to the security firm is $74,000, payable now, and the interest rate is 8.5%.Should the firm take the contract? A) It does not matter whether the contract is taken or not, since NPV=0. B) Yes, since net present value (NPV) is negative. C) Yes, since net present value (NPV) is positive. D) No, since net present value (NPV) is negative.
D) No, since net present value (NPV) is negative. NPV = -$74,000 + $80,000/1.085 = -$267.28
185. You are opening up a brand new retail strip mall. You presently have more potential retail outlets wanting to locate in your mall than you have space available. What is the most appropriate tool to use if you are trying to determine the optimal allocation of your retail space? A) Payback period B) Internal rate of return (IRR) C) Net present value (NPV) D) Profitability index
D) Profitability index Profitability Index = NPV of each outlet/Space of the outlet
166. Which of the following best explains why is it sensible for a firm to use an accelerated depreciation schedule such as MACRS rather than straight-line depreciation? A) The firm will substantially decrease its depreciation tax shield across all of the depreciation timeline. B) The firm can decide over how many years an item may be depreciated, thus allowing it full control of its depreciation expenses. C) The firm will have substantially fewer depreciation expenses later in the depreciation timeline. D) The firm will receive greater benefits to its cash flow earlier in the depreciation timeline and thus increase net present value (NPV).
D) The firm will receive greater benefits to its cash flow earlier in the depreciation timeline and thus increase net present value (NPV). The faster a firm can depreciate its assets, the higher will be the depreciation expenses and the associated deprecation tax shields (tax savings) during the earlier years of the project's lifetime. The earlier the firm realizes its depreciation tax savings, the greater is their present value due to the time value of money. This increases the project's NPV.
136. Caprica Company reported an unlevered net income of $300 million for the most recent fiscal year. The firm had depreciation expenses of $125 million and capital expenditures of $150 million. Although it had no interest expense, the firm did have an increase in net working capital of $20 million. What is Caprica's free cash flow?
FCF = Unlevered net income + Dep - Capital Ex - increase in NWC = 300 + 125 - 150 - 20 = 255
131. A firm reports that in a certain year it had an unlevered net income of $4.5 million, depreciation expenses of $2.8 million, capital expenditures of $2.3 million, and Net Working Capital decreased by $1.5 million. What is the firm's free cash flow for that year?
FCF = Unlevered net income + Depreciation - CAPEX - Increase in NWC FCF = 4.5 + 2.8 - 2.3 - (-1.5) = $6.5 million
Year 0. 1. 2. 3. 4 Cash Flow -10,000 4000 4000 4000 4000 115. If the appropriate discount rate (cost of capital) for this project is 15%, then what is its net present value (NPV)?
Financial Calculator Solution:CF0 = -10,000; CF1 = 4,000; CF2 = 4,000; CF3 = 4,000; CF4 = 4,000; I/YR = 15; Compute NPV = 1,419.91.
163. A firm is considering changing their credit terms. It is estimated that this change would result in sales increasing by $1,000,000. This in turn would cause inventory to increase by $150,000, accounts receivable to increase by $100,000, and accounts payable to increase by $75,000. What is the firm's expected change in net working capital?
Increase in inventory + Increase in Accounts Receivable - Increase in Accounts Payable = $150,000 + $100,000 - $75,000 = $175,000
158. Mary is in contract negotiations with a publishing house for her new novel. She has two options. She may be paid $100,000 up front, and receive royalties that are expected to total $26,000 at the end of each of the next five years. Alternatively, she can receive $200,000 up front and no royalties. Which deal should she take given a discount rate of 8%?
PV of the first deal for r = 8% = $203,810 𝟏𝟎𝟎,𝟎𝟎𝟎 + 𝟐𝟔,𝟎𝟎𝟎 × 𝟏/.08 ×[𝟏−(1/1.08^5)] = $203,810 PV of the second deal = $200,000
117. A florist is buying a number of motorcycles to expand its delivery service. These will cost $87,000, but are expected to increase profits by $3000 per month over the next four years. What is the payback period (in number of months) in this case?
Payback period = 87,000 / 3000 = 29 months
Year 0. 1. 2. 3. 4 Cash Flow -10,000 4000 4000 4000 4000 116. What is the IRR of the project above? If the cost of capital is 15%, apply the IRR rule to accept or reject this project.
To determine the IRR that satisfies the above equation, we have to use the financial calculator: CF0 = -10,000 CF1 = 4,000 CF2 = 4,000 CF3 = 4,000 CF4 = 4,000 Compute IRR = 21.86%. Or PV = -10,000; PMT = 4,000; N = 4; FV = 0; Solve for I/YR and find 21.86%. ANSWER= Applying the IRR rule: IRR = 21.86% > Cost of Capital = 15%. Accept the project.
159. A local government awards a landscaping company a contract worth $1.2 million per year for five years for maintaining public parks. The landscaping company will need to buy some new machinery before they can take on the contract. If the cost of capital is 7%, what is the most that this equipment could cost if the contract is to be worthwhile for the landscaping company?
Using a financial calculator, enter PMT = 1,200,000, N = 5, I/YR = 7%; calculate PV = $4,920,237. Thus, the most that the equipment could cost is $4,920,237. If the cost of the project were greater than the PV of future cash flows from the contract, the NPV of the contract would be negative.
110. Valence Electronics has 217 million shares outstanding. It expects earnings at the end of the year of $760 million. Valence pays out 40% of its earnings in total: 15% paid out as dividends and 25% used to repurchase shares. If Valence's earnings are expected to grow by 6% per year, these payout rates do not change, and Valence's equity cost of capital is8%, what is Valence's share price?
Using the total payout model: P0 = PV(Future Total Dividends and Repurchase)/(Shares Outstanding at time 0) PV = (0.4 x 760) / (0.08 - 0.06) = $15,200 million; P0 = $15,200 million / 217 million =$70.05
137. Temporary Housing Services Incorporated (THSI) is considering a project that involves setting up a temporary housing facility in an area recently damaged by a hurricane. THSI will lease space in this facility to various agencies and groups providing relief services to the area. THSI estimates that this project will initially cost $5 million to set up and will generate $20 million in revenues during its first and only year in operation (paid in one year). Operating expenses are expected to total $12 million during this year and depreciation expense will be another $3 million. THSI will require no working capital for this investment. THSI's marginal tax rate is 35%. a) Ignoring the original investment of $5 million, what is THSI's free cash flow for the first and only year of operation? b) Assume that THSI's cost of capital for this project is 15%. What is the net present value (NPV) of this temporary housing project is closest to:
a) Ignoring the original investment of $5 million, what is THSI's free cash flow for the first and only year of operation? FCF = (revenues - expenses - depreciation) × (1 - tax rate) + depreciation FCF = (20 - 12 - 3) × (1 - 0.35) + 3 = 6.25 b) Assume that THSI's cost of capital for this project is 15%. What is the net present value (NPV) of this temporary housing project is closest to: NPV = -$5,000,000 + $6,250,000 / 1.15 = $434,782.
84. Which of the following is NOT a way that a firm can increase its dividend per share? A) by increasing its retention rate B) by decreasing its shares outstanding C) by increasing its earnings (net income) D) by increasing its dividend payout rate
A) by increasing its retention rate
43. Why, in general, do investment opportunities offer a rate greater than that offered by U.S. Treasury securities for the same horizon? A) Most investment opportunities offer far greater risk than those offered by U.S. Treasury securities. B) The return from U.S. Treasury securities generally attracts less tax than the returns from other investments. C) The opportunity cost of capital for a given horizon is generally based on U.S. Treasury securities with that same horizon. D) U.S. Treasury securities are generally considered to be the best alternative to most investments.
A) Most investment opportunities offer far greater risk than those offered by U.S. Treasury securities.
51. How much will be the coupon payments of a 20-year $500 bond with an 8% coupon rate and quarterly payments? A) $3.33 B) $10.00 C) $20.00 D) $40.00
B) $10.00 ($500 x 0.08) / 4 = $10
35. In which of the following situations would the reserve bank in a certain country be most likely to lower interest rates? A) The economy is growing slowly or not at all. B) Inflation is rising rapidly. C) The level of investment is very high. D) The level of unemployment is low.
A) The economy is growing slowly or not at all.
49. An investor places $3000 in a bank account. The bank promises an interest rate of 8% in year 1, 9% in year 2 and 10% in year 3. What is the account balance at the end of 3 years? A) $4400.21 B) $3884.76 C) $3589.84 D) $2780.13 E) $2411.29
B) $3884.76 FV = $3,000*1.08*1.09*1.10 = $3,884.76
24. A businessman wants to buy a truck. The dealer offers to sell the truck for either $120,000 now, or six yearly payments of $25,000. What is the interest rate being offered by the dealer?
Calculate the interest rate using financial calculator: PV = 120,000, N= 6, FV = 0; PMT = -25,000; Solve for interest rate (I/YR) to find 6.77%.
91. Which of the following statements is FALSE? A) We cannot use the general dividend-discount model to value the stock of a firm with rapid or changing growth. B) As firms mature, their growth slows to rates more typical of established companies. C) The dividend-discount model values the stock based on a forecast of the future dividends paid to shareholders. D) The simplest forecast for the firm's future dividends states that they will grow at a constant rate, i.e., forever.
A) We cannot use the general dividend-discount model to value the stock of a firm with rapid or changing growth. Explanation: A multistage model can be used for these kinds of firms.
13. You are considering an investment that will pay $150 after 1 year, $500 after 2 years and $600 after 3 years. What is the present value of the cash flows if the appropriate discount rate is 10% per year? A) $1000.38 B) $1150.12 C) $1260.35 D) $1270.91
A) $1000.38 In your financial calculator enter cash flows one by one: 0, 150, 500, 600. I/YR = 10. Orange + NPV = ?
Suppose the term structure of interest rates is shown below: Term 1 yr 2 yrs 3 yrs 5 yrs 10 yrs 20 yrs Rate (EAR%) 5.00% 4.80% 4.60% 4.50% 4.25% 4.15% 41. Given the term structure table above, the present value (PV) of receiving $1000 per year with certainty at the end of the next three years is closest to: A) $2737 B) $2723 C) $2733 D) $2744
A) $2737 PV = 1000 / (1.05) + 1000 / (1.048)2 + 1000 / (1.046)3 = 2737
9. You are thinking about investing in a mine that will produce $10,000 worth of ore in the first year. As the ore closest to the surface is removed it will become more difficult to extract the ore. Therefore, the value of the ore that you mine will decline at a rate of 8% per year forever. If the appropriate interest rate is 6%, then the value of this mining operation is closest to: A) $71,429 B) $500,000 C) $166,667 D) This problem cannot be solved.
A) $71,429 𝑷𝑽 = 𝑪/(𝒓- 𝒈) = 𝟏𝟎,𝟎𝟎𝟎/(𝟎.𝟎𝟔 − −𝟎.𝟎𝟖) = 𝟏𝟎,𝟎𝟎𝟎/𝟎.𝟏𝟒 = $𝟕𝟏,𝟒𝟐𝟗
47. You purchase a car for $15,000. The car loan is financed with a 5% per year, 5-year loan with annual payments starting at time 1 (1 year from today) through time 5. Each payment reduces the principal by a certain amount until the loan is completely paid off. What is the interest component of the first payment? A) $750 B) $600 C) $530 D) $420 E) $395
A) $750 Interest = Loan Balance * interest rate = $15,000*0.05 = $750.
44. What is the effective annual rate when the APR equals 15% for monthly compounding? A) 16.08% B) 15.00% C) 14.25% D) 13.38% E) 12.47%
A) 16.08% EAR = ((1+APR/m)^m) -1
78. Patar Inc. Bonds are zero coupon bonds with a maturity of 30 years. If the price of each bond is $41.19 per $100 face value, what is the annual yield to maturity of these bonds? A) 3% B) 5% C) 6% D) 8%
A) 3% PV = -41.19; PMT = 0; FV = 100; N = 30; I/YR = ?
33. What is the real interest rate given a nominal rate of 8% and an inflation rate of 4.5%? A) 3.3% B) 4.5% C) 4.9% D) 8.0%
A) 3.3% (1 + nominal rate) / (1 + inflation rate) = 1 + real rate 1.08 / 1.045 = 1.03349; real rate = 3.349%
70. A treasury bond has an annual coupon rate of 4% that is paid semi-annually. The face Value of the bond is $1,000 and it has 10 years to maturity with a yield to maturity of 6% (expressed as an APR with semi-annual compounding). Compute the price of the bond. A) 851.23 B) 891.33 C) 907.42 D) 925.61 E) 1002.31
A) 851.23 Coupon = $1,000*0.04/2 = $20 FV = 1,000; PMT = 20; I/YR = 6/2 = 3; N = 10*2 = 20; PV = ?
89. Which of the following statements is FALSE regarding profitable and unprofitable growth? A) If a firm wants to increase its share price, it can always cut its dividend and invest more. B) If the firm retains more earnings, it will be able to pay out less of those earnings, which means that the firm will have to reduce its dividend. C) A firm can increase its growth rate by retaining more of its earnings. D) Cutting the firm's dividend to increase investment will raise the stock price if, and only if, the new investments have a positive net present value (NPV).
A) If a firm wants to increase its share price, it can always cut its dividend and invest more. The statement in choice A is not always true. Cutting dividends and investing more will increase the share price only if the reinvested money is invested in positive-NPV projects, where the return on new investment is greater than the cost of equity capital.
26. What is the effective annual rate (EAR)? A) the amount of interest that will be earned at the end of one year. B) the ratio of the annual percentage rate to the number of compounding periods per year 6 C) the discount rate for an n-year time interval, where n may be more than one year or less than or equal to one year (a fraction) D) the cash flows from an investment over a one-year period divided by the number of times that interest is compounded during the year
A) the amount of interest that will be earned at the end of one year.
16. You wish to buy a music system for $2000. Best Buy is offering to finance your purchase for 12 equal monthly installments at 2% per month for 12 months starting one month from today, and a final additional payment of $1000 after one year. What is your monthly payment if the first payment is due 1 month from today? A) $101.2 B) $110.3 C) $114.5 D) $123.2
C) $114.5 PV = 2,000; N = 12; I/YR = 2; FV = -1,000; PMT = ?
19. You will receive payments of $500 each year and forever where the payments start at t = 8. Compute the present value of these payments at t = 0 if the rate of interest is 10% per year? A) $2,272 B) $2,301 C) $2,566 D) $2,639
C) $2,566 PV of this perpetuity at t = 7 = $500/0.10 = $5,000. Thus, this perpetuity is equivalent to receiving a lump-sum payment of $5,000 seven years from now. PV = $5,000/1.107 = $2,565.79
58. Consider a zero-coupon bond with a $1,000 face value and ten years left until maturity. If the bond is currently trading for $459, then what is the yield to maturity on this bond?
Calculate the discount rate that equates the PV of $1.000 in ten years to $459. FV = 1,000; PV = -459; PMT = 0; N =10; Compute I/YR = 8.098 or 8.1%.
15. A car dealer offers you a BMW Z4 for payments of $400 a month for 60 months. There is a grace period of the first 2 months where you do not make any payments Thus, you therefore make 60 equal installments from t = 2 to t = 61. If the rate of interest charged by the dealer is 1% per month, what amount are you borrowing? A) $17,986 B) $17,804 C) $18,162 D) $18,357
B) $17,804 First, find the present value of these payments at t = 1 as follows: PMT = 400; N = 60; I/YR = 1; FV = 0; PV = ? (17,982.01) Thus, these payments are equivalent to paying $17,982.01 one month from now. The PV of this is equal to $17,982.01/1.01 = $17,803.98
52. How much will the coupon payments be of a 30-year $10,000 bond with a 4.5% coupon rate and semiannual payments? A) $30 B) $225 C) $350 D) $450
B) $225 ($10,000 x 0.045) / 2 = $225
21. An annuity of $2000 with 10 payments starts today (10 payments from t = 0 to t = 9). If the rate of interest is 6% per year, what is the future value of this annuity at t = 10? A) $26,403 B) $27,943 C) $21,154 D) $33,323
B) $27,943 PMT = 2,000; I/YR = 6; N = 10; PV = 0; FV =? (26,361.59); 26,361.59*1.06 = 27,943
76. Zoro Sword Company bonds have a coupon of 10% paid annually. The bonds have 10 years to remaining to maturity and a Face Value of $1,000. What is the price of the bonds today, if the investors' required rate of return is 10% per year? (Round your answer to the nearest $1.) A) $900 B) $1,000 C) $913 D) $1,064
B) $1,000 FV = 1,000; I/YR = 10; N = 10; PMT = 100; PV = ?
175. Books Inc. purchases a new machine for $100,000 that is to be depreciated on a straight line basis over 10 years. After 5 years, Books Inc. sells the machine for $90,000. If the capital gains tax rate is 40%, what is the cash inflow from this sale? A) $72,000 B) $74,000 C) $80,000 D) $70,000 Depreciation per year = $100,000/10 = $10,000 Accumulated Depreciation after 5 years = 5*$10,000 = $50,000 Book value of the machine after 5 years = $100,000 - $50,000 = $50,000 Capital gain on sale = $90,000 - $50,000 = $40,000 Tax = 0.40*$40,000 = $16,000 Cash inflows from sale = $90,000 - $16,000 = $74,000
B) $74,000 Depreciation per year = $100,000/10 = $10,000 Accumulated Depreciation after 5 years = 5*$10,000 = $50,000 Book value of the machine after 5 years = $100,000 - $50,000 = $50,000 Capital gain on sale = $90,000 - $50,000 = $40,000 Tax = 0.40*$40,000 = $16,000 Cash inflows from sale = $90,000 - $16,000 = $74,000
17. Jason plans on purchasing a house for $120,000. If a local bank is willing to lend the entire amount for a 30 year term at an APR of 7.2%, what is the monthly payment on the loan? A) $701.2 B) $814.5 C) $714.5 D) $823.2
B) $814.5 PV = -120,000; N = 360; I/YR = 7.2/12 = 0.6; FV = 0; PMT = ?
83. Suppose you invested $100 in the iShares High Yield Fund (HYG) a month ago. It paid a dividend of $1 today and then you sold it for $101. What was your dividend yield and capital gains yield on the investment? A) 2%, 1% B) 1%, 1% C) 3%, 1% D) 1%, 0%
B) 1%, 1% Dividend yield = Div1/P0 = $1/$100 = 0.01 = 1% Capital gains yield = (P1-P0)/P0 = ($101 - $100)/$100 = 0.01 = 1%.
18. You are prepared to make monthly payments of $200, beginning the end of this month, into an account that pays an interest of 12% quoted as an APR with monthly compounding. How many payments will you have made when your account balance reaches $50,000? A) 129.1 B) 125.9 C) 140.2 D) 123.2
B) 125.9 Monthly interest rate = 12%/12 = 1% PMT = -200; FV = 50,000; I/YR = 1; PV = 0; N = ?
75. In general a corporate bond with the same cash flows as a treasury bond, with the same maturity, and same face value as the treasury bond will sell at a price that is: A) Higher than the treasury bond because of credit risk. B) Lower than the treasury bond because of credit risk. C) Exactly the same as the treasury bond D) Cannot say for sure. Who knows?
B) Lower than the treasury bond because of credit risk.
57. Which of the following statements is FALSE? A) One advantage of quoting the yield to maturity rather than the price is that the yield is independent of the face value of the bond. B) Prior to its maturity date, the price of a zero-coupon bond is always greater than its face value. C) Because we can convert any bond price into a yield, and vice versa, bond prices and yields are often used interchangeably. D) The internal rate of return (IRR) of an investment in a bond (and holding it until its maturity) is given a special name, the yield to maturity (YTM).
B) Prior to its maturity date, the price of a zero-coupon bond is always greater than its face value.
5. Which of the following statements regarding annuities is FALSE? A) PV of an annuity = 𝐶 × 1 × [1 − 1 ] B) The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments. C) An annuity is a stream of N equal cash flows paid at regular intervals. D) Most car loans, mortgages, and some bonds are annuities.
B) The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments.
53. A corporate bond makes payments of $9.67 every month for ten years with a final payment of $2009.67. Which of the following best describes this bond? A) a 10-year bond with a face value of $2000 and a coupon rate of 4.8% with monthly payments B) a 10-year bond with a face value of $2000 and a coupon rate of 5.8% with monthly payments C) a 10-year bond with a face value of $2009.67 and a coupon rate of 4.8% with monthly payments D) a 10-year bond with a face value of $2009.67 and a coupon rate of 5.8% with monthly payments
B) a 10-year bond with a face value of $2000 and a coupon rate of 5.8% with monthly payments ($9.67 x 12) / 2000 = 5.802%
59. The above information is for a corporate bond issued by the Markel Corporation. What sort of bond is this? A) a high-risk bond B) an investment grade bond C) a speculative bond D) a high-yield bond
B) an investment grade bond
63. A corporate bond which receives a BBB rating from Standard and Poor's is considered A) a junk bond. B) an investment grade bond. C) a defaulted bond. D) a high-yield bond.
B) an investment grade bond.
72. If the yield to maturity on a coupon bond is equal to the coupon rate, it must be the case that ______________________. (If you cannot figure it out use some numbers to see what you get). A) the coupon rate is very high. B) the bond sells for par value (face value). C) the yield to maturity is very low. D) the bond sells at a premium to par value (face value). E) the bond sells at a discount to par value (face value).
B) the bond sells for par value (face value).
42. What, typically, is used to calculate the opportunity cost of capital on a risk-free investment? A) the best available expected return offered in any investment available in the market B) the interest rate on U.S. Treasury securities with the same term C) the interest rate of any investments alternatives that are available D) the best rate of return offered by U.S. Treasury securities
B) the interest rate on U.S. Treasury securities with the same term
38. In which of the following situations would it not be appropriate to use the following formula: PV = C0 + C1/(1 + r) + C2/(1 + r)2 + . . . . + Cn/(1 + r)n when determining the present value (PV) of a cash flow stream? A) when yield curves are flat B) when short-term and long-term interest rates vary widely C) when the inflation rate is high D) when the discount rate is high
B) when short-term and long-term interest rates vary widely
61.Security: AAA AA A BBB. BB vvYield (%): 5.6 5.7 5.9 6.4 7.0 A mining company needs to raise $100 million in order to begin open pit mining of a coal seam. The company will fund this by issuing 30-year bonds with a face value of $1000 and a coupon rate of 6%, paid annually. The above table shows the yield to maturity for similar 30-year corporate bonds of different ratings. If the mining company's bonds receive an A rating, what will be their selling price? A) $947.22 B) $967.64 C) $1013.91 D) $1016.41
C) $1013.91 Calculate the PV of the bond with FV = $1000, I/YR = 5.9%, PMT = 60, and N = 30, which = $1,013.91.
32. A truck costing $112,000 is paid off in monthly installments over four years with 8% APR. After three years the owner wishes to sell the truck. What is the closest amount from the following list that he needs to pay on his loan before he can sell the truck? A) $24,867 B) $28,678 C) $31,432 D) $87,255
C) $31,432 The first step is to calculate the monthly payment using a present value (PV) of $112,000 monthly interest rate of 8/12 = 0.6667%, and 48 periods, which = $2,734.27. PV = -$112,000; FV = 0; I/YR = 0.6667; N = 48; PMT = ? (2,734.27) The second step is to use that monthly payment to calculate the present value (PV) of 12 months remaining payment keeping the interest rate unchanged.PMT = 2,734.27; I/YR = 0.6667; N = 12; FV = 0; PV = ? (31,432.50)
2. A perpetuity has a PV of $32,000. If the interest rate is 10%, how much will the perpetuity pay every year? A) $2909 B) $3100 C) $3200 D) $3520
C) $3200 𝑷𝒂𝒚𝒎𝒆𝒏𝒕 = 𝑪 = 𝑷𝑽×𝒓= 𝟑𝟐,𝟎𝟎𝟎𝒙𝟎.𝟏𝟎 = $𝟑,𝟐𝟎𝟎
73. Suppose you purchase a zero coupon bond with a face value of $1,000 and a maturity of 25 years, for $320. If the yield to maturity on the bond remains unchanged, what will the price of the bond be 5 years from now? Hint: compute the YTM first and then compute the bond price in 5 years. A) $253.64 B) $387.49 C) $401.90 D) $529.40 E) $598.00
C) $401.90 first: FV = 1,000; PV = -320; N = 25; PMT = 0; I/YR = ? (4.6632) second: FV = 1,000; PMT = 0; N = 20; I/YR = 4.6632; PV = ?
14. You plan to deposit $1,000 today (t = 0), and then follow it by 10 equal payments of $500 each year for the next 10 years (from t = 1 to t = 10), into your savings account. What will your account balance be 10 years from today (at t = 10)? Assume your account pays 6% per year interest on all deposits. A) $9,313.1 B) $7,824.2 C) $8,381.2 D) $7,899.2
C) $8,381.2 PV = -1,000; PMT = -500; N = 10; I/YR = 6; FV = ?
79. Which of the following will probably increase a bond price? (i) Increase in default risk. (ii) Decrease of expected inflation rates. (iii) Increase of real rates of interest. A) (i) and (iii) B) (ii) and (iii) C) (ii) only D) none of the above.
C) (ii) only Anything that lowers the yield on the bond will increase its price.
55. You are considering investing in a zero-coupon bond that will pay you its face value of $1000 in ten years. If the bond is currently selling for $485.20, then the internal rate of return (IRR) for investing in this bond is closest to: A) 12% B) 8.0% C) 7.5% D) 10%
C) 7.5% Using financial calculator: PV = -485.20; FV = 1000; PMT = 0; N = 10; Compute I/YR = to find 7.5%.
29. A house costs $138,000. It is to be paid off in exactly ten years, with monthly payments of $1,675. What is the APR of this loan? A) 7.52% B) 7.80% C) 8.00% D) 8.33%
C) 8.00% Calculate the monthly interest rate r, when PV = $138,000; N = 120; PMT = $1,675; Solve for monthly interest rate = 0.6674%, which multiplied by 12 gives an APR = 8%. PV = 138,000; PMT = -1,675; N = 120; FV = 0; I/YR = ? (0.6674) 𝑨𝑷𝑹 = 𝒓×𝒎= 𝟎.𝟔𝟔𝟕𝟒%×𝟏𝟐=𝟖%
68. Which of the following statements are true? A) A fall in bond prices causes interest rates to fall. B) A fall in interest rates causes a fall in bond prices. C) A rise in interest rates causes bond prices to fall. D) Bond prices and interest rates are not connected.
C) A rise in interest rates causes bond prices to fall.
62.Security: AAA AA A BBB BB Yield (%): 5.7 5.8 6.0 6.6 6.9 Lloyd Industries raised $28 million in order to upgrade its roller kiln furnace for the production of ceramic tile. The company funded this by issuing 15-year bonds with a face value of $1000 and a coupon rate of 6.2%, paid annually. The above table shows the yield to maturity for similar 15-year corporate bonds of different ratings issued at the same time. When Lloyd Industries issued their bonds, they received a price of $962.63. Which of the following is most likely to be the rating these bonds received? A) AA B) A C) BBB D) BB
C) BBB Calculate the YTM of the bond: PV = -962.63; FV = $1000, PMT = 62, N = 15, which is I/YR = 6.6%; the table shows that the bonds received a BBB rating.
71. As a zero coupon bond approaches maturity, the price gets closer to the: A) Coupon Rate B) Market Price C) Face Value D) Inverse of the Market Price E) Equivalent Coupon Bond Price
C) Face Value
34. Given that the inflation rate in 2006 was about 3.24%, while a short term municipal bond offered a nominal rate of 2.9%, which of the following statement is correct? A) The purchasing power of investors in these bonds grew over the course of the year. B) The real interest rate for investors in these bonds was greater than the rate of inflation. C) Investors in these bonds were able to buy less at the end of the year than they could have purchased at the start of the year. D) The nominal interest rate offered by these bonds gave the true increase in purchasing power that resulted from investing in these bonds.
C) Investors in these bonds were able to buy less at the end of the year than they could have purchased at the start of the year.
59. Why are the interest rates of U.S. Treasury notes less than the interest rates of equivalent corporate bonds? A) The U.S. government has a high credit spread. B) There is significant risk that the U.S. government will default. C) U.S. Treasury securities are widely regarded to be risk-free. D) U.S. Treasury securities are generally used to determine interest rates.
C) U.S. Treasury securities are widely regarded to be risk-free.
Suppose the term structure of interest rates is shown below: Term 1 yr 2 yrs 3 yrs 5 yrs 10 yrs 20 yrs Rate (EAR%) 5.00% 4.80% 4.60% 4.50% 4.25% 4.15% 40. What is the shape of the yield curve and what expectations are investors likely to have about future interest rates? A) inverted; higher B) normal; higher C) inverted; lower D) normal; lower
C) inverted; lower
4. An annuity is set up that will pay $1500 per year for ten years. What is the present value (PV) of this annuity given that the discount rate is 6%?
Calculate PV of a 10-year annuity discounted at 6% interest rate; PV = $11,040.13. 𝑷𝑽=$𝟏,𝟓𝟎𝟎× 𝟏 ×[𝟏− 𝟏 ]=$𝟏𝟏,𝟎𝟒𝟎.𝟏𝟑 𝟎. 𝟎𝟔 𝟏. 𝟎𝟔𝟏𝟎 PMT = 1,500 ; FV = 0; N = 10; I/YR = 6; PV = ?
6. An annuity pays $50 per year for 20 years. What is the future value (FV) of this annuity at the end of those 20 years, given that the discount rate is 7%?
Calculate the FV of a 20-year annuity compounded at 7% interest rate at the end of year 20: 𝑭𝑽𝟐𝟎 =$𝟓𝟎×[𝟏.𝟎𝟕𝟐𝟎 −𝟏/.07]=$𝟐𝟎𝟒𝟗.𝟕𝟕 PMT = 50; PV = 0; I/YR = 7; N = 20; FV = ?
98. Jumbo Transport, an air-cargo company, expects to have earnings per share of $2.00 in the coming year. It decides to retain 10% of these earnings in order to lease new aircraft. The return on this investment will be 25%. If its equity cost of capital is 11%, what is the expected share price of Jumbo Transport? A) $12.71 B) $14.83 C) $16.94 D) $21.18
D) $21.18 𝑫𝒊𝒗𝟏 =𝑬𝑷𝑺𝟏 ×𝒅𝒊𝒗𝒊𝒅𝒆𝒏𝒅𝒑𝒂𝒚𝒐𝒖𝒕𝒓𝒂𝒕𝒆=$𝟐.𝟎𝟎×(𝟏−𝟎.𝟏𝟎)=$𝟏.𝟖𝟎; 𝒈= 𝒓𝒆𝒕𝒆𝒏𝒕𝒊𝒐𝒏𝒓𝒂𝒕𝒊𝒐×𝑹𝑶𝑰 = 𝟎.𝟏 × 𝟎.𝟐𝟓 = 𝟎.𝟎𝟐𝟓; 𝑷𝟎 = 𝑫𝒊𝒗𝟏/(rE-g) = $𝟏.𝟖𝟎/(𝟎.𝟏𝟏 − 𝟎.𝟎𝟐𝟓) = $𝟐𝟏.𝟏𝟖
20. Jason bought a house ten years ago. His payments are $700 per month and the APR on the loan is 6% and the original term was 30 years. With 20 years remaining now, what is the principal component of the next payment (121st payment)? A) $217.1 B) $208.6 C) $225.3 D) $211.5
D) $211.5 PMT = 700; N = 20*12 = 240; I/YR = 6/12 = 0.5; FV = 0; PV = ? 97,706.54 The remaining loan balance at the end of 10 years (120 months) is $97,706.54. Interest payment on that remaining balance = $97,706.54*0.005 = $488.53 Principal payment = $700 - $488.53 = $211.47
36. Term in years: 2 5 10 30 Rate: 2.25% 3.125% 3.5% 4.375% The table above shows the interest rates available from investing in risk-free U.S. Treasury securities with different investment terms. If an investment offers a risk-free cash flow of $100,000 in ten years' time, what is the present value (PV) of that cash flow? A) $80,051 B) $78,320 C) $73,512 D) $70,892
D) $70,892 Since the cash flow is 10 years from now, the relevant discount rate is the risk-free rate corresponding to a term of 10 years (3.5%): Using FV = $100,000, find the present value (PV) at 3.5% for 10 years.
1. What is the present value (PV) of an investment that will pay $400 in one year's time, and $400 every year after that, when the interest rate is 5%? A) $2400 B) $3600 C) $7200 D) $8000
D) $8000 𝑷𝑽𝒐𝒇𝒑𝒆𝒓𝒑𝒆𝒕𝒖𝒊𝒕𝒚 = 𝑪/𝒓 = 𝟒𝟎𝟎/𝟎.𝟎𝟓 = $𝟖,𝟎𝟎𝟎
77. The bonds of Superman Comics Inc. pay a annual coupon. They have 15 years remaining to maturity and a Face Value of $1,000. What is the annual coupon rate on the bonds if investors require a rate of return of 10% per year and the current bond price is $1000? A) 7% B) 8% C) 9% D) 10%
D) 10% PV = -1,000; FV = 1,000; I/YR = 10; N = 15; PMT = ? PMT = 100. Coupon rate = PMT/FV = 10%
54.Maturity (years). 1 2 3 4 5 Price $97.25 $94.53 $91.83 $89.23 $87.53 The above table shows the price per $100 face value of several risk-free, zero-coupon bonds. What is the yield to maturity of the three-year, zero-coupon, risk-free bond shown? A) 2.83% B) 2.85% C) 2.86% D) 2.88%
D) 2.88% With financial calculator: FV = 100; PV = -91.83; N = 3; PMT =0; Solve for I/YR.
48. The term structure of interest rates generally refers to: A) A graphical depiction of real rates vs. inflation rates. B) A graphical depiction of spot rates vs. coupon rates of bonds. C) A graph of spreads vs. rates. D) A graphical depiction of yield to maturity of government bonds vs. maturity.
D) A graphical depiction of yield to maturity of government bonds vs. maturity.
90. Which of the following statements is FALSE? A) Estimating dividends, especially for the distant future, is difficult. B) A firm can only pay out its earnings to investors or reinvest their earnings. C) Successful young firms often have high initial earnings growth rates. D) According to the constant dividend growth model, the value of the firm depends on the current dividend level, divided by the equity cost of capital plus the grow rate.
D) According to the constant dividend growth model, the value of the firm depends on the current dividend level, divided by the equity cost of capital plus the grow rate. Explanation: According to the constant dividend growth model, the value of the firm depends on the next-period dividend level, divided by the difference between the equity cost of capital and the growth rate.
69. A bond is currently trading below par. Which of the following can be true about that bond? A) The bond's yield to maturity is less than its coupon rate. B) The bond is a zero-coupon bond. C) The bond's yield to maturity is greater than its coupon rate. D) B and C above
D) B and C above
92. Which of the following statements is FALSE? A) A common approximation is to assume that in the long run, dividends will grow at a constant rate. B) The dividend each year is the firm's earnings per share (EPS) multiplied by its dividend payout rate. C) There is a tremendous amount of uncertainty associated with any forecast of a firm's future dividends. D) During periods of high growth, it is not unusual for firms to pay out 100% of their earnings to shareholders in the form of dividends.
D) During periods of high growth, it is not unusual for firms to pay out 100% of their earnings to shareholders in the form of dividends. Explanation: During periods of high growth, it is not unusual for these firms to retain 100% of their earnings to exploit profitable investment opportunities.
39. Which of the following reasons for considering long-term loans inherently more risky than short-term loans most accurate? A) There is a greater chance that a borrower will default in a longer time-frame. B) The penalties for closing out a long-term loan early make them unattractive to many investors. C) Long-term loans typically have ongoing costs that accumulate over the life of the loan. D) Long-term loan values are much more sensitive to changes in market interest rates than short-term loan values.
D) Long-term loan values are much more sensitive to changes in market interest rates than short-term loan values.
45. A given rate is quoted as 12% APR and has an EAR of 12.68%. What is the compounding frequency during the year? A) Annually B) Semiannually C) Quarterly D) Monthly E) Daily
D) Monthly Try EAR formula with m=1,2,4,12, and 365
28. Which of the following statements is FALSE? A) Because interest rates may be quoted for different time intervals, it is often necessary to adjust the interest rate to a time period that matches that of our cash flows. B) The effective annual rate indicates the amount of interest that will be earned at the end of one year. C) The annual percentage rate indicates the amount of simple interest earned in one year. D) The annual percentage rate indicates the amount of interest including the effect of compounding.
D) The annual percentage rate indicates the amount of interest including the effect of compounding.
25. Which of the following would be LEAST likely to lower the interest rate that a bank offers a borrower? A) The number of borrowers seeking funds is low. B) The expected inflation rate is expected to be low. C) The borrower is judged to have a low degree of risk. D) The investment will be for a long period of time.
D) The investment will be for a long period of time.
50. Which of the following best illustrates why a bond is a type of loan? A) The issuers of bonds regularly pay interest on the face value of the bond to the buyers of those bonds. B) When a company issues a bond, the buyer of that bond becomes a part owner of the issuing company. C) Federal and local governments issue bonds to finance long-term projects. D) When an investor buys a bond from an issuer, the investor is giving money to the issuer, with the assurance it will be repaid at a date in the future.
D) When an investor buys a bond from an issuer, the investor is giving money to the issuer, with the assurance it will be repaid at a date in the future.
46. The monthly mortgage payment on your house is $960.34 starting one month from now. It is a 30 year mortgage at an APR of 6% compounded monthly. How much will still you owe the bank (loan outstanding) after making the required payments for 10 years? A) $115,301 B) $114,692 C) $119,298 D) $120,319 E) $134,045
E) $134,045 PMT = 960.34; N = 20*12=240; I/YR = 6/12 = 0.5; FV = 0; PV = ? (-134,045)
27. A bank offers a loan that will requires you to pay 6% interest compounded monthly. What is the EAR charged by the bank?
EAR = ((1+(APR/m))^m)-1 EAR = ((1+.06/12)^12)-1 = .O617 = 6.17%
65. What must be the price of a $10,000 bond with a 6.5% coupon rate, semiannual coupons, and two years to maturity if it has a yield to maturity of 8% APR?
FV = $10,000, N = 4, PMT = (10,000*0.065)/2 = 325, I/YR = APR/m = 8%/2 = 4%. Calculate PV = $9,727.75.
64. What is the yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semiannual coupons if this bond is currently trading for a price of $884?
FV = $1000, N = 20, PMT = (1,000*0.052)/2 = 26, PV = -$884, I/YR = ? per semiannual period; YTM = 3.4095 x 2 = 6.82%.<<<<<ANSWER
56. A risk-free, zero-coupon bond with a face value of $1,000 has 15 years to maturity. If the YTM is 5.8%, what is the price this bond will trade at?
Face value = $1,000, time to maturity = 15 years, and discount rate = 5.8%, PMT = 0. Calculate PV = $429.25.
67. What is the coupon rate of a two-year, $10,000 bond with semiannual coupons and a price of $9543.45, if it has a yield to maturity of 6.8%?
Face value = $10,000, PV = $9,543.45, periods to maturity = 4, and discount rate = 3.4%.FV = 10,000; PV = -9,543.45; N = 4; I/YR = 6.8/2 = 3.4; PMT = ? Calculate C = $216; annual coupon payment = $216 x 2 = $432; coupon rate = 4.32%.
66. What must be the price of a $1,000 bond with a 5.8% coupon rate, annual coupons, and 30 years to maturity if YTM is 7.5% APR?
Face value = $1000, periods to maturity = 30, C = 58, and discount rate = 7.5% per period, calculate PV. FV = 1,000; N = 30; PMT = 58; I/YR = 7.5; PV = ? =799.22
30. A homeowner has five years of monthly payments of $1400 before she has paid off her house. If the interest rate is 7% APR, what is the remaining balance on her loan?
Financial calculator solution: FV = 0; PMT = 1,400; I/YR = 0.58333; N = 60; solve for PV = $70,703.
88. Valorous Corporation will pay a dividend of $1.80 per share at this year's end and a dividend of $2.40 per share at the end of next year. It is expected that the price of Valorous' stock will be $44 per share after two years. If Valorous has an equity cost of capital of 8%, what is the maximum price that a prudent investor would be willing to pay for a share of Valorous stock today?
Financial calculator: CF0 = 0, CF1 = 1.80, CF2 = (44 + 2.40) = 46.40; I/YR = 8; NPV = ? Thus, PV of these cash flows calculated at 8% is equal to $41.45.
87. The Busby Corporation had a share price at the start of the year of $26.20, paid a dividend of $0.56 at the end of the year, and had a share price of $29.00 at the end of the year. Which of the following is closest to the rate of return of investments in companies with equal risk to The Busby Corporation for this period?
Financial calculator: FV = 29.56; PV = -26.20; N = 1; PMT = 0; I/YR = ? (12.82)
10. What is the internal rate of return (IRR) of an investment that requires an initial investment of $10,000 today and pays $14,000 in one year's time?
IRR is the particular discount rate r that sets NPV equal to 0: 𝑵𝑷𝑽 = −$𝟏𝟎,𝟎𝟎𝟎 + ($𝟏𝟒,𝟎𝟎𝟎+(1+r)) = 𝟎 1 + r = 14,000/10,000= 1.40 r = 0.40 = 40% = IRR Financial calculator solution: PV = -10,000, N= 1, and FV = 14,000; Solve for I/YR and find 40%.
95. The Sisyphean Company's common stock is currently trading for $25.00 per share. The stock is expected to pay a $2.50 dividend at the end of the year and the Sisyphean Company's equity cost of capital is 14%. If the dividend payout rate is expected to remain constant, then what is the expected growth rate in the Sisyphean Company's earnings?
If the dividend payout rate is constant, the growth rate of earnings is equal to the growth rate of dividends. From the constant dividend growth model: P0 = Div1 / (rE - g) = 25.00 = 2.50/(0.14 - g), so g = 0.04
37. Term in years: 1 2 3 4 5 Rate: 1.8% 2.25% 2.30% 2.66% 3.13% The table above shows the interest rates available from investing in risk-free U.S. Treasury securities with different investment terms. What is the present value (PV) of cash flows from an investment that yields $4000 at the end of each year for the next four years?
PV of $4000 at 1.8% for 1 year = $3929.27; PV of $4000 at 2.25% for 2 years = $3825.90; PV of $4000 at 2.30% for 3 years = $3736.23; PV of $4000 at 2.66% for 4 years = $3601.26; Sum of these four PVs = $15,093.
22. Dan buys a property for $250,000. He is offered a 20-year loan by the bank, at an interest rate of 6% per year. What is the annual loan payment Dan must make?
Solve for C either directly from the above equation or use the financial calculator: PV = 250,000, N= 20, I/YR = 6%, FV = 0; Solve for PMT = $21,796.139.
12. You are considering purchasing a new home. You will need to borrow $250,000 to purchase the home. A mortgage company offers you a 15-year fixed rate mortgage (180 months) at 9% APR (0.75% per month). If you borrow the money from this mortgage company, your monthly mortgage payment will be closest to:
Solve for C either directly using the equation above or use the financial calculator: PV = 250,000; I = 0.75; N = 180; FV = 0; Compute payment = $2,535.67
11. You are interested in purchasing a new automobile that costs $35,000. The dealership offers you a special financing rate of 6% APR (0.5% per month) for 48 months. Assuming that you do not make a down payment on the auto and you take the dealer's financing deal, then your monthly car payments would be closest to:
Solve for C either directly using the equation above or use the financial calculator: PV = 35,000; I = 0.5; N = 48; FV = 0; Compute PMT = $821.98.
60. A firm issues ten-year bonds with a coupon rate of 6.5%, paid semiannually. The credit spread for this firm's ten-year debt is 0.8%. New ten-year Treasury notes are being issued at par with a coupon rate of 5%. What should the price of the firm's outstanding ten-year bonds be per $100 of face value?
Ten-year treasury notes are issued at a YTM of 5% (YTM is equal to coupon rate if a bond is selling at par (face) value). If the credit spread for this firm's debt is 0.8%, this means that these bonds have a YTM of 5.8% as an annual percentage rate (5% + 0.8% = 5.8%). Since coupons are paid semiannually:Face value = $100; C = (100*0.065)/2 = 3.25; y = 0.058/2 = 0.029; N = 10 x 2 = 20 Financial calculator: FV = $100, I/YR = 2.9, PMT = 3.25, N = 20, PV = ?, which is equal to $105.26. <<<ANSWER
31. A Xerox DocuColor photocopier costing $42,000 is paid off in 60 monthly installments at 6.5% APR. After three years the company wishes to sell the photocopier. What is the minimum price for which they can sell the copier so that they can cover the cost of the balance remaining on the loan?
The first step is to calculate the monthly payment using a present value (PV) of $42,000, monthly interest rate of 6.5/12 = 0.541667%, and 60 periods, which = $821.78; PV = 42,000; N = 60; FV = 0; I/YR = 0.541667; PMT = ? (821.78) The second step is to calculate the present value (PV) of 24 remaining monthly payments, keeping the interest rate unchanged. PMT = 821.78; N = 24; I/YR = 0.541667; FV = 0; PV = ? (18,447.79)
3. A perpetuity will pay $1000 per year, starting five years after the perpetuity is purchased. What is the present value (PV) of this perpetuity on the date that it is purchased, given that the interest rate is 4%?
The first step is to calculate the value of the perpetuity at year 4:PV at year 4 = 1000 / 0.04 = $25,000; Thus, this perpetuity is equivalent to a single cash flow of $25,000 four years from now. The next step is to calculate the PV of $25,000 received to be at year 4: PV = $25,000/(1.04)4 = $21,370.10
23. Matthew wants to take out a loan to buy a car. He calculates that he can make repayments of $4,000 per year. If he can get a five-year loan with an interest rate of 7.5%, what is the maximum price he can pay for the car?
Using financial calculator: PMT = 4000, N= 5, I/YR = 7.5%, FV = 0; solve PV = $16,183.54.
80. Big-Mart stock is expected to pay a dividend of $3.15 next year. The dividends are expected to grow at 5% per year thereafter, and the market discount rate for stocks of equivalent risk is 10%. What is the value of Big-Mart stock now?
Using the constant dividend growth model (Gordon model), P = $3.15/(0.10 - 0.05) = $63
82. The stock price of Adama Industries is $80. Investors required a 9% of return on stocks with similar risk. If the company plans to pay a dividend of $4 next year, what is the expected annual growth rate of the company's dividends?
Using the constant dividend growth model (Gordon model), P0 = Div1/(r-g) 80 = 4/(0.09 - g) Thus, 0.09 - g = 4/80 = 0.05. Then, g = 0.09 - 0.05 = 0.04.
86. Credenza Industries is expected to pay a dividend of $1.20 at the end of the coming year. It is expected to sell for $62.00 at the end of the year. If its equity cost of capital is 8%, what is the expected capital gain from the sale of this stock at the end of the coming year?
With financial calculator: I/YR = 8, N = 1, FV = 63.20, PMT = 0, PV = ? (58.52) 𝑬𝒙𝒑𝒆𝒄𝒕𝒆𝒅𝒄𝒂𝒑𝒊𝒕𝒂𝒍𝒈𝒂𝒊𝒏 = 𝑷𝟏 - 𝑷𝟎 = $𝟔𝟐.𝟎𝟎 −$𝟓𝟖.𝟓𝟐 = $𝟑.𝟒𝟖
85. OwenInc has a current stock price of $14.50 and is expected to pay a $0.85 dividend in one year. If OwenInc's equity cost of capital is 12%, what price would OwenInc's stock be expected to sell for immediately after it pays the dividend?
With financial calculator: PV = -14.50, N = 1, I/YR = 12, PMT = 0, FV = ? FV will be 16.24. 𝑷𝟏 = 𝟏𝟔.𝟐𝟒 - 𝟎.𝟖𝟓 = 𝟏𝟓.𝟑𝟗
97. You expect that Bean Enterprises will have earnings per share of $2 for the coming year. Bean plans to retain all of its earnings for the next three years. For the subsequent two years, the firm plans on retaining 50% of its earnings. It will then retain only 25% of its earnings from that point forward. Retained earnings will be invested in projects with an expected return of 20% per year. If Bean's equity cost of capital is 12%, then what is the price of a share of Bean's stock?
Year Earnings. Dividends g 1 $2.00. $0. 20% 2. $2.40. $0. 20% 3. $2.88 $0 20% 4 $3.46. $1.73. 10% 5 $3.80 $1.90. 10% 6 $4.18 $3.14. 5% P0 = 1.73/(1.12)4 + 1.90/(1.12)5 + (3.14/(0.12 - 0.05))/1.125 = 27.63 Each g is calculated as the 20% return on the projects × the retention ratio.
8. Martin wants to provide money in his will for an annual bequest to whichever of his living relatives is oldest. That bequest will provide $1000 in the first year, and will grow by 7% per year, forever. If the interest rate is 11%, how much must Martin provide to fund this bequest?
𝑷𝑽𝒐𝒇𝒈𝒓𝒐𝒘𝒊𝒏𝒈𝒑𝒆𝒓𝒑𝒆𝒕𝒖𝒊𝒕𝒚 = 𝟏𝟎𝟎𝟎/(𝟎.𝟏𝟏 − 𝟎.𝟎𝟕) = $𝟐𝟓,𝟎𝟎𝟎
