A spreadsheet approach to information visualization

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JONH教你学英语出奇制胜

我知道，很多中国人都在学英语，并且有一部分学习得很吃力，苦于没有好方法。

我年轻的时候（虽然我觉得我现在也不算老吧），第一份工作其实是做私人英语老师、翻译口译员。

当时，学生会到我家里来上课。

在与他们接触的过程中，我渐渐摸到了学习英语的一些门道，不仅易上手，而且效率高。

今天，我就给大家道一道其中的奥秘。

1.绝不要放过新单词我注意到，很多英语学习者有一个不好的习惯，就是爱跳过生单词。

英语学到一定程度，很多人开始阅读英语原文书籍、杂志等。

但为了更快读到下一页，一般人遇到生单词都会跳过，充其量做个标记就抛之脑后了。

就连许多大学英语老师也是这样建议学生，说生词不会过分影响对原文的理解，过分纠结会浪费时间。

这一点在考试中可能适用，但若想真正学英语，我的建议是，绝不要放过新单词。

你可能特别想快速读到下一页，看看后面的情节怎么发展，你可能觉得一两个生词不学习也没关系。

但请一定不要这样做，因为这样你只能花更多的时间来提高自己的英语水平，你不需要字典就读懂全文的那一天也就更遥远了。

读到一半去学习新单词，听起来似乎很折磨人。

但万事开头难，一旦你下定决心，碰到的生单词超过一定数目（比如30个）时开始攻克，不过关绝不继续往下读，那么英语突飞猛进就指日可待了。

2.攻克新单词，重复重复再重复既然下决心跟单词战斗到底，接下来我就给背单词的同志们支个招：首先，将生词逐个写在一张纸上。

记在手机或者ipad上也可以，但不推荐。

把生词和对应汉语分两栏写在纸上，这样，背单词的时候看不到释义（可以将纸对折），记不起来的时候又可以迅速查看一张纸抄满单词后（我建议一张纸上的单词数在15-40个之间），接下来的就到关键部分了。

这张纸要跟着你3天，你可以揣在兜里，放到包里，夹在书里，但就是不能让它和你分开。

这样，一有空你就可以拿出来看，坐地铁的时候、午休的时候、喝咖啡的时候、等公交的时候，甚至上厕所的时候！每次不需花太多精力，浏览一到两遍即可。

但需要注意的是，浏览释义的时候，一定不要看单词，反之亦然。

公司金融课后题答案CHAPTER 18

CHAPTER 18VALUATION AND CAPITAL BUDGETING FOR THE LEVERED FIRMAnswers to Concepts Review and Critical Thinking Questions1.APV is equal to the NPV of the project (i.e. the value of the project for an unlevered firm)plus the NPV of financing side effects.2. The WACC is based on a target debt level while the APV is based on the amount ofdebt.3.FTE uses levered cash flow and other methods use unlevered cash flow.4.The WACC method does not explicitly include the interest cash flows, but it doesimplicitly include the interest cost in the WACC. If he insists that the interest payments are explicitly shown, you should use the FTE method.5. You can estimate the unlevered beta from a levered beta. The unlevered beta is the betaof the assets of the firm; as such, it is a measure of the business risk. Note that the unlevered beta will always be lower than the levered beta (assuming the betas are positive). The difference is due to the leverage of the company. Thus, the second risk factor measured by a levered beta is the financial risk of the company.Solutions to Questions and ProblemsNOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.Basic1. a.The maximum price that the company should be willing to pay for the fleet of carswith all-equity funding is the price that makes the NPV of the transaction equal tozero. The NPV equation for the project is:NPV = –Purchase Price + PV[(1 – t C )(EBTD)] + PV(Depreciation Tax Shield)If we let P equal the purchase price of the fleet, then the NPV is:NPV = –P + (1 – .35)($140,000)PVIFA13%,5 + (.35)(P/5)PVIFA13%,5Setting the NPV equal to zero and solving for the purchase price, we find:0 = –P + (1 – .35)($140,000)PVIFA13%,5 + (.35)(P/5)PVIFA13%,5P = $320,068.04 + (P)(0.35/5)PVIFA13%,5P = $320,068.04 + .2462P.7538P = $320,068.04P = $424,609.54b.The adjusted present value (APV) of a project equals the net present value of theproject if it were funded completely by equity plus the net present value of any financing side effects. In this case, the NPV of financing side effects equals the after-tax present value of the cash flows resulting from the firm’s debt, so:APV = NPV(All-Equity) + NPV(Financing Side Effects)So, the NPV of each part of the APV equation is:NPV(All-Equity)NPV = –Purchase Price + PV[(1 – t C )(EBTD)] + PV(Depreciation Tax Shield)The company paid $395,000 for the fleet of cars. Because this fleet will be fullydepreciated over five years using the straight-line method, annual depreciationexpense equals:Depreciation = $395,000/5Depreciation = $79,000So, the NPV of an all-equity project is:NPV = –$395,000 + (1 – 0.35)($140,000)PVIFA13%,5 + (0.35)($79,000)PVIFA13%,5 NPV = $22,319.49NPV(Financing Side Effects)The net present value of financing side effects equals the after-tax present value of cash flows resulting from the firm’s debt, so:NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Payments)Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt R B. So, the NPV of the financing side effects are:NPV = $260,000 – (1 – 0.35)(0.08)($260,000)PVIFA8%,5– [$260,000/(1.08)5]NPV = $29,066.93So, the APV of the project is:APV = NPV(All-Equity) + NPV(Financing Side Effects) APV = $22,319.49 + 29,066.93APV = $51,386.422.The adjusted present value (APV) of a project equals the net present value of the projectif it were funded completely by equity plus the net present value of any financing side effects. In this case, the NPV of financing side effects equals the after-tax present value of the cash flows resulting from the firm’s debt, so:APV = NPV(All-Equity) + NPV(Financing Side Effects)So, the NPV of each part of the APV equation is:NPV(All-Equity)NPV = –Purchase Price + PV[(1 – t C )(EBTD)] + PV(Depreciation Tax Shield)Since the initial investment of $1.9 million will be fully depreciated over four yearsusing the straight-line method, annual depreciation expense is:Depreciation = $1,900,000/4Depreciation = $475,000NPV = –$1,900,000 + (1 – 0.30)($685,000)PVIFA9.5%,4 + (0.30)($475,000)PVIFA13%,4 NPV (All-equity) = – $49,878.84NPV(Financing Side Effects)The net present value of financing side effects equals the aftertax present value of cash flows resulting from the firm’s debt. So, the NPV of the financing side effects are:NPV = Proceeds(Net of flotation) – Aftertax PV(Interest Payments) – PV(PrincipalPayments)+ PV(Flotation Cost Tax Shield)Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt, R B. Since the flotation costs will be amortized over the life of the loan, the annual flotation costs that will be expensed each year are:Annual flotation expense = $28,000/4Annual flotation expense = $7,000NPV = ($1,900,000 – 28,000) – (1 – 0.30)(0.095)($1,900,000)PVIFA9.5%,4–$1,900,000/(1.095)4+ 0.30($7,000) PVIFA9.5%,4NPV = $152,252.06So, the APV of the project is:APV = NPV(All-Equity) + NPV(Financing Side Effects) APV = –$49,878.84 + 152,252.06APV = $102,373.233. a.In order to value a firm’s equity using the flow-to-equity approach, discount thecash flows available to equity holders at the cost of the firm’s levered equity. Thecash flows to equity holders will be the firm’s net income. Remembering that thecompany has three stores, we find:Sales $3,600,000COGS 1,530,000G & A costs 1,020,000Interest 102,000EBT $948,000Taxes 379,200NISince this cash flow will remain the same forever, the present value of cash flowsavailable to the firm’s equity holders is a perpetuity. We can discount at the leveredcost of equity, so, the value of the company’s equity is:PV(Flow-to-equity) = $568,800 / 0.19PV(Flow-to-equity) = $2,993,684.21b.The value of a firm is equal to the sum of the market values of its debt and equity, or:V L = B + SWe calculated the value of the company’s equity in part a, so now we need tocalculate the value of debt. The company has a debt-to-equity ratio of 0.40, whichcan be written algebraically as:B / S = 0.40We can substitute the value of equity and solve for the value of debt, doing so, wefind:B / $2,993,684.21 = 0.40B = $1,197,473.68So, the value of the company is:V = $2,993,684.21 + 1,197,473.68V = $4,191,157.894. a.I n order to determine the cost of the firm’s debt, we need to find the yield tomaturity on its current bonds. With semiannual coupon payments, the yield tomaturity in the company’s bonds is:$975 = $40(PVIFA R%,40) + $1,000(PVIF R%,40)R = .0413 or 4.13%Since the coupon payments are semiannual, the YTM on the bonds is:YTM = 4.13%× 2YTM = 8.26%b.We can use the Capital Asset Pricing Model to find the return on unlevered equity.According to the Capital Asset Pricing Model:R0 = R F+ βUnlevered(R M– R F)R0 = 5% + 1.1(12% – 5%)R0 = 12.70%Now we can find the cost of levered equity. According to Modigliani-MillerProposition II with corporate taxesR S = R0 + (B/S)(R0– R B)(1 – t C)R S = .1270 + (.40)(.1270 – .0826)(1 – .34)R S = .1387 or 13.87%c.In a world with corporate taxes, a firm’s weighted average cost of capital is equalto:R WACC = [B / (B + S)](1 – t C)R B + [S / (B + S)]R SThe problem does not provide either the debt-value ratio or equity-value ratio.H owever, the firm’s debt-equity ratio of is:B/S = 0.40Solving for B:B = 0.4SSubstituting this in the debt-value ratio, we get:B/V = .4S / (.4S + S)B/V = .4 / 1.4B/V = .29And the equity-value ratio is one minus the debt-value ratio, or:S/V = 1 – .29S/V = .71So, the WACC for the company is:R WACC = .29(1 – .34)(.0826) + .71(.1387) R WACC = .1147 or 11.47%5. a.The equity beta of a firm financed entirely by equity is equal to its unlevered beta.Since each firm has an unlevered beta of 1.25, we can find the equity beta for each.Doing so, we find:North PoleβEquity = [1 + (1 – t C)(B/S)]βUnleveredβEquity = [1 + (1 – .35)($2,900,000/$3,800,000](1.25)βEquity = 1.87South PoleβEquity = [1 + (1 – t C)(B/S)]βUnleveredβEquity = [1 + (1 – .35)($3,800,000/$2,900,000](1.25)βEquity = 2.31b.We can use the Capital Asset Pricing Model to find the required return on eachfirm’s equity. Doing so, we find:North Pole:R S = R F+ βEquity(R M– R F)R S = 5.30% + 1.87(12.40% – 5.30%)R S = 18.58%South Pole:R S = R F+ βEquity(R M– R F)R S = 5.30% + 2.31(12.40% – 5.30%)R S = 21.73%6. a.If flotation costs are not taken into account, the net present value of a loan equals:NPV Loan = Gross Proceeds – Aftertax present value of interest and principalpaymentsNPV Loan = $5,350,000 – .08($5,350,000)(1 – .40)PVIFA8%,10– $5,350,000/1.0810NPV Loan = $1,148,765.94b.The flotation costs of the loan will be:Flotation costs = $5,350,000(.0125)Flotation costs = $66,875So, the annual flotation expense will be:Annual flotation expense = $66,875 / 10 Annual flotation expense = $6,687.50If flotation costs are taken into account, the net present value of a loan equals:NPV Loan = Proceeds net of flotation costs – Aftertax present value of interest andprincipalpayments + Present value of the flotation cost tax shieldNPV Loan = ($5,350,000 – 66,875) – .08($5,350,000)(1 – .40)(PVIFA8%,10)– $5,350,000/1.0810 + $6,687.50(.40)(PVIFA8%,10)NPV Loan = $1,099,840.407.First we need to find the aftertax value of the revenues minus expenses. The aftertaxvalue is:Aftertax revenue = $3,800,000(1 – .40)Aftertax revenue = $2,280,000Next, we need to find the depreciation tax shield. The depreciation tax shield each year is:Depreciation tax shield = Depreciation(t C)Depreciation tax shield = ($11,400,000 / 6)(.40)Depreciation tax shield = $760,000Now we can find the NPV of the project, which is:NPV = Initial cost + PV of depreciation tax shield + PV of aftertax revenueTo find the present value of the depreciation tax shield, we should discount at the risk-free rate, and we need to discount the aftertax revenues at the cost of equity, so:NPV = –$11,400,000 + $760,000(PVIFA6%,6) + $2,280,000(PVIFA14%,6)NPV = $1,203,328.438.Whether the company issues stock or issues equity to finance the project is irrelevant.The company’s optimal capital structure determines the WACC. In a world wi th corporate taxes, a firm’s weighted average cost of capital equals:R WACC = [B / (B + S)](1 – t C)R B + [S / (B + S)]R SR WACC = .80(1 – .34)(.072) + .20(.1140)R WACC = .0608 or 6.08%Now we can use the weighted average cost of capital to discount NEC’s unlevered cash flows. Doing so, we find the NPV of the project is:NPV = –$40,000,000 + $2,600,000 / 0.0608NPV = $2,751,907.399. a.The company has a capital structure with three parts: long-term debt, short-termdebt, and equity. Since interest payments on both long-term and short-term debt aretax-deductible, multiply the pretax costs by (1 – t C) to determine the aftertax coststo be used in the weighted average cost of capital calculation. The WACC using thebook value weights is:R WACC = (w STD)(R STD)(1 – t C) + (w LTD)(R LTD)(1 – t C) + (w Equity)(R Equity)R WACC = ($3 / $19)(.035)(1 – .35) + ($10 / $19)(.068)(1 – .35) + ($6 / $19)(.145)R WACC = 0.0726 or 7.26%ing the market value weights, the company’s WACC is:R WACC = (w STD)(R STD)(1 – t C) + (w LTD)(R LTD)(1 – t C) + (w Equity)(R Equity)R WACC = ($3 / $40)(.035)(1 – .35) + ($11 / $40)(.068)(1 – .35) + ($26 / $40)(.145) R WACC = 0.1081 or 10.81%ing the target debt-equity ratio, the target debt-value ratio for the company is:B/S = 0.60B = 0.6SSubstituting this in the debt-value ratio, we get:B/V = .6S / (.6S + S)B/V = .6 / 1.6B/V = .375And the equity-value ratio is one minus the debt-value ratio, or:S/V = 1 – .375S/V = .625We can use the ratio of short-term debt to long-term debt in a similar manner to find the short-term debt to total debt and long-term debt to total debt. Using the short-term debt to long-term debt ratio, we get:STD/LTD = 0.20STD = 0.2LTDSubstituting this in the short-term debt to total debt ratio, we get:STD/B = .2LTD / (.2LTD + LTD)STD/B = .2 / 1.2STD/B = .167And the long-term debt to total debt ratio is one minus the short-term debt to total debt ratio, or:LTD/B = 1 – .167LTD/B = .833Now we can find the short-term debt to value ratio and long-term debt to value ratio by multiplying the respective ratio by the debt-value ratio. So:STD/V = (STD/B)(B/V) STD/V = .167(.375) STD/V = .063And the long-term debt to value ratio is:LTD/V = (LTD/B)(B/V)LTD/V = .833(.375)LTD/V = .313So, using the target capital structure weights, the company’s WACC is:R WACC = (w STD)(R STD)(1 – t C) + (w LTD)(R LTD)(1 – t C) + (w Equity)(R Equity)R WACC = (.06)(.035)(1 – .35) + (.31)(.068)(1 – .35) + (.625)(.145)R WACC = 0.1059 or 10.59%d.The differences in the WACCs are due to the different weighting schemes. Thecompany’s WACC will most closely resemble the WACC calculated using targetweights since future projects will be financed at the target ratio. Therefore, theWACC computed with target weights should be used for project evaluation.Intermediate10.The adjusted present value of a project equals the net present value of the project underall-equity financing plus the net present value of any financing side effects. In the joint venture’s case, the NPV of financing side effects equals the aftertax present value of cash flows resulting from the firms’ debt. So, the APV is:APV = NPV(All-Equity) + NPV(Financing Side Effects)The NPV for an all-equity firm is:NPV(All-Equity)NPV = –Initial Investment + PV[(1 – t C)(EBITD)] + PV(Depreciation Tax Shield)Since the initial investment will be fully depreciated over five years using the straight-line method, annual depreciation expense is:Annual depreciation = $30,000,000/5Annual depreciation = $6,000,000NPV = –$30,000,000 + (1 – 0.35)($3,800,000)PVIFA5.13%,20 +(0.35)($6,000,000)PVIFA5,13%,20NPV = –$5,262,677.95NPV(Financing Side Effects)The NPV of financing side effects equals the after-tax present value of cash flows resulting from the firm’s debt. The coupon rate on the debt is relevant to determine the interest payments, but the resulting cash flows should still be discounted at the pretax cost of debt. So, the NPV of the financing effects is:NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Repayments)NPV = $18,000,000 – (1 – 0.35)(0.05)($18,000,000)PVIFA8.5%,15– $18,000,000/1.08515 NPV = $7,847,503.56So, the APV of the project is:APV = NPV(All-Equity) + NPV(Financing Side Effects)APV = –$5,262,677.95 + $7,847,503.56APV = $2,584,825.6111.If the company had to issue debt under the terms it would normally receive, the interestrate on the debt would increase to the company’s normal cost of debt. The NPV of an all-equity project would remain unchanged, but the NPV of the financing side effects would change. The NPV of the financing side effects would be:NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Repayments)NPV = $18,000,000 – (1 – 0.35)(0.085)($18,000,000)PVIFA8.5%,15–$18,000,000/((1.085)15NPV = $4,446,918.69Using the NPV of an all-equity project from the previous problem, the new APV of the project would be:APV = NPV(All-Equity) + NPV(Financing Side Effects)APV = –$5,262,677.95 + $4,446,918.69APV = –$815,759.27The gain to the company from issuing subsidized debt is the difference between the two APVs, so:Gain from subsidized debt = $2,584,825.61 – (–815,759.27)Gain from subsidized debt = $3,400,584.88Most of the value of the project is in the form of the subsidized interest rate on the debt issue.12.The adjusted present value of a project equals the net present value of the project underall-equity financing plus the net present value of any financing side effects. First, we need to calculate the unlevered cost of equity. According to Modigliani-Miller Proposition II with corporate taxes:R S = R0 + (B/S)(R0– R B)(1 – t C).16 = R0 + (0.50)(R0– 0.09)(1 – 0.40)R0 = 0.1438 or 14.38%Now we can find the NPV of an all-equity project, which is:NPV = PV(Unlevered Cash Flows)NPV = –$21,000,000 + $6,900,000/1.1438 + $11,000,000/(1.1438)2 +$9,500,000/(1.1438)3NPV = –$212,638.89Next, we need to find the net present value of financing side effects. This is equal the aftertax present value of cash flows resulting from the firm’s debt. So:NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Payments)Each year, an equal principal payment will be made, which will reduce the interest accrued during the year. Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt, so the NPV of the financing effects are:NPV = $7,000,000 – (1 – .40)(.09)($7,000,000) / (1.09) – $2,333,333.33/(1.09)– (1 – .40)(.09)($4,666,666.67)/(1.09)2– $2,333,333.33/(1.09)2– (1 – .40)(.09)($2,333,333.33)/(1.09)3– $2,333,333.33/(1.09)3 NPV = $437,458.31So, the APV of project is:APV = NPV(All-equity) + NPV(Financing side effects)APV = –$212,638.89 + 437,458.31APV = $224,819.4213. a.To calculate the NPV of the project, we first need to find the company’s WACC. Ina world with corporate taxes, a firm’s weighted average cost of ca pital equals:R WACC = [B / (B + S)](1 – t C)R B + [S / (B + S)]R SThe market value of the company’s equity is:Market value of equity = 6,000,000($20)Market value of equity = $120,000,000So, the debt-value ratio and equity-value ratio are:Debt-value = $35,000,000 / ($35,000,000 + 120,000,000)Debt-value = .2258Equity-value = $120,000,000 / ($35,000,000 + 120,000,000)Equity-value = .7742Since the CEO believes its current capital structure is optimal, these values can beused as the target weights in the firm’s weighted average cost of capital calculation.The yield to maturity of the company’s debt is its pretax cost of debt. To find thecompany’s cost of equity, we need to calculate the stock beta. The stock beta can becalculated as:β = σS,M / σ2Mβ = .036 / .202β = 0.90Now we can use the Capital Asset Pricing Model to determine the cost of equity. The Capital Asset Pricing Model is:R S = R F+ β(R M– R F)R S = 6% + 0.90(7.50%)R S = 12.75%Now, we can calculate the company’s WACC, which is:R WACC = [B / (B + S)](1 – t C)R B + [S / (B + S)]R SR WACC = .2258(1 – .35)(.08) + .7742(.1275)R WACC = .1105 or 11.05%Finally, we can use the WACC to discount the unlevered cash flows, which givesus an NPV of:NPV = –$45,000,000 + $13,500,000(PVIFA11.05%,5)NPV = $4,837,978.59b.The weighted average cost of capital used in part a will not change if the firmchooses to fund the project entirely with debt. The weighted average cost of capitalis based on optimal capital structure weights. Since the current capital structure isoptimal, all-debt funding for the project simply implies that the firm will have touse more equity in the future to bring the capital structure back towards the target.Challenge14. a.The company is currently an all-equity firm, so the value as an all-equity firmequals the present value of aftertax cash flows, discounted at the cost of the firm’sunlevered cost of equity. So, the current value of the company is:V U = [(Pretax earnings)(1 – t C)] / R0V U = [($28,000,000)(1 – .35)] / .20V U = $91,000,000The price per share is the total value of the company divided by the sharesoutstanding, or:Price per share = $91,000,000 / 1,500,000Price per share = $60.67b.The adjusted present value of a firm equals its value under all-equity financing plusthe net present value of any financing side effects. In this case, the NPV offinancing side effects equals the aftertax present value of cash flows resulting fromthe firm’s debt. Given a known level of debt, debt cash flows can be discounted atthe pretax cost of debt, so the NPV of the financing effects are:NPV = Proceeds – Aftertax PV(Interest Payments)NPV = $35,000,000 – (1 – .35)(.09)($35,000,000) / .09NPV = $12,250,000So, the value of the company after the recapitalization using the APV approach is:V = $91,000,000 + 12,250,000V = $103,250,000Since the company has not yet issued the debt, this is also the value of equity after the announcement. So, the new price per share will be:New share price = $103,250,000 / 1,500,000New share price = $68.83c.The company will use the entire proceeds to repurchase equity. Using the shareprice we calculated in part b, the number of shares repurchased will be:Shares repurchased = $35,000,000 / $68.83Shares repurchased = 508,475And the new number of shares outstanding will be:New shares outstanding = 1,500,000 – 508,475New shares outstanding = 991,525The value of the company increased, but part of that increase will be funded by the new debt. The value of equity after recapitalization is the total value of thecompany minus the value of debt, or:New value of equity = $103,250,000 – 35,000,000New value of equity = $68,250,000So, the price per share of the company after recapitalization will be:New share price = $68,250,000 / 991,525New share price = $68.83The price per share is unchanged.d.In order to v alue a firm’s equity using the flow-to-equity approach, we mustdiscount the cash flows available to equity holders at the cost of the firm’s levered equity. According to Modigliani-Miller Proposition II with corporate taxes, the required return of levered equity is:R S = R0 + (B/S)(R0– R B)(1 – t C)R S = .20 + ($35,000,000 / $68,250,000)(.20 – .09)(1 – .35)R S = .2367 or 23.67%After the recapitalization, the net income of the company will be:EBIT $28,000,000Interest 3,150,000EBT $24,850,000 Taxes 8,697,500 Net incomeThe firm pays all of its earnings as dividends, so the entire net income is availableto shareholders. Using the flow-to-equity approach, the value of the equity is:S = Cash flows available to equity holders / R SS = $16,152,500 / .2367S = $68,250,00015. a.If the company were financed entirely by equity, the value of the firm would beequal to the present value of its unlevered after-tax earnings, discounted at itsunlevered cost of capital. First, we need to find the company’s unlevered cash flows,which are:Sales $28,900,000Variable costs 17,340,000EBT $11,560,000Tax 4,624,000Net incomeSo, the value of the unlevered company is:V U = $6,936,000 / .17V U = $40,800,000b.According to Modigliani-Miller Proposition II with corporate taxes, the value oflevered equity is:R S = R0 + (B/S)(R0– R B)(1 – t C)R S = .17 + (.35)(.17 – .09)(1 – .40)R S = .1868 or 18.68%c.In a world with corporate taxes, a firm’s weighted average cost of capital equals:R WACC = [B / (B + S)](1 – t C)R B + [S / (B + S)]R SSo we need the debt-value and equity-value ratios for the company. The debt-equityratio for the company is:B/S = 0.35B = 0.35SSubstituting this in the debt-value ratio, we get:B/V = .35S / (.35S + S)B/V = .35 / 1.35B/V = .26And the equity-value ratio is one minus the debt-value ratio, or:S/V = 1 – .26S/V = .74So, using the capital structure weights, the comp any’s WACC is:R WACC = [B / (B + S)](1 – t C)R B + [S / (B + S)]R SR WACC = .26(1 – .40)(.09) + .74(.1868)R WACC = .1524 or 15.24%We can use the weighted average cost of capital to discount the firm’s unlevered aftertax earnings to value the company. Doing so, we find:V L = $6,936,000 / .1524V L = $45,520,661.16Now we can use the debt-value ratio and equity-value ratio to find the value of debt and equity, which are:B = V L(Debt-value)B = $45,520,661.16(.26)B = $11,801,652.89S = V L(Equity-value)S = $45,520,661.16(.74)S = $33,719,008.26d.In order to value a firm’s equity using the flow-to-equity approach, we can discountthe cash flows available to equity holders at the cost of the firm’s levered equity.First, we need to calculate the levered cash flows available to shareholders, which are:Sales $28,900,000Variable costs 17,340,000EBIT $11,560,000Interest 1,062,149EBT $10,497,851Tax 4,199,140Net incomeSo, the value of equity with the flow-to-equity method is:S = Cash flows available to equity holders / R SS = $6,298,711 / .1868 S = $33,719,008.2616. a.Since the company is currently an all-equity firm, its value equals the present valueof its unlevered after-tax earnings, discounted at its unlevered cost of capital. Thecash flows to shareholders for the unlevered firm are:EBIT $83,000Tax 33,200Net incomeSo, the value of the company is:V U = $49,800 / .15V U = $332,000b.The adjusted present value of a firm equals its value under all-equity financing plusthe net present value of any financing side effects. In this case, the NPV offinancing side effects equals the after-tax present value of cash flows resulting fromdebt. Given a known level of debt, debt cash flows should be discounted at thepre-tax cost of debt, so:NPV = Proceeds – Aftertax PV(Interest payments)NPV = $195,000 – (1 – .40)(.09)($195,000) / 0.09NPV = $78,000So, using the APV method, the value of the company is:APV = V U + NPV(Financing side effects)APV = $332,000 + 78,000APV = $410,000The value of the debt is given, so the value of equity is the value of the companyminus the value of the debt, or:S = V – BS = $410,000 – 195,000S = $215,000c.According to Modigliani-Miller Proposition II with corporate taxes, the requiredreturn of levered equity is:R S = R0 + (B/S)(R0– R B)(1 – t C)R S = .15 + ($195,000 / $215,000)(.15 – .09)(1 – .40)R S = .1827 or 18.27%d.In order to value a firm’s equity using the flow-to-equity approach, we can discountthe cash flows available to equity holders at the cost of the firm’s levered equity.First, we need to calculate the levered cash flows available to shareholders, whichare:EBIT $83,000Interest 17,550EBT $65,450Tax 26,180Net incomeSo, the value of equity with the flow-to-equity method is:S = Cash flows available to equity holders / R SS = $39,270 / .1827S = $215,00017.Since the company is not publicly traded, we need to use the industry numbers tocalculate the industry levered return on equity. We can then find the industry unlevered return on equity, and re-lever the industry return on equity to account for the different use of leverage. So, using the CAPM to calculate the industry levered return on equity, we find:R S = R F+ β(MRP)R S = 5% + 1.2(7%)R S = 13.40%Next, to find the average cost of unlevered equity in the holiday gift industry we can use Modigliani-Miller Proposition II with corporate taxes, so:R S = R0 + (B/S)(R0– R B)(1 – t C).1340 = R0 + (.35)(R0– .05)(1 – .40)R0 = .1194 or 11.94%Now, we can use the Modigliani-Miller Proposition II with corporate taxes to re-lever the return on equity to account for this company’s debt-equity ratio. Doing so, we find:R S = R0 + (B/S)(R0– R B)(1 – t C)R S = .1194 + (.40)(.1194 – .05)(1 – .40)R S = .1361 or 13.61%Since the project is financed at the firm’s target debt-equity ratio, it must be discounted at t he company’s weighted average cost of capital. In a world with corporate taxes, a firm’s weighted average cost of capital equals:。

证照管理指南英文

证照管理指南英文1. What is the purpose of license management?The purpose of license management is to ensure that all necessary licenses and permits are obtained and kept up-to-date in order to comply with legal and regulatory requirements. This includes maintaining accurate records of all licenses and permits, tracking renewal deadlines and ensuring that all licenses and permits are renewed in a timely manner.证照管理的目的是为了确保所有必要的证照和许可证得到并及时更新，以遵守法律和监管要求。

这包括保持所有证照和许可证的准确记录，追踪更新截止日期，并确保所有证照和许可证及时更新。

2. What types of licenses and permits do businesses need to obtain?The types of licenses and permits required by businesses can vary depending on the industry, location and type of business. Some common examples include business licenses, permits for specific activities such as building permits or food service permits, environmental permits, andprofessional licenses for certain occupations such as doctors or lawyers.企业需要取得的证照和许可证的类型因行业、地点和业务类型而异。

学生应该怎样使用电脑英语作文

学生应该怎样使用电脑英语作文Computers have become an integral part of modern education. They have revolutionized the way students learn, access information, and complete their academic tasks. However, the use of computers by students is a complex issue that requires careful consideration. While computers offer numerous benefits, they also come with potential risks if not used responsibly. In this essay, we will explore how students should use computers to maximize their educational experience while minimizing the drawbacks.Firstly, computers provide students with unprecedented access to a wealth of information. The internet has become a vast repository of knowledge, allowing students to research topics, access online libraries, and explore a wide range of subjects beyond the confines of their curriculum. This access to information empowers students to delve deeper into their areas of interest, foster critical thinking, and develop a more comprehensive understanding of the world around them. By effectively utilizing search engines, online databases, and educational websites, students can expand their knowledge and stay up-to-date with the latest developments in their fields of study.Moreover, computers have revolutionized the way students complete their academic tasks. Word processing software enables students to write and format their assignments with ease, while presentation tools allow them to create engaging and visually appealing projects. Spreadsheet programs facilitate the organization and analysis of data, enabling students to tackle complex mathematical and statistical problems. Additionally, collaborative tools, such as cloud-based platforms, enable students to work together on group projects, share resources, and receive real-time feedback from their peers and instructors.However, the use of computers in education is not without its challenges. One significant concern is the potential for distraction. With access to social media, online entertainment, and a vast array of digital distractions, students may find it challenging to maintain focus and stay on task. It is crucial for students to develop self-discipline and time management skills to ensure that their computer use is primarily directed towards educational pursuits and not recreational activities.Another concern is the risk of cyberbullying and online safety. Students must be aware of the potential dangers of online interactions and be equipped with the knowledge and skills to navigate the digital world safely. Schools and parents should worktogether to educate students on internet safety, digital citizenship, and responsible online behavior, empowering them to protect themselves and others from harmful online experiences.Furthermore, excessive computer use can have negative impacts on students' physical and mental health. Prolonged sitting, eye strain, and poor posture can lead to various health issues. It is essential for students to practice good ergonomics, take regular breaks, and balance their computer use with physical activity and other leisure pursuits to maintain a healthy lifestyle.To address these challenges, students should adopt a balanced and responsible approach to using computers in their academic endeavors. They should prioritize the educational benefits of computers while developing strategies to minimize the potential drawbacks. This can be achieved through the following practices:1. Establishing a designated study area: Students should create a dedicated workspace, free from distractions, where they can focus on their computer-based tasks.2. Practicing time management: Students should set clear boundaries and schedules for their computer use, ensuring that they allocate sufficient time for study, leisure, and physical activity.3. Developing self-discipline: Students should cultivate the ability to resist the temptation of digital distractions and maintain their focus on educational objectives.4. Embracing a diverse learning approach: While computers are valuable tools, students should not solely rely on them for their learning. They should also engage in traditional learning methods, such as reading physical books, participating in discussions, and hands-on activities.5. Prioritizing physical and mental well-being: Students should take regular breaks, exercise, and engage in activities that promote their overall health and well-being to counteract the potential negative effects of prolonged computer use.6. Seeking guidance and support: Students should not hesitate to seek assistance from teachers, school counselors, or IT professionals when they encounter challenges or have questions about the responsible use of computers in their academic pursuits.In conclusion, the use of computers in education is a complex and multifaceted issue. While computers offer numerous benefits, students must approach their use with care and responsibility. By adopting a balanced approach, developing self-discipline, and prioritizing their physical and mental well-being, students canharness the power of computers to enhance their educational experience and achieve academic success. As the digital landscape continues to evolve, it is crucial for students to cultivate the skills and mindset necessary to navigate the ever-changing technological landscape effectively.。

关于学生如何使用电脑的英语作文

关于学生如何使用电脑的英语作文全文共3篇示例，供读者参考篇1Computers and How Students Can Make the Most of ThemAs a student in the digital age, computers have become an integral part of my life and education. From conducting research to writing papers, creating presentations, and even taking classes online, these powerful machines have revolutionized the way we learn and interact with information. However, merely owning a computer is not enough; it's how we utilize these tools that truly matters. In this essay, I'll share my insights and experiences on how students like myself can make the most out of our computer usage.First and foremost, it's crucial to have a solid understanding of the software and applications available to us. Word processing programs like Microsoft Word or Google Docs are essential for writing papers, essays, and reports. These tools not only allow us to type and format our work seamlessly but also offer features like spell-check, grammar assistance, and even citationmanagement, which can greatly improve the quality of our written assignments.Spreadsheet applications, such as Microsoft Excel or Google Sheets, are invaluable for organizing and analyzing data. Whether it's keeping track of our grades, budgeting for expenses, or working with large datasets for research projects, these programs provide a structured and efficient way to manage and manipulate information.Presentation software like Microsoft PowerPoint or Google Slides is a must-have for creating visually appealing and engaging presentations. These tools allow us to combine text, images, videos, and animations, making it easier to convey complex ideas and concepts to our classmates and instructors.In addition to these core productivity tools, there are countless educational resources and applications available online that can enhance our learning experience. Online libraries and databases provide access to a wealth of scholarly articles, journals, and e-books, enabling us to conduct in-depth research on any topic imaginable.Educational websites and platforms like Khan Academy, Coursera, and edX offer a vast array of video lectures, interactive exercises, and even full-fledged online courses on varioussubjects. These resources can supplement our traditional classroom learning, allowing us to explore topics of interest at our own pace and reinforce our understanding of challenging concepts.Furthermore, computers have enabled new forms of collaboration and communication among students and instructors. Online forums, discussion boards, and messaging platforms facilitate the exchange of ideas, questions, and feedback, fostering a more interactive and engaged learning community.However, with all these powerful tools at our disposal, it's easy to become distracted or overwhelmed. Time management and self-discipline are essential when using computers for academic purposes. Setting specific goals, creating schedules, and utilizing productivity apps like Pomodoro timers or website blockers can help us stay focused and avoid procrastination.It's also crucial to develop strong digital literacy skills, such as evaluating the credibility of online sources, understanding copyright and fair use policies, and practicing good cybersecurity habits to protect our personal information and devices from potential threats.While computers have undoubtedly transformed the educational landscape, it's important to recognize that they are tools, and like any tool, they should be used responsibly and effectively. Striking a balance between digital and traditional learning methods is key to ensuring a well-rounded and enriching educational experience.In conclusion, as students in the digital age, we have an incredible opportunity to leverage the power of computers to enhance our learning, productivity, and creativity. By mastering the essential software and applications, exploring online educational resources, fostering collaboration and communication, and practicing good time management and digital literacy skills, we can truly make the most of these remarkable tools and excel in our academic pursuits.篇2Computers Have Become an Indispensable Tool for StudentsAs a student in the 21st century, it's hard to imagine life without computers. These amazing devices have become an integral part of our academic journey, transforming the way we learn, research, and communicate. In this essay, I'll share myinsights on how students like myself can effectively utilize computers to enhance our educational experiences.First and foremost, computers have revolutionized the way we access information. Gone are the days when we had to rely solely on physical libraries and textbooks. With just a few clicks, we can explore a vast ocean of knowledge on the internet. Online databases, academic journals, and educational websites provide us with an incredible wealth of resources, allowing us to delve deeper into any subject we're studying.One of the most significant advantages of computers for students is their ability to facilitate research and writing. Word processing software has made it incredibly easy to organize our thoughts, edit and format our work, and collaborate with classmates on group projects. Additionally, citation tools and online libraries have streamlined the process of researching and properly crediting sources, ensuring academic integrity.Computers have also transformed the way we engage with multimedia content. Educational videos, interactive simulations, and virtual reality experiences have made learning more immersive and engaging than ever before. We can visualize complex concepts, explore historical events, and even conduct virtual experiments, all from the comfort of our desks.Moreover, computers have played a crucial role in enabling remote learning opportunities. During times of crisis, such as the COVID-19 pandemic, online learning platforms and video conferencing tools have allowed us to continue our education without interruption. We can attend virtual classes, participate in discussions, and even take exams remotely, ensuring that our academic progress is not hindered by external circumstances.However, it's important to note that while computers offer incredible advantages, they also come with challenges. Distractions from social media, online gaming, and other digital diversions can easily derail our focus and productivity. It's essential to develop self-discipline and time management skills to strike a balance between our academic responsibilities and leisure activities.Another potential pitfall is the overreliance on technology. While computers are powerful tools, they should not replace critical thinking and analytical skills. We must learn to evaluate the information we find online, cross-reference sources, and form our own informed opinions. Additionally, we should cultivate digital literacy and understand the ethical implications of using technology, such as respecting copyright laws and maintaining online privacy and security.Despite these challenges, the benefits of computers for students far outweigh the drawbacks. By embracing these technologies responsibly and strategically, we can unlock our full academic potential. Whether it's collaborating on group projects using cloud-based tools, creating visually stunning presentations, or analyzing complex data sets, computers have become an indispensable tool for modern learners.In conclusion, as students in the digital age, we are fortunate to have access to such powerful tools that can enhance our educational experiences. By leveraging the capabilities of computers while maintaining a balanced approach, we can not only excel academically but also develop valuable skills that will serve us well in our future careers and endeavors. Embracing technology while cultivating critical thinking and ethical practices is the key to unlocking the full potential of computers in our academic pursuits.篇3How to Make the Most of Computers as a StudentAs a student in today's digital age, computers have become an indispensable tool for learning, research, and productivity. From writing essays and creating presentations to collaboratingwith classmates and accessing a wealth of online resources, computers offer a myriad of opportunities to enhance our academic experience. However, with great power comes great responsibility, and it's crucial to understand how to harness the full potential of these digital devices while avoiding potential pitfalls. In this essay, I will share my perspectives and insights on how students can effectively utilize computers to maximize their academic success.First and foremost, it's important to recognize that computers are not just mere tools but powerful engines of knowledge and discovery. With a few keystrokes, we can access a vast array of information on virtually any topic imaginable. This access to knowledge is both a blessing and a curse – while it empowers us to learn and explore, it also presents the challenge of navigating through an overwhelming amount of information. As students, we must develop critical thinking skills to evaluate the credibility and reliability of online sources, separating fact from fiction and valuable insights from misinformation.One of the most significant advantages of computers in academia is their ability to streamline and enhance productivity. Word processing software, such as Microsoft Word or Google Docs, allows us to create well-structured and professionallyformatted documents with ease. Presentation tools like PowerPoint or Prezi enable us to create engaging and visually appealing presentations that can captivate audiences and effectively convey our ideas. Spreadsheet applications, like Excel, are invaluable for data analysis, calculations, and creating graphs and charts, which can be particularly useful in fields like mathematics, science, and business.Collaboration is another area where computers truly shine. Online collaborative platforms, such as Google Drive or Microsoft Teams, facilitate seamless teamwork, allowing multiple students to work on the same document simultaneously, share files, and communicate effectively. This not only enhances productivity but also fosters teamwork and communication skills, which are essential in both academic and professional settings.Furthermore, computers provide access to a wealth of educational resources, including online libraries, educational websites, and multimedia content. Resources like Khan Academy, Coursera, and edX offer a plethora of free online courses, tutorials, and educational videos, enabling students to supplement their classroom learning and explore topics of interest at their own pace. Additionally, many universities and colleges offer online databases and digital libraries, providingstudents with access to a vast array of scholarly articles, journals, and research materials.However, as with any powerful tool, computers also present potential pitfalls and distractions that can hinder our academic progress. Social media, online gaming, and mindless web browsing can quickly consume our time and attention, leading to procrastination and poor time management. It's crucial to develop self-discipline and establish boundaries to ensure that our computer usage remains focused and productive.To effectively manage these distractions, I recommend setting specific goals and time limits for computer usage. Create a dedicated workspace that is free from distractions and use productivity apps or website blockers to restrict access tonon-essential websites during study or work periods. Additionally, it's important to take regular breaks and engage in physical activity to prevent eye strain, muscle tension, and mental fatigue.Another potential challenge with computer usage is the temptation to engage in academic dishonesty, such as plagiarism or cheating. While the internet provides a wealth of information, it's essential to understand and respect intellectual property rights and academic integrity guidelines. Alwaysproperly cite sources, use plagiarism detection tools, and adhere to ethical standards when utilizing online resources.In conclusion, computers are powerful tools that can significantly enhance our academic experience as students. By leveraging their capabilities for research, productivity, collaboration, and access to educational resources, we can unlock new levels of learning and achievement. However, it's crucial to develop critical thinking skills, maintain focus andself-discipline, and uphold ethical standards to avoid potential pitfalls. As students, it's our responsibility to use computers responsibly and effectively, harnessing their power to support our academic growth and success.。

面对很多选择做决定英语作文

面对很多选择做决定英语作文英文回答：When confronted with a multitude of choices, the path to making a well-informed decision can be fraught with uncertainty. However, through careful consideration and a systematic approach, one can navigate this intricate maze and arrive at a decision that aligns with their values and objectives.To begin, it is essential to gather as much information as possible about each choice. This may involve conducting thorough research, consulting with experts, and seeking perspectives from those who have experience in the relevant field. By gaining a comprehensive understanding of the potential outcomes associated with each option, you can make a more informed assessment of their respective merits and drawbacks.Once you have gathered sufficient information, the nextstep is to identify your priorities and values. What arethe most important factors that you want to consider inyour decision-making process? What are your non-negotiables? By establishing clear criteria, you can effectively filter out less desirable options and narrow down your choices.With your priorities in mind, it is time to critically evaluate each choice. Consider both the potential benefits and risks associated with each option. Weigh the pros and cons carefully, and assess how each choice aligns with your values and goals. It may be helpful to create a table or spreadsheet to compare the different options side by side.While it is important to be rational and analytical in your decision-making process, it is equally important to listen to your intuition. Sometimes, our gut instinct can provide valuable insights that may not be apparent througha purely logical analysis. Trust your judgment and pay attention to the inner voice that guides you.However, it is also crucial to be aware of potential cognitive biases that may influence your decision-makingprocess. Heuristics and biases can lead us to makeirrational choices, so it is important to be mindful of these potential pitfalls and make conscious efforts to mitigate their impact.Once you have carefully considered all the available information and evaluated each choice, it is time to make a decision. Be confident in your choice and do not second-guess yourself unnecessarily. Remember that every decision carries some degree of risk, and the best decision is the one that you make with conviction and clarity of purpose.中文回答：面对琳琅满目的选择，做出明智的决定并非易事。

房地产材料表格模板

房地产材料表格模板英文回答：Real Estate Material Spreadsheet Template.Introduction:In the real estate industry, keeping track of various materials and their costs is crucial for effective project management. To streamline this process, I have developed a comprehensive spreadsheet template that can be used to record and analyze real estate materials. This template is designed to provide a systematic approach to managing materials, ensuring transparency, and facilitating cost control.Features of the Template:1. Material Inventory:The template includes a dedicated section for recording the details of each material used in a project. This section allows you to enter the material name, quantity, unit price, and supplier information. By maintaining an updated inventory, you can easily track the availability and cost of materials.2. Cost Analysis:The template provides an automatic cost analysis feature that calculates the total cost of each material based on the quantity and unit price entered. This allows you to monitor the overall expenditure on materials and make informed decisions regarding cost control.3. Supplier Management:Efficient supplier management is essential for ensuring timely delivery and competitive pricing. The template includes a section where you can record supplier details, such as contact information, payment terms, and delivery schedules. This information helps you maintain a goodrelationship with suppliers and negotiate better deals.4. Project-specific Material Lists:The template allows you to create project-specific material lists by categorizing materials based on their usage. For example, you can create separate lists for plumbing materials, electrical materials, and finishing materials. This helps in organizing materials and facilitates easy retrieval when needed.5. Budget Tracking:To ensure that your project stays within budget, the template includes a budget tracking feature. You can set a budget for each material category and track the actual expenditure against the allocated budget. This helps in identifying any deviations and taking corrective measures to control costs.6. Reporting and Analysis:The template generates comprehensive reports and charts to provide a visual representation of material costs, supplier performance, and budget utilization. These reports help in identifying trends, making data-driven decisions, and presenting project progress to stakeholders.中文回答：房地产材料表格模板。

高中英语数据处理单选题30题

高中英语数据处理单选题30题1. When collecting data, we need to make sure the information is _____.A. accurateB. inaccurateC. approximatelyD. inaccurately答案：A。

本题考查形容词的用法。

“accurate”表示“准确的”，符合收集数据时对信息的要求。

“inaccurate”表示“不准确的”，与题意相悖。

“approximately”是副词“大约”，不符合此处语境。

“inaccurately”是副词形式，也不正确，此处需要形容词修饰“information”。

2. In the process of data collection, we should ______ all the relevant details.A. includeB. excludeC. concludeD. refuse答案：A。

“include”意思是“包括”，在数据收集过程中应该包括所有相关细节。

“exclude”表示“排除”，不符合。

“conclude”意为“得出结论”。

“refuse”是“拒绝”，均不符合数据收集的语境。

3. Before整理data, we need to ______ it first.A. classifyB. realizeC. recognizeD. memorize答案：A。

“classify”有“分类”的意思，整理数据前先分类。

“realize”是“意识到”，“recognize”是“认出”，“memorize”是“记住”，都不符合整理数据前的动作。

4. To collect useful data, we have to ______ a proper method.A. chooseB. loseC. refuseD. use答案：A。

“choose”是“选择”，收集有用数据要选择合适方法。

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A Spreadsheet Approach to Information VisualizationEd Huai-hsin Chi,Joseph Konstan,Phillip Barry,John RiedlDepartment of Computer Science,University of Minnesota4-192EE/CS Building,200Union St.SE,Minneapolis,MN55455echi,konstan,barry,riedl@ABSTRACTIn information visualization,as the volume and complexity of the data increases,researchers require more powerful vi-sualization tools that allow them to more effectively explore multi-dimensional datasets.In this paper,we show a novel new visualization framework built upon the spreadsheet meta-phor,where each cell can contain an entire dataset.Just as a numerical spreadsheet enables exploration of numbers,a vi-sualization spreadsheet enables exploration of visualizations of data.Our prototype spreadsheets enabled users to compare visualizations in cells using the tabular ers can use the spreadsheet to display,manipulate,and explore multiple visual representation techniques for their data.By applying different operations to the cells,we showed how visualiza-tion spreadsheets afford the construction of’what-if’scenar-ios.The possible set of operations that users can apply con-sists of animation,ﬁltering,and algebraic operators. KEYWORDS:Visualization,Information Visualization,In-teractive Graphics,SpreadsheetINTRODUCTIONVisualization research spans a remarkable range of scientiﬁc disciplines and corresponding visualization techniques.Vi-sualization researchers have discovered that certain operations are needed across this entire range.These operations include comparing visualizations of two different datasets,as well as performing algebraic operations between two or more visual-izations,such as visualizing the differences between two data-sets.Furthermore,the need to explore multiple visual repre-sentations simultaneously arises especially in information vi-sualization,because different techniques often extract differ-ent visual features and the complexity of the data.A visual-ization spreadsheet is an ideal way to address these issues that involve multiple visualizations.Spreadsheets have proven to be highly successful tools for interacting with numerical data by applying algebraic oper-ations,manipulating rows or columns,and exploring“what–if”scenarios.Spreadsheet techniques have recently been ex-tended from numeric domains to other domains[3,2,5].HereFigure1:Visualization of3D random point generationand Delaunay triangulation of the resulting point set.Thecolumns visualize the outcome of the algorithm after5,6,25,and50steps,respectively.The last row shows the re-sult of several addition operations.For example,Cell(4,4)shows the result of adding all of the cells in Row3together,resulting in a visualization that shows the progress of the al-gorithm by representing the steps using colored tube edges.we show a novel spreadsheet framework designed to support cells containing complex datasets,viewed through powerful information visualizations,with constraints between cells link-ing both data and view attributes.By studying a spreadsheet approach to the display and ex-ploration of scientiﬁc and information visualizations,we can build upon current interaction methods by consolidating all the operations under one paradigm.In this demonstration,we present two prototype systems to illustratesome of the impor-tant capabilities offered by the spreadsheet paradigm.We dis-cuss how spreadsheet techniques can provide a structured,in-tuitive,and powerful interface for investigating information visualizations of abstract multidimensional datasets. VISUALIZATION SPREADSHEETIn this demonstration,we will demonstrate the utility of the spreadsheet paradigm using two prototype spreadsheets.Oneprototype visualization spreadsheet is built on top of VTK[4] and Tcl/Tk,and has several advanced capabilities such as user-deﬁned operators and script language support.This proto-type,which we call the Spreadsheet for Information Visual-ization(SIV),is shown in Figure1.Here we show how a spreadsheet can be used to visualize sev-eral steps of the3D Delaunay triangulation algorithm.This example shows how algorithm visualization can be supported in our visualization spreadsheet.The columns show the re-sults of the algorithm after5,6,25,and50steps,from left to right respectively.The layout is accomplished by loading in a25line script that describes the content of each cell and how they are inter-related.We can utilize multiple visual representations to enhance the comprehensibility of the visualization.Even though each cell in Column1represents the same point set,each cell shows a different view of the data,and extracts different visual fea-tures.Row1shows the point set using3D scatter plots.Row 2shows the same data using transparent tetrahedra after3D Delaunay triangulation has been performed on the point sets. Row3represents the tetrahedra using edges between vertices. The last row aggregates several cells together to form new vi-sualizations.For example,cell(4,1)=(3,2)+(3,1)+(2,2)+(2,1). The combination of geometries from several cells results in visualizations that show differences between successive steps of the algorithm.The aggregation is performed using an addi-tion operator that adds the geometric content in several cells. Subtraction between cells is also available.Another prototype,shown in Figure2,is built for viewing biological sequence similarity reports.The cells are loaded with similarity data for genetic sequences.Each comb glyph within a cell represents an alignment,which is region of sim-ilarity between the input sequence and a sequence from the database[1].The prototypeimplements domain-speciﬁc sub-traction and addition operators to enable users to compare and contrast between different datasets.The user can explore the data further by such means as in-teractively rotating,translating or scaling the representation, following a hyperlink to the textual report,mapping the data into a different geometric representation,animating the infor-mation over a variable,andﬁltering the data.The animation tool providesaccumulative,or sliced animation over any vari-able[1],and adds an extra dimension to the spreadsheet.A synchronized animation can be performed on a group of cells simultaneously.Theﬁltering tool enables the user to explore subsets of the data.When the user interactively adjusts slid-ers controlling each variable,the view is updated in real-time. The mapping tool enables the user to select the variable that she wishes to be represented on the scatter plot axes.Having these capabilities inside the spreadsheet environment enables a wide range of different explorationtasks.Figure2:A screen snapshot of theﬁrst system(SSR)after performing three operations.(Step1)Ini-tially,we loaded each column with a slightly different,but related,dataset(A1=B1=C1=D1,A2=B2=C2=D2,A3=B3=C3=D3).(Step2)We selected Row B,andthen subtracted cell A3from it(B1=B1-A3,B2=B2-A3,B3=B3-A3).Cell B3contains the empty set as ex-pected.(Step3)We changed Row C and D to showdifferent views of Row A.The views show differentsets of variables using a different representation,thusincreasing our ability to see other dimensions of themultivariate datasets simultaneously. AcknowledgmentsThis work has been supported in part by the National Science Foundation under grants BIR940-2380and CDA9414015. REFERENCES1. 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