98 2 Fin Homework Part 04

靜宜大學 98 學年度企管系『財務管理』作業 Part IV 最後更新日期：2010 年 6 月 21 日 第1題 MM Propositions （第 15 章，#23，452 頁。） Locomotive Corporation is planning to repurchase part of its common stock by issuing corporate debt. As a result, the firm's debt-equity ratio is expected to rise from 40 percent to 50 percent. The firm currently has CAD 7.5 million worth of debt outstanding. The cost of this debt is 10 percent per year. Locomotive expects to have an EBIT of CAD 3.75 million per year in perpetuity. Locomotive pays no taxes. a. What is the market value of Locomotive Corporation before and after the repurchase announcement? b. What is the expected return on the firm's equity before the announcement of the stock repurchase plan? c. What is the expected return on the equity of an otherwise identical all-equity firm? d. What is the expected return on the firm's equity after the announcement of the stock repurchase plan? （CAD 是『加拿大元』 ，加拿大的貨幣單位。） 【題意】 L 公司計畫發行公司債來買回部分權益，使其負債權益比從 40%提升至 50%。L 公司目前 有市值$7.5M，利率 10%之公司債在外。L 公司每年的 EBIT 為$3.75M，沒有公司稅。 (a)L 公司在執行該計畫前、後的公司價值為何？(b)執行該計畫前的權益報酬率為何？(c) 若 L 公司為全部權益公司，其權益報酬率為何？(d)執行該計畫後的權益報酬率為何？ 【分析】 VL = VU ， rS = r0 + B S ( r0 − rB ) ， V = EBIT r0 (a) VL = VU = $7.5M （原解答誤解題意） B S = 0.4 ⇒ S = B 0.4 = $7.5M 0.4 = VL = S + B = (b) rS = (c) r0 = (d) rS = r0 + B S ( r0 − rB ) = r0 + 0.5 × ( r0 − rB ) ©2010/6/21 陳欣得 財務管理‧作業 Part IV 1/6 EBIT − B × rB $3.75 − $7.5M × 10% = = S S EBIT V 第2題 MM with Taxes （第 15 章，#25，452 頁。） Rajan. Inc., has a debt-equity ratio of 2.5. The firm's weighted average cost of capital is 15 percent, and its pretax cost of debt is 10 percent. Rajan is subject to a corporate tax rate of 35 percent. a. What is Rajan's cost of equity capital? b. What is Rajan's unlevered cost of equity capital? c. What would Rajan's weighted average cost of capital be if the firm's debt-equity ratio were 0.75? What if it were 1.5? 【題意】 R 公司的財務資料： B S = 2.5 、 rWACC = 15% 、 rB = 10% 、 TC = 35% 。 (a)求 rS ；(b)求 r0 ；(c)求 B S = 0.75 情況下之 rWACC 、求 B S = 1.5 情況下之 rWACC 。 【分析】 VL = VU + B × TC ， rS = r0 + B S B rS + rB (1 − TC ) ( r0 − rB )(1 − TC ) ， rWACC = S S+B S+B (a) B S B = 2.5 ⇒ , S S+B S+B S B rWACC = rS + rB (1 − TC ) ⇒ rS S+B S+B (b) rS = r0 + B ( r0 − rB )(1 − TC ) ⇒ r0 S (c) B ( r0 − rB )(1 − TC ) ⇒ rS , B S =0.75 , rS , B S =1.4 S S B rWACC , B S = 0.75 = rS , B S = 0.75 + rB (1 − TC ) S+B S+B S B rWACC , B S =1.5 = rS , B S =1.5 + rB (1 − TC ) S+B S+B rS = r0 + ©2010/6/21 陳欣得 財務管理‧作業 Part IV 2/6 第3題 Financial Distress （第 16 章，#8，485 頁。） Good Time Company is a regional chain department store. It will remain in business for one more year. The probability of a boom year is 60 percent and the probability of a recession is 40 percent. It is projected that the company will generate a total cash flow of $250 million in a boom year and $100 million in a recession. The company's required debt payment at the end of the year is $150 million. The market value of the company's outstanding debt is $108.93 million. The company pays no taxes. Assume a discount rate of 10 percent. a. What payoff do bondholders expect to receive in the event of a recession? b. What is the promised return on the company's debt? c. What is the expected return on the company's debt? 【題意】 G 公司只有年底一個現金流量：$250M 之機率 60%、$100M 之機率 40%。年底應付之債 務為$150M，該債務的市值為$108.93M。G 公司不需付稅，適用折現率為 10%。 求(a)債權人在不景氣時的收益；(b)債務之名目利息；(c)債務之期望報酬。 【分析】 (a) min {$150 M , $100M } = $100M (b) rB = $150 M −1 $108.93M (c) rB = $150M × 60% + $100M × 40% −1 $108.93M ©2010/6/21 陳欣得 財務管理‧作業 Part IV 3/6 第4題 APV （第 17 章，#10，506 頁。） Triad Corporation has established a joint venture with Ottoman Road Construction, Inc., to build a toll road in Adana. The initial investment in paving equipment is TRL 25 million. The equipment will be fully depreciated using the straight-line method over its economic life of five yean. Earnings before interest, taxes, and depreciation collected from the toll road are projected to be TRL 3.4 million per annum for 20 years starting from the end of the first year The corporate tax rate is 35 percent. The required rate of return for the project under all-equity financing is 13 percent. The pretax cost of debt for the joint partnership is 8.5 percent. To encourage investment in the country's infrastructure, the Turkish government will subsidize the project with a TRL 15 million, 15-year loan at an interest rate of 5 percent per year. All principal will be repaid in one balloon payment at the end of year 15. What is the adjusted present value of this project? （TRL 是『土耳其盧比』 ，土耳其的貨幣單位。） 【題意】 T 公司評估某投資計畫，該計畫期初投資金額為$25M，5 年內以直線法提折舊，沒有殘值。 該專案從第一年底開始連續 20 年，每年可以帶來$3.4M 之 EBIT。T 公司之稅率為 35%， 適用投資報酬率為 13%，負債利息為 8.5%。政府會提供一筆$15M 低利貸款：年利率 5%， 本金於第 15 年底一次償還。該投資計畫的調整現值為何？ 【分析】 APV = NPV + 附帶收益現值 不考慮折舊、政府補貼貸款情況： 每年稅後現金流量 CF = $3.4 M × (1 − 35% ) NPV = −$25M + CF × PVIFA13%,20 折舊、補貼貸款利息稅盾： $25M × 35% × PVIFA13%,5 5 補貼貸款利息稅盾 S L = $15M × 5% × 35% × PVIFA13%,15 折舊稅盾 S D = 補貼貸款價值： 補貼貸款靜現值 VL = $15M − $15M × 5% × PVIFA13%,15 − $15M × PFIV13%,15 APV = NPV + S D + S L + VL ©2010/6/21 陳欣得 財務管理‧作業 Part IV 4/6 第5題 WACC （第 17 章，#13，507 頁。） Neon Corporation's stock returns have a covariance with the market portfolio of 0.048. The standard deviation of the returns on the market portfolio is 20 percent, and the expected market risk premium is 7.5 percent. The company has bonds outstanding with a total market value of $30 million and a yield to maturity of 8 percent. The company also has 5 million shares of common stock outstanding, each selling for $20. The company's CEO considers the firm's current debt-equity ratio optimal. The corporate tax rate is 38 percent, and Treasury bills currently yield 6 percent. The company is considering the purchase of additional equipment that would cost $40 million. The expected unlevered cash flows from the equipment are $13 million per year for five years. Purchasing the equipment will not change the risk level of the firm. a. Use the weighted average cost of capital approach to determine whether Neon should purchase the equipment. b. Suppose the company decides to fund the purchase of the equipment entirely with debt. What is the cost of capital for the project now? Explain. 【題意】 N 公司權益報酬率與市場報酬率資料為： σ N , M = 0.048 、 σ M = 20% 、 rM = 7.5% 。 該公司的負債、權益資料為： B = $30 M 、 rB = 8% 、 S = $20 × 5M 。 其它財務資訊： TC = 38% 、 rF = 6% 。 N 公司考慮一設備投資專案：期初投資 P0 = $40M 、每年現金流量 CF = $13M ，共 5 年。 (a)以加權平均資金成本法評估該專案。 (b)若以全部債務融資投資該設備，則其資本成本為何？ 【分析】 (a) σ N ,M = 2 σM 由 rM = 7.5% 、 rF = 6% 、 β N 可以得到： rS = rF + β N ( rM − rF ) = 由 σ N , M = 0.048 、 σ M = 20% 可以得到： β N = 由 B = $30M 、 rB = 8% 、 S = $20 × 5M 、 TC = 38% 、 rS 可以得到： S B rWACC = × rS + × rB (1 − TC ) = S+B S+B 最後以 rWACC 為折現率計算該專案的淨現值： NPV = − P0 + CF × (1 − TC ) × PVIVArWACC ,5 = (b) 新的負債額度為 B = $30 M + $40M ，重算 rWACC 即為答案： S B rWACC = × rS + × rB (1 − TC ) = S+B S+B ©2010/6/21 陳欣得 財務管理‧作業 Part IV 5/6 第6題 Dividends and Firm Value （第 18 章，#18，545 頁。） The net income of Takamaka Cruises is SCR 32,000. The company has 10,000 outstanding shares and a 100 percent payout policy. The expected value of the firm one year from now is SCR 1,545,600. The appropriate discount rate for Takamaka is 12 percent, and the dividend tax rate is zero. a. What is the current value of the firm assuming the current dividend has not yet been paid? b. What is the ex-dividend price of Takamaka's stock if the board follows its current policy? c. At the dividend declaration meeting, several board member claimed that the dividend is too meager and is probably depressing Takamaka's price. They proposed that Takamaka sell enough new shares to finance an SCR 4.25 dividend. i. Comment on the claim that the low dividend is depressing the stock price. Support your argument with calculations. ii. If the proposal is adopted, at what price will the new shares sell? How many will be sold? （SCR 是『塞席爾盧比』 ，東非島國塞席爾的貨幣單位。） 【題意】 T 公司的財務資料為：每年淨利 CF = $32,000 、 10,000 股在外，100%股利分配率、一年 後的公司價值 V1 = $1,545,600 ；適用折現率 r = 12% 、股利不需課稅。 (a)股利未發放前的公司現值為何？ (b)股利發放後的股價為何？ (c)T 公司準備以新權益 融資，讓每股股利為 D = $4.25 ，則新權益每股售價為何？共賣出幾股？ 【分析】 (a) 股利發放後的公司價值： V0 = V1 × PVIFr ,1 = $1,545,600 = $1,380,000 1 + 12% 股利發放前的公司價值： V0′ = V0 + CF = $1,380,000 + $32,000 = $1, 412,000 (b) 股利發放後的股價 p = V0 = $138 10,000 (c) 每股多發放股利 $4.25 − $32,000 = $1.05 10,000 因此，股利發放後的新股價 p′ = p − $1.05 = $136.95 需融資金額 $1.05 × 10,000 $10,500 = = = 76.67 需出售股數為 n = p′ p′ $136.95 ©2010/6/21 陳欣得 財務管理‧作業 Part IV 6/6