练习6解答
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Choose project A because it has a higher IRR than project B. The difference in scale was ignored. Project B has a substantially larger initial investment than project A has. Thus, the simple IRR calculation may not lead to the best decision.
练习3解答
P = Div / r = 4 / 0.14 = 28.57 g = (0.25) (0.4)= 0.1 NPVGO = [(Investment + Return / r) / (r – g)] / (1+r)2 = [(-1 + 0.40 / .14) / (0.14 – 0.1)] / (1.14)2 = 35.73 P = PV(EPS) + NPVGO = 28.57 + 35.73 = 64.30
练习2解答
• （1）摇钱树的价值：PV = C1 / r= $100,000,000 / 0.15= $666,666,666.67 • 每股股票价格= $666,666,666.67 / 20,000,000= $33.33 • （2）NPVGO =C0 + C1 +[C2 / r] / (1+r)T • =-$15,000,000 -$5,000,000 / 1.15 + [$10,000,000 / 0.15] / (1.15) • =$38,623,188.41 • （3）每股股票价格= （1）+ NPVGO / (股数) • = $33.33 + $38,623,188.41 / 20,000,000 • = $35.26
Suppose you observe that a three-year, default-free security with an annual coupon rate of 10% and a face value of $1000 has a price today of $1183.50. Is there an arbitrage opportunity? If so, show specifically how you would take advantage of this opportunity. If not, why not?
练习6解答
• For investing-type projects, accept the larger project when the incremental rate of return is greater than the discount rate. Therefore, choose project B since the incremental IRR (19.1%) is greater than the 15 percent discount rate.
Solve for the IRR. IRR(Project A) = C0 + C1 / (1+IRR) + C2 / (1+IRR)2 0 = -$5,000 + $3,500 / (1+IRR) + $3,500 / (1+IRR)2 IRR = 0.2569 The IRR of project A is 25.69%. IRR(Project B) = C0 + C1 / (1+IRR) + C2 / (1+IRR)2 0 = -$100,000 + $65,000 / (1+IRR) + $65,000 / (1+IRR)2 IRR = 0.1943 The IRR of project B is 19.43%.
练习1解答
a. This security has the same cash flows as a portfolio of one share of B1 and one share of B2. Therefore, its noarbitrage price is 94 + 85 = $179. b. This security has the same cash flows as a portfolio of one share of B1 and five shares of B2. Therefore, its noarbitrage price is 94 + 5 × 85 = $519 c. There is an arbitrage opportunity because the noarbitrage price should be $132 (94 / 2 + 85). One should buy two shares of the security at $130/share and sell one share of B1 and two shares of B2. Total profit would be $4 (94 + 85 × 2 – 130 × 2).
The price of the coupon bond is too low, so there is an arbitrage opportunity. To take advantage of it:
课堂练习6
• • • • • 考虑两个互斥投资项目，现金流如下： 年份 项目A 项目B 0 -5000 -100000 1 3500 65000 2 3500 65000
练习6解答
• Calculate the incremental IRR. The incremental IRR is the IRR on the incremental investment from choosing the larger project instead of the smaller project. The incremental cash flows are the differences between the cash flows of project B and those of project A. Always subtract the project with the smaller initial cash outflow from the project with the larger initial cash outflow. In this way, the initial incremental cash flow will be negative.
练习6解答
• B–A： • -$95,000 $61,500 $61,500 • Next, find the IRR of those incremental cash flows. • IRR(B – A) = C0 + C1 / (1+IRR) + C2 / (1+IRR)2 • 0 = -$95,000 + $61,500 / (1+IRR) + $61,500 / (1+IRR)2 • IRR = 0.191
课堂练习3
某公司如果不从事新的投资项目，它每年 的每股盈利为4元，在此情形下，公司把所 有的盈利当作股利分发出去（假设第一笔 股利刚好在一年后收到）。在另一种情形 中，假设距今三年后的每一年，公司将其 盈利的25%投资于新的项目，每一个投资 项目将在一年后获得40%的收益率（直至 永远）。设贴现率为14%，分别求公司在 不从事新的投资项目和从事新的投资项目 时的股票价格。
练习4解答
• Using dividend model, price of a stock can be written as P = D/(k – g)
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Or it can be written as P = E*PO/(k – g) where PO is the dividend payout ratio and denotes multiplication Rearranging terms we get, P/E = PO/(k – g) Substituting values 12 = .4/(k – g) → 1/(k – g) = 12/0.4 → 1/(k – g) = 30 P = E*PO/(k – g) Now substituting P = $32, PO = 40%, 1/(k – g) = 30 we get 32 = E*.4*30 → E = 8/3 If the dividend payout ratio were 60% P = E*PO/(k – g) P = (8/3)*.6*30 = $48
课堂练习1
Consider two securities that pay risk-free cash flows over the next two years and that have the current market prices shown here:
a. What is the no-arbitrage price of a security that pays cash flows of $100 in one year and $100 in two years? b. What is the no-arbitrage price of a security that pays cash flows of $100 in one year and $500 in two years? c. Suppose a security with cash flows of $50 in one year and $100 in two years is trading for a price of $130. What arbitrage opportunity is available?