一个关于CAPM的综合型问题，德国人说题目错了，大家看看

在德国法兰克福金融学院交换，今天刚刚考完最后一门Corporate Banking，两个计算题发上来大家分享下，高手解答下。我自己考试的时候算的还挺自信的，尽管这么课实在比较**。下面是回忆的题目，数字没问题，但是可能细节的文字上有出入。
Q1: a company has an expected annual earnings (EBIT before tax) of 350,000 in perpetuity, and currently it has an unlevered cost of equity at 15%. It also has an outstanding debt of 1,500,000 paying a interest rate of 6% in perpetuity. The tax rate is 40%.

a. calculate the value of tax shield, the value of equity and the value of the firm.
b. assume that the risk free rate is 4%, and the market risk premium is 7%. calculate the WACC?
c. The company is going to invest in a project which needs an initial investment of 100,000(assume this is purely from equity so no change in capital structure). The life time of the project is 4 years. The after tax.EBIT is 15000 per year.
1). from the perspective of shareholders (see the cash flow to equity), what's the NPV of this project?
2). from the perspective of all capital providers, what's the NPV of the project?

Q2: Two companies A and B are investing all their asset in a project which last only one year. The company A is sure to get a total value of asset of 100,000 in one year. The company B's asset will worth 200,000 with a probability of 0.4, 100,000 with probability of 0.4 and nothing with probability of 0.2. Currently they all need a bank loan of 50,000. The risk free rate is 10% and the bank is risk neutral.

a. Suppose that the bank can distinguish company A from B. What's the interest rate for the two companies respectively? Assume that the bank only wants to break-even.
b. Suppose the bank can not distinguish company A from B, and it provides two plans for the company to choose by itself. Plan 1 is an unsecured loan with an interest of 37.5%; Plan 2 is a secured loan with a collateral worth of 25,000 and an interest rate of 20%. Which loan will the two company choose?
c. Now according to your answer from the question b, calculate the expected cash flow to the bank in the loans chosen by A and B respectively. Do you think the bank's strategy works or not?

先自己上个考试中写的答案，请大家指教！
Q1.
a. Tax shield= 1,500,000*40%=0.6 million; value of equity=0.35*(1-40%)/15%=1.4million; value of company, APV approach, tax shield + value of equity= 2million.
b.use CAPM, we have risk free rate, market premium and cost of equity unleverd, work out beta unleverd is 1.571; so beta levered is 1.571*(1+(1.5/1.4)*(1-40%))=2.81; then again use CAPM, cost of equity levered is 23.67%. then WACC is 14.53%.
c.1. when calculate CF to equity, use 23.67% as hurdle rate, annuity factor is 2.42, NPV=-63700;
c.2. when calculate CF to all capital provider, use WACC as hurdle rate, annuity factor is 2.88, NPV =-56800.

先自己上个考试中写的答案，请大家指教！
Q1.
a. Tax shield= 1,500,000*40%=0.6 million; value of equity=0.35*(1-40%)/15%=1.4million; value of company, APV approach, tax shield + value of equity= 2million.
b.use CAPM, we have risk free rate, market premium and cost of equity unleverd, work out beta unleverd is 1.571; so beta levered is 1.571*(1+(1.5/1.4)*(1-40%))=2.81; then again use CAPM, cost of equity levered is 23.67%. then WACC is 14.53%.
c.1. when calculate CF to equity, use 23.67% as hurdle rate, annuity factor is 2.42, NPV=-63700;
c.2. when calculate CF to all capital provider, use WACC as hurdle rate, annuity factor is 2.88, NPV =-56800.

这里的问题主要在第二问。德国同学说BETA unlevered题目没有给出，所以是不可知的，他们就假设它等于1然后进行之后的计算；我提出这个CAPM的时候，他们说CAPM只对levered资产计算才有效，所以说这里CAPM是不适用的，不能用unleverd cost of equity 去算BETA unlevered。最后一问我不确定，尽管NPV 为负是肯定的，但是具体第二小问的时候除数上还要加上tax shield吗？我没加是觉得用的已经是WACC after tax了。

Q2：(two more conditions forget to say, the interest rate will never be more than 100% and the collateral in b is not included in the asset but from other sources) a. firm is A is sure to pay back the loan, so interest is 10%; for firm b, 0.8*(1+r)*50000=50000, r=25%
b. for A, as it is sure to pay back, so the less interest rate the better, so it will choose secured loan; for firm b, when choose unsecured loan, CF to equity is 0.4*200000+0.4*100000-0.8*(1+37.5%)*50000=51250;  when choose secured loan,  CF to equity is  0.4*200000+0.4*100000-0.8*(1+20%)*50000-0.2*25000=55000; B also chooses secured loan.
c.CF to creditors, for firm a, 50000*1.2=60000; for firm b is, 0.8*1.2*50000+0.2*25000=53000, note that when firm b choose plan 1, it's 1.375*0.8*50000=55000. we can conclude that the scheme is not successful and more collateral should be required in the secured loan so that to distinguish the two firms from each other.

这个题目问题小点，就是不大确定第三问这么回答对不对，请指教

没人能回答吗。。。