| 99 | 【題組】(1) Vincent Swift is a risk neutral investor, he will choose (A)A (B)B (C)C (D)D  |
| 99 |  Based on NPV, which project would you choose if the opportunity cost of capital is 12%? (A) A,
(B) B, (C)the same, (D)cannot be decided. |
| 99 | 【題組】(3) Based on M&M model, A firm has a debt-to-equity ratio of 1.0. If it had no debt, its cost of equity would be 15%. Its cost of debt is 10%. What is its cost of equity if there are no taxes or other imperfections? (A)21%. (B)18%. (C)15%. (D)20%. |
| 99 | 【題組】(4) Both call and put options are impacted by the ex-dividend date. Put options become more and Call options become________ due to the dividend payment. (A) expensive, expensive (B)cheaper, cheaper (C)expensive, cheaper (D)cheaper, expensive. |
| 99 | 【題組】(5) A company (NTU Ltd) that has paid a dividend of $4 this year. Assuming a higher growth for the next 3 years at 12% and stable growth of 6% thereafter, let's calculate the value of the stock using a two-stage dividend discount model. The required rate of return is 10%. (A)4.48 (B)5.95 (C)124.33 (D)154.54 |
| 申論題 | 1. (15 points)
Capital structure overlooks that firms have different capital requirements across their life cycle. In
addition, the finance literature highlights various theoretical models that explain how the firms' life
stages influence capital struc cture decisions, such as the Pecking Order, Trade-Off, and Agency Cost
Theories. We like to know how firms in highly innovative industries have' different capital
requirements over their life cycle. 【題組】(1) (5points) In the beginning of the life cycle, firms are more likely to raise funds through issuing equity or using borrowing, why? |
| 申論題 | 【題組】(2) (5 points) When firms are matured, they are more likely to use debt or equity financing, why? |
| 申論題 | 【題組】(3) (5 points) Tony Lin is a founder of a highly innovative company. The company is facing a high-growth period. Tony insists to use debt financing to support the firm's new investment. Does Tony make the right decision? Why, or why not? Why does Tony make such a decision? Is there anything related to his personal preference? |
| 申論題 | 2. (15 points) To construct a portfolio using the mean-variance framework, one needs cstimates of the expected return r, the variance σ2i and the co-variance aj for each stocks, j. Forn stocks, you have to estimate a total of n(n-1)/2 correlation coefficients. Single index models are used, to reduce this hugc amount of needed estimates. Now we are going to construct a portfolio with two assets using the single index model. 【題組】 (1) (3 points) Please calculate the mean and variance of the stock index return and mean return for asset B. |
| 申論題 | 【題組】 (2) (2 points) Please find out the estimates of αi and βi for Asset A
|
| 申論題 | 【題組】 (3) (4 points) A Single Index Model (SIM) specifies two sources of uncertainty for a security's
21.078
return: Systematic risk and firm-specific risk
Return variance Systematic risk
Firm-specific risk |
| 申論題 | 【題組】 (4) (6 points) Now assuming a portfolio with weights for asset A and asset B are 0.7 and 0.3.
Plcase find out E(rp) and |
| 申論題 | 3.(10 points)
The equity in a firm is a residual claim, i.e., equity holders lay claim to all cashflows left over after
other financial claim-holders (debt, preferred stock ctc,) have been satisfied. Ifa firm is liquidated,
the same principle applies, with equity investors receiving whatever is left over in the firm atter all
outstanding debts and other financial claims are paid off. The principle of limited liability, however,
protects equity investors in publicly traded firms if the value of the firm is less than the valuc of the
outstanding debt, and they cannot lose more than their investment in the firm. 【題組】(1) (2 points) Beside the residual claim right mentioned above, what elise rights that an equity investor hold? |
| 申論題 | 【題組】 (2) (1.5 point) The payoff to equity investors, on liquidation, can therefore be written as: Payof |
| 申論題 | 【題組】 (3) (1.5 point) The payoff to equity investors, on liquidation, can therefore be written as: Payoff |
| 申論題 | 【題組】 (4) The relationship between equity/debt and firm value can be described by the following assets,
call option, put option, and pure bond. Please fill in the correct position (long, short, or NO)
for an investor to take to desctribe the relation between equity/debt and firm value. (3 points) |
| 申論題 | 第二部分:財金數學
|
| 申論題 | 2. (5 points) Following previous question, please find reduced row cchelon form (iret) |
| 申論題 | 3. (5 points) Please find a matrix C solution so that (BC)T - A = 0, where |
| 申論題 | 4. Consider a two-period economy (/ = 0, 1). The operating profit of firm j can be expressed as 【題組】(1) (10 points) Please drive FOC for maximum firm value, and express it as a form of marginal cost equal to marginal revenue. |
| 申論題 | 【題組】 (2) (10 points) Note that the investment return |
| 申論題 | 【題組】 (3) (10 points) Please derive expected excess return: |
| 申論題 | 【題組】(4) 5 points) Show that the expected excess return of firm j is positively associated with technology shock at time 1. |
We run the following regression for each asset.
. 
where x1, x2, x3 are unknown. Please use the matrix-vector product to express the 3 x 3 linear
system
is the exogenous profitability shock; At is a technology shook at time
t;
is private capital of fimm j. a ＞ 0 is assumed. The depreciation rate of capital k for firm / is
δj. Thus, the investment of firm
, firm j has a liquidation
value of
. The investment in private capital involves adjustment cost 
. The stochastic discount factor between time 0 and 1 is m, where log(m) = logβ + γ(x0 -x1), where 0 ＜β＜ 1, and γ＞ 0. Firm j then chooses ij.0 to maximize its value, which is the sum
of the discounted cash flows from the two periods:
E[.] is an expectation operator. From standard asset pricing equation, 
-Cov0(r1,m). Specifically, the cash flows from t = 0 are equal to the operating profit minus the
investment cost and the adjustment cost. The cash flows from ! = I are equal to the operating
profit plus the liquidation value.
, defined as the ratio of marginal benefit to
marginal cost of investment, is equal to the firm's stock return (rl) under equilibrium. Please
show that 
, which is a function of the
covariance between the operating profit at t = 1 of firm y and the aggregate productivity shock.