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Over the next year, the management of an unlevered company plans to:

Achieve firm free cash flow (FFCF or CFFA) of $1m.
Pay dividends of $1.8m
Complete a $1.3m share buy-back.
Spend $0.8m on new buildings without buying or selling any other fixed assets. This capital expenditure is included in the CFFA figure quoted above.

Assume that:

All amounts are received and paid at the end of the year so you can ignore the time value of money.
The firm has sufficient retained profits to pay the dividend and complete the buy back.
The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.

How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?

Question 398 financial distress, capital raising, leverage, capital structure, NPV

A levered firm has zero-coupon bonds which mature in one year and have a combined face value of $9.9m.

Investors are risk-neutral and therefore all debt and equity holders demand the same required return of 10% pa.

In one year the firm's assets will be worth:

$13.2m with probability 0.5 in the good state of the world, or
$6.6m with probability 0.5 in the bad state of the world.

A new project presents itself which requires an investment of $2m and will provide a certain cash flow of $3.3m in one year.

The firm doesn't have any excess cash to make the initial $2m investment, but the funds can be raised from shareholders through a fairly priced rights issue. Ignore all transaction costs.

Should shareholders vote to proceed with the project and equity raising? What will be the gain in shareholder wealth if they decide to proceed?

Question 428 takeover

Question 491 capital budgeting, opportunity cost, sunk cost

A man is thinking about taking a day off from his casual painting job to relax.

He just woke up early in the morning and he's about to call his boss to say that he won't be coming in to work.

But he's thinking about the hours that he could work today (in the future) which are:

Question 591 short selling, future, option

After doing extensive fundamental analysis of a company, you believe that their shares are overpriced and will soon fall significantly. The market believes that there will be no such fall.

Which of the following strategies is NOT a good idea, assuming that your prediction is true?

Question 723 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Here is a table of stock prices and returns. Which of the statements below the table is NOT correct?

Price and Return Population Statistics
Time	Prices	LGDR	GDR	NDR
0	100
1	99	-0.010050	0.990000	-0.010000
2	180.40	0.600057	1.822222	0.822222
3	112.73	0.470181	0.624889	0.375111

Arithmetic average		0.0399	1.1457	0.1457
Arithmetic standard deviation		0.4384	0.5011	0.5011

(a) The geometric average of the gross discrete returns (GAGDR) equals 1.04075 which is 104.075%.

(b) ##\exp \left( \text{GAGDR} \right) = \text{AALGDR}##. The natural exponent of the GAGDR equals the arithmetic average of the logarithms of the gross discrete returns (AALGDR).

(c) ##\text{GAGDR}^T = \left( P_T/P_0 \right)##. The GAGDR raised to the power of the number of time period that it's measured over equals the ratio of the first and last prices.

(d) ##\text{GAGDR} = \exp \left( \text{AALGDR} \right)##. This is always true, regardless of the distribution of the prices or returns. The logarithm of the geometric average of the gross discrete returns (LGAGDR) is always equal to the arithmetic average of the logarithm of the gross discrete returns (AALGDR).

(e) ##\text{AAGDR} \approx \exp \left( \text{AALGDR} + \text{SDLGDR}^2/2 \right)##. This is only approximately true and depends on the distribution of the prices and returns. It's asymptotically true as the time period that the returns are measured over reaches infinity.

Question 733 DDM, income and capital returns

A share’s current price is $60. It’s expected to pay a dividend of $1.50 in one year. The growth rate of the dividend is 0.5% pa and the stock’s required total return is 3% pa. The stock’s price can be modeled using the dividend discount model (DDM):

##P_0=\dfrac{C_1}{r-g}##

Which of the following methods is NOT equal to the stock’s expected price in one year and six months (t=1.5 years)? Note that the symbolic formulas shown in each line below do equal the formulas with numbers. The formula is just repeated with symbols and then numbers in case it helps you to identify the incorrect statement more quickly.

Question 772 interest tax shield, capital structure, leverage

A firm issues debt and uses the funds to buy back equity. Assume that there are no costs of financial distress or transactions costs. Which of the following statements about interest tax shields is NOT correct?

Question 876 foreign exchange rate, forward foreign exchange rate, cross currency interest rate parity

Suppose the yield curve in the USA and Germany is flat and the:

USD federal funds rate at the Federal Reserve is 1% pa;
EUR deposit facility at the European Central Bank is -0.4% pa (note the negative sign);
Spot EUR exchange rate is 1 USD per EUR;
One year forward EUR exchange rate is 1.011 USD per EUR.

You suspect that there’s an arbitrage opportunity. Which one of the following statements about the potential arbitrage opportunity is NOT correct?

Question 956 option, Black-Scholes-Merton option pricing, delta hedging, hedging

A bank sells a European call option on a non-dividend paying stock and delta hedges on a daily basis. Below is the result of their hedging, with columns representing consecutive days. Assume that there are 365 days per year and interest is paid daily in arrears.

Delta Hedging a Short Call using Stocks and Debt

Description	Symbol	Days to maturity (T in days)
		60	59	58	57	56	55
Spot price ($)	S	10000	10125	9800	9675	10000	10000
Strike price ($)	K	10000	10000	10000	10000	10000	10000
Risk free cont. comp. rate (pa)	r	0.05	0.05	0.05	0.05	0.05	0.05
Standard deviation of the stock's cont. comp. returns (pa)	σ	0.4	0.4	0.4	0.4	0.4	0.4
Option maturity (years)	T	0.164384	0.161644	0.158904	0.156164	0.153425	0.150685
Delta	N[d1] = dc/dS	0.552416	0.582351	0.501138	0.467885	0.550649	0.550197
Probability that S > K at maturity in risk neutral world	N[d2]	0.487871	0.51878	0.437781	0.405685	0.488282	0.488387
Call option price ($)	c	685.391158	750.26411	567.990995	501.487157	660.982878	?
Stock investment value ($)	N[d1]*S	5524.164129	5896.301781	4911.152036	4526.788065	5506.488143	?
Borrowing which partly funds stock investment ($)	N[d2]K/e^(rT)	4838.772971	5146.037671	4343.161041	4025.300909	4845.505265	?
Interest expense from borrowing paid in arrears ($)	rN[d2]K/e^(r*T)		0.662891	0.704985	0.594994	0.551449	?
Gain on stock ($)	N[d1]*(SNew - SOld)		69.052052	-189.264008	-62.642245	152.062648	?
Gain on short call option ($)	-1*(cNew - cOld)		-64.872952	182.273114	66.503839	-159.495721	?
Net gain ($)	Gains - InterestExpense		3.516209	-7.695878	3.266599	-7.984522	?

Gamma	Γ = d^2c/dS^2	0.000244	0.00024	0.000255	0.00026	0.000253	0.000255
Theta	θ = dc/dT	2196.873429	2227.881353	2182.174706	2151.539751	2266.589184	2285.1895

In the last column when there are 55 days left to maturity there are missing values. Which of the following statements about those missing values is NOT correct?