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Cash Flows of a Stock

Time (yrs)

Dividend ($)

The equations for Net Income (NI, also known as Earnings or Net Profit After Tax) and Cash Flow From Assets (CFFA, also known as Free Cash Flow to the Firm) per year are:

###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c)###

###CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp###

For a firm with debt, what is the formula for the present value of interest tax shields if the tax shields occur in perpetuity?

You may assume:

the value of debt (D) is constant through time,
The cost of debt and the yield on debt are equal and given by ##r_D##.
the appropriate rate to discount interest tax shields is ##r_D##.
##\text{IntExp}=D.r_D##

Question 199 NPV, DDM, no explanation

A stock is expected to pay the following dividends:

After year 4, the dividend will grow in perpetuity at 5% pa. The required return of the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What will be the price of the stock in 7 years (t = 7), just after the dividend at that time has been paid?

Question 201 DDM, income and capital returns

The following is the Dividend Discount Model (DDM) used to price stocks:

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

If the assumptions of the DDM hold and the stock is fairly priced, which one of the following statements is NOT correct? The long term expected:

Question 345 capital budgeting, break even, NPV

Project Data
Project life	10 yrs
Initial investment in factory	$10m
Depreciation of factory per year	$1m
Expected scrap value of factory at end of project	$0
Sale price per unit	$10
Variable cost per unit	$6
Fixed costs per year, paid at the end of each year	$2m
Interest expense per year	0
Tax rate	30%
Cost of capital per annum	10%

Notes

The firm's current liabilities are forecast to stay at $0.5m. The firm's current assets (mostly inventory) is currently $1m, but is forecast to grow by $0.1m at the end of each year due to the project.
At the end of the project, the current assets accumulated due to the project can be sold for the same price that they were bought.
A marketing survey was used to forecast sales. It cost $1.4m which was just paid. The cost has been capitalised by the accountants and is tax-deductible over the life of the project, regardless of whether the project goes ahead or not. This amortisation expense is not included in the depreciation expense listed in the table above.

Assumptions

All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
All rates and cash flows are real. The inflation rate is 3% pa.
All rates are given as effective annual rates.

Find the break even unit production (Q) per year to achieve a zero Net Income (NI) and Net Present Value (NPV), respectively. The answers below are listed in the same order.

Question 368 interest tax shield, CFFA

A method commonly seen in textbooks for calculating a levered firm's free cash flow (FFCF, or CFFA) is the following:

###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + \\ &\space\space\space+ Depr - CapEx -\Delta NWC + IntExp(1-t_c) \\ \end{aligned}###

Question 581 APR, effective rate, effective rate conversion

A home loan company advertises an interest rate of 6% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given to four decimal places.

Question 676 option, option profit, no explanation

Which of the below formulas gives the profit ##(\pi)## from being short a call option? Let the underlying asset price at maturity be ##S_T##, the exercise price be ##X_T## and the option price be ##f_{LC,0}##. Note that ##S_T##, ##X_T## and ##f_{LC,0}## are all positive numbers.

Question 718 arithmetic and geometric averages

The symbol ##\text{GDR}_{0\rightarrow 1}## represents a stock's gross discrete return per annum over the first year. ##\text{GDR}_{0\rightarrow 1} = P_1/P_0##. The subscript indicates the time period that the return is mentioned over. So for example, ##\text{AAGDR}_{1 \rightarrow 3}## is the arithmetic average GDR measured over the two year period from years 1 to 3, but it is expressed as a per annum rate.

Which of the below statements about the arithmetic and geometric average GDR is NOT correct?

(a) Arithmetic average gross discrete return is ##\text{AAGDR}_{0\rightarrow T} = \dfrac{\text{GDR}_{0 \rightarrow 1}+\text{GDR}_{1\rightarrow 2}+...+\text{GDR}_{T-1 \rightarrow T}}{T}##

(b) Geometric average gross discrete return is ##\text{GAGDR}_{0\rightarrow T} = \dfrac{\text{GDR}_{0 \rightarrow 1} . \text{GDR}_{1\rightarrow 2} ... \text{GDR}_{T-1 \rightarrow T}}{T}##

(c) The geometric average gross discrete return can be quickly found using the first ##(P_0)## and last ##(P_T)## prices. ##\text{GAGDR}_{0\rightarrow T} = \left( \dfrac{P_T}{P_0} \right)^{1/T}##

(d) The arithmetic average is always bigger than or equal to the geometric average, ##\text{AAGDR} \ge \text{GAGDR}##.

(e) The arithmetic and geometric averages of returns will be equal if the variance of the stock's returns is zero.

Question 823 option, option payoff at maturity, option profit, no explanation

A European call option should only be exercised if:

Question 934 standard deviation, risk

Which of the following statements about an asset’s standard deviation of returns is NOT correct? All other things remaining equal, the higher the asset’s standard deviation of returns: