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Question 236  diversification, correlation, risk

Diversification in a portfolio of two assets works best when the correlation between their returns is:

Question 333  DDM, time calculation

When using the dividend discount model, care must be taken to avoid using a nominal dividend growth rate that exceeds the country's nominal GDP growth rate. Otherwise the firm is forecast to take over the country since it grows faster than the average business forever.

Suppose a firm's nominal dividend grows at 10% pa forever, and nominal GDP growth is 5% pa forever. The firm's total dividends are currently $1 billion (t=0). The country's GDP is currently $1,000 billion (t=0).

In approximately how many years will the company's total dividends be as large as the country's GDP?

Question 350  CFFA

Find Sidebar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

Sidebar Corp
Income Statement for
year ending 30th June 2013
Sales 405
COGS 100
Depreciation 34
Rent expense 22
Interest expense 39
Taxable Income 210
Taxes at 30% 63
Net income 147
Sidebar Corp
Balance Sheet
as at 30th June 2013 2012
  $m $m
Inventory 70 50
Trade debtors 11 16
Rent paid in advance 4 3
PPE 700 680
Total assets 785 749
Trade creditors 11 19
Bond liabilities 400 390
Contributed equity 220 220
Retained profits 154 120
Total L and OE 785 749


Note: All figures are given in millions of dollars ($m).

The cash flow from assets was:

Question 497  income and capital returns, DDM, ex dividend date

A stock will pay you a dividend of $10 tonight if you buy it today. Thereafter the annual dividend is expected to grow by 5% pa, so the next dividend after the $10 one tonight will be $10.50 in one year, then in two years it will be $11.025 and so on. The stock's required return is 10% pa.

What is the stock price today and what do you expect the stock price to be tomorrow, approximately?

Question 517  DDM

A stock is expected to pay its next dividend of $1 in one year. Future annual dividends are expected to grow by 2% pa. So the first dividend of $1 will be in one year, the year after that $1.02 (=1*(1+0.02)^1), and a year later $1.0404 (=1*(1+0.02)^2) and so on forever.

Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.

Calculate the current stock price.

Question 635  continuously compounding rate

A $100 stock has a continuously compounded expected total return of 10% pa. Its dividend yield is 2% pa with continuous compounding. What do you expect its price to be in 2.5 years?

Question 766  CFFA, WACC, interest tax shield, DDM

Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the cash flow from assets including and excluding interest tax shields are constant (but not equal to each other).

Data on a Levered Firm with Perpetual Cash Flows
Item abbreviation Value Item full name
##\text{CFFA}_\text{U}## $100m Cash flow from assets excluding interest tax shields (unlevered)
##\text{CFFA}_\text{L}## $112m Cash flow from assets including interest tax shields (levered)
##g## 0% pa Growth rate of cash flow from assets, levered and unlevered
##\text{WACC}_\text{BeforeTax}## 7% pa Weighted average cost of capital before tax
##\text{WACC}_\text{AfterTax}## 6.25% pa Weighted average cost of capital after tax
##r_\text{D}## 5% pa Cost of debt
##r_\text{EL}## 9% pa Cost of levered equity
##D/V_L## 50% pa Debt to assets ratio, where the asset value includes tax shields
##t_c## 30% Corporate tax rate


What is the value of the levered firm including interest tax shields?

Question 779  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Fred owns some BHP shares. He has calculated BHP’s monthly returns for each month in the past 30 years using this formula:

###r_\text{t monthly}=\ln⁡ \left( \dfrac{P_t}{P_{t-1}} \right)###

He then took the arithmetic average and found it to be 0.8% per month using this formula:

###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.008=0.8\% \text{ per month}###

He also found the standard deviation of these monthly returns which was 15% per month:

###\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly} - \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.15=15\%\text{ per month}###

Assume that the past historical average return is the true population average of future expected returns and the stock's returns calculated above ##(r_\text{t monthly})## are normally distributed. Which of the below statements about Fred’s BHP shares is NOT correct?

Question 795  option, Black-Scholes-Merton option pricing, option delta, no explanation

Which of the following quantities from the Black-Scholes-Merton option pricing formula gives the Delta of a European put option?

Question 850  gross domestic product, gross domestic product per capita, no explanation

Below is a table showing some countries’ GDP, population and GDP per capita.

Countries' GDP and Population
  GDP Population GDP per capita
  USD million millions of people USD
United States 18,036,648 325 55,492
China 11,158,457 1,383 8,066
Japan 4,383,076 127 34,586
Germany 3,363,600 83 40,623
Norway 500,519 5 95,027


Source: "GDP and its breakdown at current prices in US Dollars" United Nations Statistics Division. December 2016.

Using this data only, which one of these countries’ citizens have the highest living standards?

Copyright © 2014 Keith Woodward