financial valuation and decision

Question 1

Annuity

Answer 1

a series of equal payments or receipts occurring over a specified number of periods.
Ordinary annuity: payments or receipts occur at the end
Annuity due: payments or receipts occur at the beginning
Perpetuity: an ordinary annuity whose payments or receipts continue forever.

Question 2

An investor wants to withdraw $1,000 at the end of each period over the next 3 years, how much would she have to place in the account right now at an annual interest rate of 8%?
PV interest factor annuity (PVIFA)
3y… 2.6243 (7%) ….2.5771(8%)

Answer 2

PV of ordinary annuity = 1000*2.5771 = 2,577.1

Question 3

An investor wants to withdraw $1,000 at the beginning of each period over the next 3 years, how much would she have to place in the account right now at an annual interest rate of 8%?
PV interest factor annuity (PVIFA)
2y… 1.808(7%) … 1.7833(8%)
3y… 2.6243 (7%) ….2.5771(8%)

Answer 3

PV of annuity due = 1000+1000*1.7833 =1000+1783.3 =2783.3

Question 4

If $1,000 is received each year forever and the interest rate is 8%, what is the ultimate PV of this perpetuity

Answer 4

PV = CF/i
PV = 1000/8% = 12500

Question 5

Constant Growth Dividend Discount Model (DDM)

Answer 5

Assumptions:
- Intrinsic value of the company’s stock is the present value of the expected future dividends
- Dividends are assumed to grow at a constant rate
- Stock price will grow at the same rate as the dividend in perpetuity
- Required rate of return is greater than the dividend growth rate
P = [D(1+G)]/(R-G)

Question 6

Baker pays a current dividend per share of $5 per year and is projected to grow at 4% per year. Able wants to invest in Baker and earn a 20% return. Calculate the value of Baker’s stock today.

Answer 6

D =5
G = 4%
P = 5*(1+4%) / (20%-4%) = $32.5
The intrinsic value of Baker’s stock today is 32.50

Question 7

Baker pays a current dividend per share of $5 per year and is projected to grow at 4% per year. Able wants to invest in Baker and earn a 20% return. Calculate the amount that Able will pay for Baker’s stock 3 years from today.

Answer 7

P0 = [D(1+G)]/(R-G)
P3 = [D(1+G)^4]/(R-G) = [5*(1+4%)^4] / 16% = 36.56
In order to value Baker in 3 years, the dividend to be paid in the 4th year is required. Able should pay $36.56 for Baker in 3 years.

Question 8

Discounted Cash Flow

Answer 8

Discounted cash flow (DCF) analysis: determine the intrinsic value of an equity security by determining the present value of its expected future cash flows.

Step 1: Choose an appropriate model and forecast the security’s cash flows
Dividend discount model (DDM) use the stock’s expected dividends as the relevant cash flows, e.g. Constant Growth DDM
Free cash flow model: discount the cash flow left over by the firm after satisfying certain required obligations including working capital needs and fixed capital investment.
Residual income model: the income left over after the firm satisfies the investor’s required return.

Step 2: Estimate the required return by selecting a discount rate methodology, such as CAPM.

Step 3: Apply to the appropriate DCF model to calculate the equity security’s intrinsic value and compare to its current market value.

Question 9

Baker has current year earnings per share of $1.50 and anticipates earnings per share in the coming year of $2. if P/E ratio is 7.5x, calculate the expected value of Baker’s shares.

Answer 9

P0 = P0/E1 *E1
P = 7.5 *2 =15
An investor would expect the current stock price to be 15, if current price >15, could be overvalued or have more growth. If current price <15, could be undervalued.

Question 10

If a company is trading at 12 times earnings (12x), what is the estimated value per share of the company? Selected financial information for the company is as follows:
Long-term debt (8%) …10million
common equity par $1 … 3m
APIC … 24m
RE … 6m
total assets … 55m
net income … 3.75m
dividend (annual) … 1.5m

Answer 10

P/E = 12
p = 12* EPS
outstanding shares = 3m/$1=3m shares
EPS = 3.75m/3m = 1.25
P = 12* 1.25 = 15

Question 11

If a company is trading at a market to book ratio of 1.5 (P/B ratio), what is the estimated value per share of the company? Selected financial information for the company is as follows:
Long-term debt (8%) …10million
common equity par $1 … 3m
APIC … 24m
RE … 6m
total assets … 55m
net income … 3.75m
dividend (annual) … 1.5m

Answer 11

P/B = 1.5
booking value = 3+24+6=33m
outstanding shares = 3m/$1 =3m shares
booking value per share = 33m/3m =11
P = 1.5 * booking value per share = 1.5 *11 =16.5

Question 12

A company is expected to earn EPS of $5 and its growth rate will be 5%. what is current market price of its common stock if it has a PEG ratio of 4?

Answer 12

PEG ratio = (P/E ratio ) / G * 100 = 4
P/E = 4G
P = 4(G100)E
EPS = 5 (EXPECTED, SO IT IS E1)
P= 455 = 100

Question 13

P/S ratio

Answer 13

to replace P/E ratio as no or little profit earned for start-up firm. P/S ration = Current market price P0/Sales revenue S

Question 14

P/C ratio

Answer 14

Stock price ultimately linked to cash flows generated by company.
P/C ratio = current market price / cash flow

Question 15

An investor is comparing market ratios for C company to those of its industry. the ratios were calculated at the end of the current fiscal year:
P/E 16.2 (industry 14.9)
PEG 4.8 (industry 5.3)
P/S 18.1 (industry 19.4)
P/CF 13.6 (industry 13.7)
P/B 19.2 (industry 17.8)
Discuss what each ratio indicates regarding C stock valuation and how the numbers can be interpreted.

Answer 15

Higher P/E ratio, indicating that the stock price for C is overvalued relative to that of its peers. investors would expect the price to decline in order to align with that of its peers.
Lower PEG ratio means growth rate (16.2/4.8=3.38) is higher than its peers (14.9/5.3=2.81), indicating that C stock may actually be undervalued.
Lower P/S ratio is another indicator that C stock may actually be undervalued. However, this ratio alone does not account for cost structure, capital structure, or tax effects that should be evaluated before determining whether a stock is relatively overvalued or undervalued.
Similar P/CF indicate that the stock price for C is fairly valued.
Higher P/B ratio may indicate that the market thinks that C’s net assets are undervalued.

Question 16

F wants to buy shares of G company in two years. F uses a constant growth dividend discount model with a presumed dividend growth rate of 5%. If F’s discount rate is 10% and G’s current year dividend is $20, what is the approximate price F will pay?

Answer 16

In two years, so calculate P2
P2 = [D0 (1+g)^(2+1)] / (r-g)
P2 = (201.05^3)/(10%-5%)
= (201.157625)/0.05
= 463.05

Question 17

Black-Scholes option model

Answer 17

Assumptions：
Stock prices behave randomly.
The risk-free rate and volatility of the stock prices are constant over the option’s life.
No taxes or transaction costs.
No dividends
The options are European style (exercisable only at maturity).
Five determinants of option value:
- Variability of stock price.
- Distance of expiration date
- Interest rate
- Exercise price
- Stock price

Question 17

C is using a constant growth dividend discount model to forecast the value of a share of common stock. inherent in C’s assumption is the idea that:
a. Compounding growth is linear.
b. Dividends will grow at a rate faster than the presumed discount rate.
c. Stock price will grow at the same rate as the dividend
d. Stock price will grow at the same amount as the dividend

Answer 17

c

Question 17

Investors are likely to view a high price-earnings (P/E) ratio as an indication that:
a. Earnings have growth potential
b. Earnings have peaked and will remain flat.
c. Earnings have peaked and will likely fall.
d. There is no logical conclusion to reach about the relationship between price and earnings.

Answer 17

a

Question 18

Binomial model

Answer 18

Assumptions of Binomial Model
A perfectly efficient stock market; and
The underlying security price will move up or down at certain points in time during the life of the option.
Binomial Model: A variation of the original Black-Scholes model
This model is useful for valuing American-style options, which can be exercised over a period of time.
it can be used for stocks that pay dividends without modifying the model.
The result is a tree diagram showing the possible values of the options at different points in time.

Question 19

Valuation techniques for tangible assets

Answer 19

Cost Method
Original cost paid to acquire the asset with depreciation adjustments to reduce value

Market Value Method
- Replacement cost method: Cost to replace the valued asset in the marketplace
- Net realizable value method: The asset selling price minus selling cost in the marketplace

Appraisal Method: a professional appraiser determines the value of the asset

Liquidation Value: the amount selling asset today assuming that there is an active market for the asset

Question 20

Valuation techniques for Intangible Assets

Answer 20

• Market approaches
  Valuation based on market information for similar assets
• Income approaches
  Estimation of fair value by estimating and discounting the future amounts
• Cost approaches
  Determination of value by estimating replacement cost

Question 21

Factors need to be considered for accounting estimate

Answer 21

Historical Information
e.g. allowance for uncollectible accounts be estimated using historical information of collectability
Market Information
e.g. current value of inventory items determines whether inventory should be written down or written off due to obsolescence.
Expected Usage
e.g. Depreciation methods may be based on expected patterns of fixed‑asset usage.
Estimates From Experts
e.g. Attorneys provide estimates of probable future losses on pending litigation

Question 22

An investor wants to have high yield with stock investment. Certain information on XYZ is collected by the investor, presented as follows:
I. Current cash dividend: $3
II. Investor’s required rate of return: 10%
III. Growth rate of XYZ: 5%
IV. Current stock price: $80
It is correct to infer that
A. The investor will loss money, if all these information is correct
B. The investor will earn profit, if all these information is correct
C. The investor should not invest XYZ’s stock, as the stock is risky
D. The investor should invest XYZ’s stock, as the stock is less risky

Answer 22

A&C
the intrinsic value of the stock = 3*(1+5%)/(10%-5%) = 63
63 <80, price is higher then its value.

Question 23

Fair value

Answer 23

Fair value is the price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants in the principal (or most advantageous) market at the measurement date under current market conditions.

Question 24

Fair Value Measurement Framework

Answer 24

Market Approach
Includes quoted prices in an active market, but often derive market multiples from a set of comparable assets.
Income Approach
Convert future amounts such as cash flows or income streams to a current amount on the measurement date.
Cost Approach
Reflect the amount that would be required to replace the service capacity of an asset.

Question 25

Valuation techniques should maximize the use of observable inputs (Level 1 & 2) and minimize the use of unobservable inputs (Level 3).

Answer 25

Level 1 Inputs (highest): unadjusted quoted prices in active markets at the measurement date.
Level 2 Inputs: quoted prices for similar assets/ liabilities in all markets, adjusted as appropriate for differences. Includes the quoted prices:
For similar assets/liabilities in active markets.
For identical or similar assets in markets that are not active.
Level 3 Inputs:
Unobservable inputs for the asset/liability. only be used without observable inputs (level 1&2)
Entity’s own assumptions about the market and are based on the best information available.

Question 26

Marginal analysis

Answer 26

To be relevant, both revenue and cost must occur in the future and
differ among the alternative courses of action.
Sunk cost is irrelevant because it incurred in the past.
Unavoidable cost is the cost that will be incurred regardless of what decision is made by management.