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CFP Canada Exam Study 2024 Needs Updating > Financial Math > Flashcards

Financial Math Flashcards

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1
Q

What is the Formula for the Nominal* Approximate Rate of Return?*

A

Nominal Rate = Real + Inflation or Real = Nominal - inflation

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2
Q

What is the Formula for the Nominal Exact Rate of Return

This will be the one used on the exam!

A

Nominal Rate = (1+Real Rate) (1+ Inf) - 1 or Real Rate = [Nom Rate/(1+ inf)] -1

If asked for Real Rate of return adjust formula

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3
Q

What is the Formula for the After-Tax Rate of Return

A

After-Tax Rate of Return (ATRR) = (Pre-tax Rate of Return) (1- MTR)

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4
Q

What is the Formula for the Effective Annual Rate (EAR)

A

EAR = (1 + i/n)n - 1

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5
Q

What is the Formula for FV?

A

FV= PV x (1+i)n

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6
Q

What is the formula for the FV of an annuity?

(Beware of BGN or END for the timing of cashflows)

A

FVA = PMT x (1+i)<u>n</u>-1

i

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7
Q

What is the formula for PV?

A

PV = FV

(1+i)n

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8
Q

What is the formula for PVA?

(Finding an income)

A

PVA = PMT x 1 - (1+i)<u>-n</u>

i

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9
Q

What is the decision rule for IRR?

A

IF the IRR is greater than the cost of capital then the investment will be wealth enhancing.

Is it less? then wealth reducing.

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10
Q

What is the stated interest rate?

A

Nominal annual rate or the contractual rate (i.e. coupon)

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11
Q

What is the periodic rate?

A

Rate of interest earned over 1 compounding period (i.e. semi-annual)

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12
Q

What is the effective Annual Rate

A

Rate of return actually being earned after adjustments for compounding frequency.

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13
Q

What type of annuity makes payments at the end of a period?

A

Ordinary Annuity

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14
Q

What type of annuity makes payments at the beginning of a period?

A

An Annuity Due

(Remember the FUTURE VALUE is always ZERO for an annuity)

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15
Q

What are some indicator words for an Annuity Due?

A
  • payments on your birthday
  • anniversary
  • at the beginning of the year
  • on Jan 1
  • starting today
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16
Q

What are some indicator words for an Ordinary Due?

A
  • At the end of the year
  • starting next month
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17
Q

Current Yield Stocks and Bonds

What is the Current yield (Dividend Yield) for Stocks?

A

Current Yield = (Dividend/Current Market Price) x 100

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18
Q

Current Yield Stocks and Bonds

What is the Current yield (Dividend Yield) for Bonds?

A

Current Yield = (Coupon in $/ Current Market Price) x 100

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19
Q

What is the formula for ATRR?

(After-tax real rate of return)

THIS IS THE SHORTCUT FORMULA

A

ATRR = [Nominal Return x (1 - MTR)] - Expected Inflation

(1 + Expected Inflation)

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20
Q

What is the formula for Yield to Maturity

(Market Value for Bonds)

A

Yield to Maturity = Coupon + (1,000 - Market Price<u>B</u>)

n

(1000 + Market PriceB) /2

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21
Q

If you are looking for YTM when working with bonds what are you looking for?

A

The market value of a bond.

Watch for annual pay

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22
Q

What are P-Strips and C-Strips

A

P-Strips - no coupons (use the PV of a lump sum formula here)

C-Strips - are the coupons

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23
Q

If you were an investor would you rather have the return on a common stock or income from debentures

A

An investor would be better to choose the common stock because of the dividend tax credit as it applies to dividend-paying stocks. The resulting tax credit will put more money in their pocket after tax

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24
Q

Bond Pricing

As yields rise what happens to the price of bonds?

A

Yields Rise

Bond Price Falls

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25
Q

What is the Bond Price Formula?

A

Bond Price = PV (Cash Flows) + PV (Maturity Value) [This last part is the clean price of a bond]

This looks like our old friend…PV of an Annuity + PV of a lump sum

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26
Q

What are the 3 steps to calculating the Current Market price of a bond?

A
  1. PV (Coupon PMTS)
  2. PV (Maturity Value)
  3. Add your results in steps 1 and 2 together to get your bond price

PB = PV PV (Coupon PMTS) + PV (Maturity Value)

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27
Q

If you want money with certainty, what type of Bond will ensure it will happen?

A

Choose a strip bond

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28
Q

Bonds and Accrued Interest Calculations

When do bonds pay?

A

On the Coupon Payment Date (very specific date)

When a bond is purchased on any other date there will be accrued interest that will be owed and paid to the seller.

29
Q

When a bond is sold on a date other than the coupon payment date what is the name of the price for the bond to be paid?

A

Dirty price or the full price

The clean price is the payment less the accrued interest

30
Q

To calculate the accrued interest what 3 things must you know?

A
  1. Coupon payment date
  2. Settlement date
  3. coupon rate
31
Q

What is the settlement date for any bond maturity?

A

T + 2 BUSINESS days

  • Interest accrues from the first day following the last coupon payment date up to and including the settlement date
32
Q

Accrued Interest in Bonds

The last coupon date was Jan 1

Today is Feb 6

$200,000, 8% Govt Canada Bond, due in 7 years on Jan 1, YTM 8%

How many days of interest have accrued?

A

January 2nd is the first day of interest, so Jan 31-1 = 30

Feb (6 + 2) = 8 Remember settlement T2

Total 38 days

$200,000 x 8% x 38/365 = $1,665.75 accrued interest

Now Calc the full price of the bond

$200,000 + $1665.75 = $201665.75

33
Q

What is the accrued interest formula for bonds?

A

Accrued Interest = (coupon) x (Par amount) x (# days/365)

Where: # days = the number of days of accrued interest

34
Q

What is the dirty price formula?

A

Dirty Price = Clean price + Accrued Interest

35
Q

Reinvestment Risk

When interest rates fall what happens to the prices of bonds and the subsequent coupon payments as it relates to the return for an investor?

A

The YTM of a bond assumes that all bond coupons are reinvested at the same yield to maturity.

If interest rates fall after the bond has been issued the coupon payments will be reinvested at a lower rate of return and the investor will realize a total return that is less than the originally estimated YTM

36
Q

Factors Affecting Reinvestment Risk

A

Higher Coupon => Higher Reinvestment Risk

Lower Coupon => Lower Reinvestment Risk

Longer Time to Maturity => Higher Reinvestment Risk

Shorter Time to Maturity => Lower Reinvestment Risk

37
Q

What is the Reinvestment Risk on Zero-Coupon Bonds?

A

Zero = 0

No Reinvestment Risk

38
Q

When calculating the Reinvestment Risk of a bond…

holding a 6%, 3 yr annual pay bond with YTM 8%

What is the payment?

Then if the interest rate drops to 7% what is the realized return?

(remember it is no longer the same as the YTM 8%)

A
  1. 1000 x 6% = $60 PMT
  2. USE TVM: FV 1000, N 3, PMT 60, I 8%, CPT PV $948.46

Now… the interest rate has fallen to 7%.

  1. USE TVM: PV -$948.46, N 3, PMT 60, I 7%, CPT FV $969.01
39
Q

Time-Weighted Rate of Return (TWRR)

What formula do I use?

A

Geometric Average!

HPR is used in this formula for Rn

TWRR = [(1+R1)(1+R2)(1+R3)…(1+Rn)]1/n -1

Use y 1/x button on the calculator

40
Q

What is used as a measure for the risk-free rate of return?

A

Government T-Bills

41
Q

What is the measure of level of risk in investment theory?

A

Standard Deviation

SD = Square root of Sum of (actual return - expected return)<u>2</u>

N-1

Two parts to this:

  1. find arithmetic return or expected return… %
  2. Calculate the SD…%
42
Q

Holding Period Return (HPR) and Total Return

What is the HPR?

A

Calculated as the growth or difference between the ending value and the beginning value of an investment over a specific period of time (the holding period)

43
Q

Holding Period Return (HPR) and Total Return

What is the Total Return?

A

It is made up of the income (ie. interest or dividends) earned plus the capital gain/loss on the principal.

44
Q

What is the Holding Period Return (HPR) formula

A

HPR% = Income + (END Value - BEG Value) x 100

BEG Value

45
Q

What is the Holding Period Return (HPR) formula annualized?

A

HPR% = Income + (END Value - BEG Value) x (365/#days) x 100

BEG Value

  • Remember # days in the denominator
  • Can use months if question focuses on that
46
Q

Exam Tips

Total Return for a stock = ?

Total Return for a bond = ?

Capital gainss (losses) = ?

Income for Stocks =?

Income for Bonds =?

A

Total Return for a stock = Dividend Yield + Growth

Total Return for a bond = YTM

Capital gains (losses) = END - BEG

Income for Stocks =Dividends

Income for Bonds = Coupon Interest PMTS

47
Q

T-Bill Yield formula?

A

T-Bill Yield = [$100,000 - Price Paid x 365/#Days] x 100 = __%

Price Paid

  • Again #days is the denominator
48
Q

STOCKS

What is the Security Market Line Formula?

and

What is the Dividend Discount Model (DDM) formula?

A

Step 1: r = (required rate of return)

r = Rf + B ( Rm - Rf )

Step 2: then may need to find D1 first given the D0 only

D1 = D0 (1 + g)

Step 3: Plugin r and D1 …where Ps is the stock price

Ps = D<u>1</u>

(r - g)

49
Q

Portfolio Return and Variance (Standard Deviation)

What is the Asset Weighting formula?

What is the Expected Return?

A

Wn = Market Value of Asset <u>N</u>

Total Market Value of the Portfolio

  • The expected return for a portfolio of securities is simply the weighted average of the expected returns for each individual asset.

Er = (w1)(Ex. Return Assets1) + (w2)(Ex. Return Assets2) +…+(wn)(Ex. Return Assetsn)

50
Q

Arithmetic Average Formula

A

Average = sum of x/ number

51
Q

What is the Geometric Average formula for HPR?

A

Average = [(1 + HPR1)(1 + HPR2)….(1 + HPRn)]1/n - 1

52
Q

What do you notice about the geometric average in comparison to the arithmetic average?

A

The geometric average is less and more accurate!

53
Q

Portfolio Variance (Standard Deviation) measures what?

A

The riskiness of an investment portfolio

  • The square root of the variance is the SD*
  • The higher the variance or SD the higher the risk!*
54
Q

What are the Portfolio Variance and Standard Deviation formulas?

A

Portfolio Variance = (W12 V12) + (W22 V22) + 2W1W2 COV1 2

Portfolio Standard Deviation = Square Root of the Variance

55
Q

Mutual Fund Calculations

What is considered the ACB of a Mutual Fund?

A

The purchase price plus any commission paid

56
Q

What are the 3 Commission structures or options

A
  1. No Load
  2. Front-End Load
  3. Back-End Load or Deferred Sales Charge ‘DSC’
57
Q

What is the formula for No Load Commissions?

A

Price Paid = NAVPS = Total Assets - Liabilities

#Shares Outstanding

No commission is charged to the investor. We only calculate the price paid.

58
Q

What is the formula for Front-End Commissions?

A

Price Paid = NAVPS

1 - % Sales Charge)

The price paid is not the same as the NAVPS. They pay more now!

59
Q

What is the Deferred Sales Charge Formula?

A

Price Received = NAVPS x (1 - % Redemption)

The investor does not pay a commission upfront, but a redemption fee or back-end load.

The charge may be based on the initial purchase value or the current market value at the time of disposal

60
Q

What is the Total Return of a Mutual Fund Formula?

A

The difference between the beginning and the ending value includes any distributions.

Total Return = (Final NAV + Distributions) - Original NAV x 100

Original NAV

61
Q

Financial Statement Analysis

****What are the 3 liquidity formulas?***

A
  1. Current Ratio = Current Assets / Current Liabilities
  2. Quick Ratio = [Current Assets- Inventory} / Current Liabilities
  3. Working Capital = Current Assets - Current Liabilities

*How well the company handles short term obligations

62
Q

Financial Statement Analysis

What are the 3 Riskiness formulas?

A
  1. Debt to Equity Ratio = Short Term Debt + Long Term Debt / Total Equity
  2. Debt-to-total Assets Ratio = Short Term Debt + Long Term Debt / Total Assets
  3. Interest Coverage (“times earned interest”) = Operating Income / Interest Expense

*The greater amount of debt used by a company, the greater the financial risk.

63
Q

Financial Statement Analysis

What are the 2 formulas that show the ability to manage various business expenses?

A
  1. Net Profit Margin = Net Income / Sales
  2. Gross Profit Margin = [Sales - Cost of Good Sold] / Sales
64
Q

Financial Statement Analysis

What are the 2 formulas that show the ability to generate profits?

A
  1. Return on Common Equity = Net Income / Common Equity
  2. Return on Total Assets = Net Income / Total Assets
65
Q

Financial Statement Analysis

***What is the formula to show the intrinsic value of a share?***

A

EPS = Earnings Available to Common Shareholders

Weighted Average Number of Shares Outstanding

EPS is commonly used to calculate the intrinsic value of a share. The growth of EPS is considered to be a positive signal to investors.

66
Q

Financial Statement Analysis

***What is the formula to show investor confidence in the growth potential of a company’s earnings?***

A

P/E = Dividend Payout

r-g

Where r = discount rate

g = growth rate

  • *Higher PE Ratio signals growth stocks*
  • *Lower PE Ratio signals value stocks*
67
Q

Financial Statement Analysis

****What is the formula that indicates the % of a company’s earnings that are paid out to shareholders as dividends?****

What are dividends called that are not paid out to investors?

A

Dividend Payout = Dividends per Share

EPS

Dividends not paid are called Retained Earnings!

68
Q

Financial Statement Analysis

What is the Market Capitalization formula?

A

Market Capitalization = (Number of Shares Outstanding) x (Share Price)

  • Market capitalization refers to how much a company is worth as determined by the stock market. It is defined as the total market value of all outstanding shares.
69
Q

Financial Statement Analysis

What 3 formulas show management’s ability to effectively utilize the assets to generate sales?

A
  1. Asset Turnover = Sales / Total Assets
  2. Inventory Turnover = Cost of Goods Sold / Inventory
  3. Receivable Turnover = Sales / Average Accounts Receivable

CFP Canada Exam Study 2024 Needs Updating (13 decks)

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