Formulas to Memorize

Question 1

Coefficient of Variance

Answer 1

Coefficient of Variation is a way to compare the relative variation of two or more securities. The security with the lowest CV should be chosen.

Standard Deviation divided by the mean (average). All other risk related formulas have risk (SD or Beta) measurment in the denominator and this forfula (Coefficient of Variation) has it in the numerator and has the retuns in the denominator.

CV = SD / Mean

Question 2

Correlation Coefficient (R)?

Answer 2

Not provided but you can do algebra to get it from the Covariance Formua (which is provided)

COV_ij = R x σ_i σ_j

R = COV_ij / σ_i σ_j

R or rho equal the Correlation Coefficient

Question 3

Valuation of Real Estate?

Answer 3

Property Value = NOI / Cap Rate

To get NOI, you have to Add all Operating Income to get Gross Operating Income (rent + laundry, etc.).

Then apply the Vacancy rate (usually about 7%, so you will multiply by 93% to get the Operating Income)

Then you will subtract all the costs like property taxes, property insurance, property management, utilities, administration, repairs, maintenance, etc. (No not include Financing Costs or Depreciation). This number will give you your NOI.

Question 4

Risk adjusted return using Beta?

Answer 4

Risk Adj = Mean / Beta

Question 5

Growth Rate

Answer 5

This is used in the Discount Dividend Model

g = ROE x RR -or- ROE = g / RR

g = growth rate

ROE = Return on Equity (ROE is calculated by net income / shareholders equity)

RR = Retained Rate of Earnings => the remaining percentage is the Dividend Payout Rate, so if the RR = 80%, then the company paid 20% in Dividends.

RR = To calculate Divedend payout ratio => take Dividend / EPS = Payout then take (1-payout ratio ) to get Retained Earnings.

EPS = Divide current dividend by the dividend payout ratio (expressed as a decimal)

P/E = Divide price per share by the earnings per share

Question 6

Taxable Equivalent Yield for Federal and State Tax

Answer 6

TEY = Tax Free Yield / (1-Federal) x (1-State)

Question 7

DDM formula

Answer 7

V = D₁ / (r - g)

V = Intrinsic Value

D₁ = Next year Dividend Rate [D₁ = D₀ x (1 + dividend growth rate)] or D₁ = $1.50 (1 + 4%) so D₁ = $1.50 (1.04) or $1.56

r = required rate of return

g = growth rate of stock

Question 8

DDM Formula for Non-Constant Rates of Growth?

Answer 8

Earnings and dividends per share are expected to grow at a rate of 18% over the next three years, and a constant rate of 6% thereafter. The last dividend was $1.15. The required return is 12%. What is the price of the stock today? This is done in 3 steps.

Step 1: What is the dollar amount of the dividend at the end of the each of the first three years?

Year 1: 1.15 x 1.18 = 1.3570

Year 2: 1.3570 x 1.18 = 1.6013

Year 3: 1.6013 x 1.18 = 1.8895

Step 2: What is the value of the stock at the end of Year 3 based on the dividend at the end of Year 4? Use Constant Growth Formula here.

[1.8895*(1.06) / 0.12-0.06] = 33.380

Step 3: What is the discounted value today of the stock price and the dividend at the end of Year 3 and each of the dividends for years 1 and 2?

Use calculator and solve for NPV as an irregular cash flow:

Entry Keystrokes

12 I

0 CFj₀

1. 3570 CFj₁
2. 6013 CFj₂
   (1. 8895 + 33.3809) = 35.2704 CFj₃

SHIFT, NPV = 27.59

Question 9

Expected Return vs. Required Return

Answer 9

Expected Rate of Return Formula on the Exam Sheet is

r = (D₁ / P) + g

Need to write the Capital E on the formula sheet and title it Expected Return

E_r = (D₁ / P) + g

Required Rate of Return Formula on the Exam Sheet is

r_i = r_f + (r_m - r_f)β_i

Need to write Required Rate of Return on the formula sheet

Question 10

Alimony Recapture Formula

Answer 10

P₁ + P₂ - 2P₃ - $37,500 = Alimony Recapture

P₁ = Payment in year 1

P₂ = Payment in year 2

P₃ = Payment in year 3

Question 11

Tips when making calculations for PV/FV and CF

Answer 11

PV/FV: Create Write a timeline to track Int Rate and Inflation to make sure that it is balanced. Especially in 3 part college tuition question.

PV/FV: Create a table with B/E - N - I/YR - PV - PMT - FV

CF: Write a table for Cash Flows and write a timeline with positive numbers on top and negagive numbers below timeline. Make sure to be in the correct term (monthly, semi-monthly, quarterly, yearly). Make sure to use $ signs and % where available so I track what is going on better.

Write out the Units ($ or %) explicitly

Question 12

How do I calculate the Price of when a Margin Call will occur?

Question:

An investor wants to buy 100 shares of a stock on margin. The stock is selling for $40 per share. The initial margin is 55% and the maintenance margin is 35%. Assuming she can purchase the stock at the current market price, at what price will a margin call occur?

Answer 12

The formula is [(1 − initial margin) / (1 − maintenance margin)] × price of stock = margin call price.

Answer:

the formula is [(1 − .55) / (1 − .35)] × 40 = 27.69

Question 13

Margin Price Formula?

Answer 13

(1 - Initial Margin Rate / 1 - Maintenance Margin Call) x price of stock

Example:

Margin Rate is 50%

Maintenance Margin Percent is 30%

Price of Stock is $40

[(1 - 0.50) / (1 - 0.30)] x 40 = $28.57

Question 14

How do you calculate the Price of a Convertible Bond?

Answer 14

Conversion Value = [($1,000 / Conversion Price) x Market Price of Common Stock

Example:

Zim Convertible Corp Bond at 9%

Comparable Debt Yields are at 8%

Zim Converrible Corp Bond Conversion Price is $40

Zim Corp Stock Price is $46

[(1,000 / 40) x 46 = 1,150

Question 15

HO - Property Insurance calculation when underinsured?

Answer 15

[(insurance carried / insurance required) x loss] - deductible = maximum amount of recovery

* Coinsurance requirement is usually 80% of replacement cost. This is primarily a concern in the event of a partial loss.

Ex: Question

Andrew purchased an automotive service station seven years ago for $500,000. The building’s current replacement value is $900,000. Andrew originally insured the building for its replacement cost of $500,000 and has not increased the coverage. His policy has an 80% coinsurance clause and a $5,000 deductible. Last week a fire caused $200,000 of damage.

Payment = ((Amount of insurance owned/Amount of insurance required) × Loss) - Deductible

Amount of insurance required = $900,000 × .8 = $$720,000

(($500,000/$720,000) × $200,000) − $5,000 = $133,889
(CFP D23)

Question 16

SE Tax Calculation and Contribution to a SEP

Answer 16

EX: Client net profit of $130,000

SS Wage Base is $127,200

What is max contribution to a SEP for owner?

STEP 1: CALCULATE SE SUBJECT TO TAXES: Schedule C Net Income of $130,000. Subtract 7.65% of ER FICA Tax from net income or multiply it by .9235 to get ($130,000 x .9235 = $120,055)

STEP 2: CALCULATE SE TAX: Multiply $120,055 by ER + EE FICA of 15.3% for a SE Tax of $18,368.

STEP 3: BUSINESS PROFIT: $130,000

STEP 4: LESS INCOME TAX DEDUCTION ALLOWED (1/2 of SE Tax): 1/2 of SE Tax is $18,368 / 2 = $9,184

STEP 5: NET EARNINGS: $130,000 - $9,184 = $120,816

STEP 6: SEP CONTRIBUTION: Owner can only contribute 20% of $120,816 = $24,163

Question 17

RMD Formula? Which Table do you use?

Answer 17

RMD Single Life Table - Life Expectancy

RMD Joint and Last Survivor Table - Life Expectancy

Uniform Table

We use the Uniform Table

Question 18

How much consumer debt is considered acceptable?

Answer 18

Co = 2 Co-Captains = 2 captains

Lucas is co-captain of his soccer team and soccer goals have a net.

Complaints is 20 days and Consumer debt is 20 percent.

≤20% of NET income

Question 19

What is back-end ratio?

How much Total Monthly Debt is considered acceptable?

Answer 19

≤36% of GROSS income

Question 20

What is a front end ratio?

How much PITI is considered acceptable?

Answer 20

≤28% of GROSS income

Question 21

How to calculate QP contributions for a SP when net income is over SSA limit of $127,200.

If contribute 25% to EE’s then contribute (0.25/1.25 = 0.20)

If contribute 20% to EE’s then contribute (0.20/1.20 = 0.1667)

Answer 21

STEP 1: To calculate the self-employment tax, subtract 7.65% or multiply by 0.9235 from her net earnings ($180,000 - $13,770 = $166,230)

STEP 2: Then subtract the 2017 wage base of $127,200 to calculate the remaining dollars ($166,230 - $127,200 = $39,030) that are subject only to the 2.9% Medicare rate.

STEP 3: Multiply the wage base by 15.3% for a total of $19,462 and add that to the Medicare amount ($39,030 × 2.9%) of $1,132 for a total of $20,594.

STEP 4: One-half of the self-employment tax, or $10,297 is deductible as an adjustment to income.

STEP 5: Reduce the net profit of $180,000 by $10,297 (=$169,703) and we then multiply that by Cheryl’s contribution percentage.

STEP 6: Since she contributes 20% into the money purchase plan for her employees, she would contribute 16.67% (16.67% is arrived at by taking .20/1.20 = .1667) the contribution for Cheryl would be 16.67% × $169,703 = $28,289.

Question 22

What is the charitable deduction when using a Charitable Lead Annuity Trust (CLAT)?

Answer 22

The charitable deduction is the PV of the income interest. The IRS will give a Table B giving a factor to use to compute the PV of income interest.

Annuity Payout x Table B factor = PV of charitable deduction

See Q below:

Henry’s will directed that $300,000 be placed in a charitable lead annuity trust (CLAT), with $40,000 per year payable for 10 years to a qualified charity, with the remainder being paid equally to his two children. The applicable interest rate for the month of Henry’s death was 8.0% and the annuity factor is 6.7101. Payments of income are to be made annually, starting one year from Henry’s death. How much of this bequest, if any, qualifies for the charitable deduction?

Answer:

Only the present value of the income interest qualifies for the charitable deduction. IRS Table B must be used to compute the present value of this income interest since the trust is to last for a term certain. The appropriate annuity factor from Table B is 6.7101, which, when multiplied by the annuity payment of $40,000, yields a present value of $268,404.

Question 23

Weighted average standard deviation of a 2 security portfolio.

Stock A: 40% weight / 10% Return / 3.0 Standard Deviation

Stock B: 60% weight / 14% Return / 5.0 Standard Deviation

Correlation Coefficient is -0.10

Answer 23

Use the 2 Security SD of a portfolio formula

2nd of top right of formula sheet

Solve the Expected Return & Standard Deviation

Expected Return is (.4)(.10) + (.6)(.14) = 12.4%,

Standard Deviation isTHE SQUARE ROOT of [(.4)² (3)² + (.6)²(5)² + 2 (.4)(.6)(3)(5)(-0.10)]^{0.50(represents square root)} = 3.118

Question 24

ABC stock has the following annual returns: +12%, −5%, +18%. What are the arithmetic and geometric average returns?

Answer 24

The arithmetic average is (.12 - .05 + .18)/3 = 0.0833 = 8.33%.

The geometric return is the cube root of (1.12 × 0.95 × 1.18), which is the cube root of 1.2555. On the HP 10BII+ the keystrokes would be: 1.2555, SHIFT, y_x (“x” key) .3333 = 1.0788 = 7.88%

Question 25

Maximum Current Year Charitable Deductions for Public or Private Charity?

Answer 25

Type of Property__Public - Private

Ordinary Income or STCG 50% of AGI - 30% of AGI

use-related tangible personalty Adj Basis - Adj Basis

LTCG Property 30% of AGI - 20% of AGI

use-related tangible personalty FMV - FMV

1st Step: Is it 50% (Public) or 30% (Private) Charity?

2nd Step: Is it ST or LT?

3rd Step: Apply proper formula, but make sure to note you select to take the 50% Public Charity Election for LTCG Property but its at Adj Basis instead of the 30% at FMV.