Wednesday, June 19, 2019

Net Present Value of Biennial Dividend Payments

This post uses two methods – Calculation in Excel and the Gordon Growth model – to calculate the net present value of biennial dividend payments.

Question:   A stock pays a $10 dividend every two years.   The first dividend is two years from the present date.   The growth rate in dividends is zero.     The dividends will occur forever.   The cost of capital is 9 percent per year.

Use Excel to calculate the net present value of the dividend payments for this firm.

Evaluate the relative importance of dividends after 50 payments have been made.

The Gordon Growth model gives the sum of the net present value all future dividend payments.   Modify the Gordon Dividend model to obtain the sum of biennial dividend payments.  

How does the Gordon growth model result differ from the sum of net present value of the first 100 payments?

Analysis:  The net present value of the dividend payments is the SUMPRODUCT of the dividend payments and the discount factor.   The discount factor D is 1/(1+0.09)t where t is the number of years from the current period where the dividend payment is made.

On the 50th payment  t is 100 and the discount factor is 0.00018.   The discounted value of the 50th dividend payment is $10 times the discount factor or around 1/5 of a cent.  

When the cost of capital is high and there is no growth in dividends the early dividend payments dominate the calculation for the net present value of all dividend payments.

The net present value of the first 100 dividend payments is the SUMPRODUCT of the dividend payment and the discount factor.   My spreadsheet gives us the value of $53.163 for the sum of the first 100 discounted payments.

Now how can we get this value using the Gordon growth model?

Payments are biennial so we need the two-year cost of capital.  The one year cost of capital is 0.09.   The two year cost of capital is therefore  R=(1+0.09)2 -1, which is 0.1881

The first dividend payment D1 is $10.   The growth rate of dividends is 0.   The  
Gordon growth estimate for net present value of all dividends is 10/0.1881 or $53.163.

The two approaches give the same answer.

Tuesday, June 18, 2019

Gordon Growth Model and viability of Apple and Microsoft Stock Prices

This post applied the Gordon Growth to Microsoft and Apple Stock in 2014.   Would love if one of my readers updated this piece.

Question:   The Gordon Growth Model asserts that the value of a stock can be modeled as

P = D/(k-g)

Where D is the expected price on a stock.  

D is next year’s expected annual dividend per share

k is the investor’s discount rate

g is the expected growth in dividends.

Use the Gordon Growth Model to compare the viability of the current stock prices for Apple and Microsoft.

Here is a discussion of the Gordon Growth Model:

Here is my assessment of Microsoft and Apple.  (I am using current market prices for P and current dividends for expected next year’s dividends and a 0.12 discount rate for investors in both companies.

Input for Gordon Dividend Growth Model Calculation
Price of Shares
Expected Dividends Per Share
Discount Rate

Given these admittedly arbitrary assumptions, what is the value of g (the expected growth in dividends) that is consistent with current market prices for the two stocks?


Rearrange the Gordon Growth Model equation to solve for g.

g= (Pk-D)/P

Below is the calculation for g and the check for the calculation.

Calculation for g and check of calculation
Price of Shares
Expected Dividends Per Share
Discount Rate


Based on the Gordon growth model and my assumptions I calculate the dividend growth rate consistent with current stock price.

The model finds g=0.101 for Apple and g=0.091 for Microsoft.

What projection of future dividend growth is more realistic?

The answer I believe is that at this point in time Apple is much better positioned than Microsoft.      


The current dividend yields for Microsoft and Apple are 2.9% and 1.9& respectively.  Based on these yields Apple has more upside on dividends.

Microsoft is already paying more of its income on dividends than Apple – payout ratios are 41% for Microsoft and 29% for Apple.

Why I could be wrong on this:  

Microsoft has more cash per share than apple $10.31 for Microsoft and $6.33 for Apple.

Financial Statistics are from Yahoo:  

Other interesting posts on Apple and Microsoft:

Yesterday I looked at wealth accumulated by an investor who bought 100 shares in the Microsoft and Apple IPO.

Interestingly, the Microsoft beat the Apple IP by a lot.  The Windows franchise was incredibly dominant for a long time and the finance people at Microsoft were very good at making sure previous investors were not diluted down. 

However, Apple got hot with new products – ipod, ipad, iphone, and now even icash.  The struggle continues.


Monday, June 17, 2019

House Equity and Mortgage Payoff Spread Sheet

This post looks at the decision to sell a house and move or payoff the mortgage.  Decision day is 12 years after purchasing the home.   The decision is analyzed for a person in a 15-year FRM and for a person in a 30-year FRM.  It is assumed the person has no liquid assets and that any mortgage payoff occurs from fully taxed disbursements from a 401(k) plan.

The Issue: Your client is  purchasing a house.  She is 12 years away from retirement.  At retirement she will either sell the house, take equity and move or she will pay off the mortgage and remain in the house.

There are costs associated with moving to a new home, which impact the amount of house equity that your client will receive if she decides to sell and move.   

Your client has no liquid assets outside her 401(k) plan.  Hence, any mortgage payoff would occur with 401(k) disbursements which, are fully taxed at ordinary income tax rates.  
Build a spread sheet that provides estimates of available house equity and mortgage payout for both a 15-year and 30-year fixed rate mortgage. Design the spread sheet so it is easily modified for different financial assumptions.

Comment on advantages and disadvantages of the different mortgage terms for this older buyer.

Your Client’s Information:   Information on the house purchase is presented in the table below.  

The 30-year FRM analysis is on the left and the 15-year FRM analysis is on the right.

The mortgage interest rate for the the 15-year FRM is 3.3 percent 0.7 percentage points less than the interest rate on the 30-year FRM.  This differential is not atypical of the market.

Assumptions and Input for
 Mortgage Choice Question
Purchase Price of House
Down payment percentage
Initial Loan Balance
Mortgage Term
House appreciation rate
Mortgage Interest Rate
Years until retirement & change in mortgage status
Cost of selling and moving to a new home as % of house value
Tax Rate on Disbursements from 401(K) Plan

The only difference in the two scenarios is the mortgage term – 30 years versus 15 years. 

Forecasted House Equity and Mortgage Payoff Amounts:

The bottom two rows of the table provide information on forecasted house equity after selling and moving costs and forecasted mortgage payoff amounts for your client for a 30-year and 15-year mortgage.

House Equity and Mortgage Payoff Calculations

Expected house value at sale date
Mortgage Payment
Mortgage Balance on Date of House Sale
House Equity after Selling and Moving Costs
Forecasted Amount Needed to Retire Mortgage Including Taxes on 401(k) Disbursements

Discussion of Results:  

The older worker who brings a larger mortgage balance into retirement is almost certainly going to have to sell her house and move. 

One of the factors driving the results presented here is the person pays off the mortgage from 401(k) funds, which are fully taxed at ordinary income tax rates.

The use of a 15-year mortgage substantially decreases the amount needed to pay off the mortgage.

Appendix: Describing the House Equity and Mortgage Payoff Calculations:

The description of the documented spread sheet for the available house equity calculation and the mortgage payoff calculation are available at the link below.

Go Here:

Concluding Thoughts   The use of a 15-year FRM substantially increases the probability your client will be able to stay in her home after retirement.

However, the higher payment on the 15-year FRM will require your client to reduce contributions to her 401(k) plan.    Spread sheets which examine issues pertaining to 401(k) growth will be available shortly.