## 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.