Question

Guff plc, an all-equity firm, has the following earnings per share and dividend history (paid annually).

Year Earnings per share Dividend per share
This year 21p 8p
Last year 18p 7.5p
2 years ago 16p 7p
3 years ago 13p 6.5p
4 years ago 14p 6p

This year’s dividend has just been paid and the next is due in one year. Guff has an opportunity to invest in a new product, Stuff, during the next two years.

The directors are considering cutting the dividend to 4p for each of the next two years to fund the project. However, the dividend in three years can be raised to 10p and will grow by 9 per cent per annum thereafter due to the benefits from the investment. The company is focused on shareholder wealth maximization and requires a rate of return of 13 per cent for its owners.
Required
a. If the directors chose to ignore the investment opportunity and dividends continued to grow at the historical rate what would be the value of one share using the dividend valuation model?
b. If the investment is accepted, and therefore dividends are cut for the next two years, what will be the value of one share?
c. What are the dangers associated with dividend cuts and how might the firm alleviate them?

Answer 1

a. Using the dividend valuation model, we can calculate the value of one share as the present value of all future dividends. Assuming that dividends continue to grow at the historical rate of 5% per year, we can calculate the expected future dividends as follows:

- Next year: 8p x 1.05 = 8.4p
- Year 2: 8.4p x 1.05 = 8.82p
- Year 3: 8.82p x 1.05 = 9.26p
- Year 4: 9.26p x 1.05 = 9.72p
- Year 5: 9.72p x 1.05 = 10.21p

Using a discount rate of 13%, we can calculate the present value of each year's dividend and sum them up to get the value of one share:

PV of year 1 dividend = 8.4p / (1 + 0.13) = 7.43p
PV of year 2 dividend = 8.82p / (1 + 0.13)^2 = 6.88p
PV of year 3 dividend = 9.26p / (1 + 0.13)^3 = 6.18p
PV of year 4 dividend = 9.72p / (1 + 0.13)^4 = 5.54p
PV of year 5 dividend = 10.21p / (1 + 0.13)^5 = 4.98p

Value of one share = 7.43p + 6.88p + 6.18p + 5.54p + 4.98p = 31.01p

b. If the investment is accepted, the dividend will be cut to 4p for each of the next two years. Then, in year 3, the dividend will be raised to 10p and will grow by 9% per year thereafter. We can calculate the expected future dividends as follows:

- Year 1: 4p
- Year 2: 4p
- Year 3: 10p
- Year 4: 10p x 1.09 = 10.9p
- Year 5: 10.9p x 1.09 = 11.9p

Using a discount rate of