Question

In an earnings announcement, XYZ corporation estimates it will pay $5 dividends next year, which represents 100% of its earnings. The required return of its investors is 12%. If the company decides to plow back 60% of the earnings at the firm's current return on equity of 15%.

1. What is XYZ corporation's present value of growth opportunity (PVGO)?

1. Calculate the PVGO for XYZ if the plow back ratio is 40% and 20%, respectively.
2. Given the results in 2), conclude the relationship between plow back ratio and the valuation of stock, and the relationship between plow back ratio and PVGO.
3. Rework you 1) and 2) with a new ROE of 10% and conclude how ROE affect PVGO.

Answer 1

1) when plow back ration is equal to 60%

growth rate = ROE*plow back ratio

= 15%*50%

= 7.5%

present value of growth opportunity = Dividend/(r-g)

= 2.5/(0.12-0.075)

=$55.56

2)

when plow back ration is equal to 40%

growth rate = ROE*plow back ratio

= 15%*40%

= 6%

present value of growth opportunity = Dividend/(r-g)

= 3/(0.12-0.06)

=$50

when plow back ration is equal to 20%

growth rate = ROE*plow back ratio

= 15%*20%

= 3%

present value of growth opportunity = Dividend/(r-g)

= 4/(0.12-0.03)

=$44.44

as retaintion ratio decrease the value of the stock decreases.

3)

when retaintion ratio=60% , ROE= 10%

growth rate = 10%*60%

= 6%

present value of growth opportunity = Dividend/(r-g)

= 2/(0.12-.06)

= 33.33

when retaintion ratio= 40%

growth rate = 10%*40% = 4%

present value of growth opprtunity = 3/(0.12-0.04)

=37.5

when retaintion ratio=20%

growth rate=10%*20% = 2%

present value of growth opportunity = 4/(0.12-0.02)

=40

when the ROE is less than required rate of return as you decrease the retaintion ration value of the stock will going to increase.

i hope my efforts will be fruitful to you.