Answer to Question #108053 in Financial Math for Shreethini

Question

A company issues 2,000,000 ordinary shares at a purchase price of 55p each to an investor.
No dividend is expected to be paid for 3 years. The first dividend payable in 3 years’ time is expected to be 6p per share, and dividends are expected to be paid every 6 months thereafter in perpetuity. The two dividend payments in each year are expected to be the same, but dividends are expected to increase at the end of each year, at a rate of 4% per annum compound.

Assuming that the investor pays income tax at 30%, calculate the net present value of the investment at an effective rate of interest of 7% per annum. (Total 6 marks)

Answer 1

Find the initial investment amount:

$2 000 000\times55=110 000 000$

Payments after 3 years

$2 000 000\times6=12 000 000$

Find the perpetual dividend on the model of constant growth of Gordon:

$P=\frac{DPS\times(1+g)}{k-g}=\frac{6(1+0.04)}{0.07-0.04}=208$

$2 000 000\times208=416 000 000$

Find the net present value:

$12 000 000+416 000 000-(12 000 000+416 000 000)\times0.3- 110 000 000=428 000 000-128 400 000-110 000 000=189 600 000$