Final answer:
To determine the current value of a Transurban share, calculate the present value of dividends during its exclusive ownership until 2026 growing at 7.5% annually, and then the present value of perpetual dividends growing at 3% semi-annually from 2027 onwards.
Step-by-step explanation:
The question revolves around calculating the current value of a share of Transurban, based on its future dividend growth projections. The approach to solve this includes two phases: calculating the dividends during the exclusive ownership period and estimating the perpetual dividends from 2027 onwards when the M5 South West motorway returns to government ownership.
Firstly, we calculate the dividends during the exclusive period using the given growth rate of 7.5% annually until the end of 2026. Starting with a dividend of $0.29 at the end of 2019, we would apply the growth formula for each year to find the dividend at 2026. Following this, we would discount these future dividends back to the present value using the appropriate discount rate (not given in the question).
After 2026, since the dividends are projected to grow at a stable rate of 3% compounded semi-annually forever, we would use the Gordon Growth Model (also known as the Dividend Discount Model for perpetuity) to calculate the perpetual value of dividends. Then, this value would also be discounted back to the present value.
The sum of the present value of dividends during the exclusive ownership period and the present value of perpetual dividends would give us the total current value of one share of Transurban.