Using the Dividend Discount Model when no current dividend exists?
With what you say and using the DDM we know that

$P_{t=4} = \frac{D_{t=5}(1+g)}{r-g}$

Via the above equation, it is assumed that from year $5$, dividends will annually grow at a $g$ rate and that investors' required rate will be $r$, both forever. Since this calculation is nothing but a simplification (future growth and return rates will a fortiori change, etc...), we will not do more complicated.

Taking into account the share of debt in the capital structure of the company, say $X\%$, we can compute the average cost of capital (average over equity and debt), $r'$, needed to discount $P_{t=4}$. One may have an idea of $X$ or make assumptions about it. It follows that $r'$ is such that

$r' = X\% r_D + (1-X\%) r$

where $r_D$ is the interest rate or the cost of debt (naturally $r_S &lt; r$). Thus the company's IPO may be valued by involving that 

$P_{t=0} = \frac{P_{t=4}}{(1+r')^4}$

Finally, as you can see there are many assumptions in this valuation, which is the job of experts, with the most fundamental about $D_{t=5}$.