The company needs to raise $40 million via a rights issue.

Current share price = $10

Rights issue at a 20% discount, so issue price =

10×(1−0.20)=10×0.8=$810 \times (1 - 0.20) = 10 \times 0.8 = \$810×(1−0.20)=10×0.8=$8

Number of new shares needed:

New shares=40m8=5 million shares\text{New shares} = \frac{40\text{m}}{8} = 5\text{ million shares}New shares=840m​=5 million shares

There are currently 20 million shares in issue, so the rights issue ratio is:

New sharesExisting shares=520=14\frac{\text{New shares}}{\text{Existing shares}} = \frac{5}{20} = \frac{1}{4}Existing sharesNew shares​=205​=41​

So, shareholders will receive 1 new share for every 4 existing shares.