Construct a simple numerical example to show the following (Assume that there are 100 shares outstanding at $10 per share, before issue):

a. Existing shareholders are made worse off when a company makes a cash offer of new stock below the market price (Say, the company sells 20 shares for cash at $5 per share)

b. Existing shareholders are not made worse off when a company makes a rights issue of new stock below the market price even if the new stockholders do not wish to take up their rights ( the company makes a rights issue of 20 shares at $5 per share).

please show your workflow.