Based on the information provided, it does not appear that the promotional campaign would be worthwhile for Vesper Systems when the discount rate is 8%. The campaign would cost $55 million, and would only generate $1 million in annual after-tax cash flow over the next five years, for a total of $5 million in cash flow over the five-year period. When the discount rate is 8%, this amount of cash flow would not be sufficient to justify the cost of the campaign.
In contrast, if Vesper Systems does not undertake the promotional campaign, it expects its after-tax cash flow to be -$15 million annually for the same five-year period. This would result in a total cash flow of -$75 million over the five-year period. While this is still a negative cash flow, it would be less negative than the cash flow generated by the promotional campaign.
Overall, the decision to undertake the promotional campaign would not be worthwhile for Vesper Systems when the discount rate is 8%, as the expected cash flow from the campaign would not be sufficient to justify the cost of the campaign. It would be more beneficial for the company to not undertake the campaign and instead focus on other strategies to improve its profitability.