A retailer ran display ads and wants to calculate the ROI on the display ads. The analyst wants to account for purchases via both click throughs and view throughs. All calculations are done for a two week period.

The average click through rate on a display ad is 0.1%, which we will assume can be attributed fully to the display ad. In terms of view throughs, there are two effects. First, when a customer is exposed to a display impression, her probability of searching for a relevant company keyword on a search engine increases by 50% (see Lewis and Nguyen (2015) 1 for experimental evidence of spillover of approximately this magnitude from display to search). The baseline (i.e., without seeing a display impression) probability of a customer to conduct a relevant search on a search engine is 0.8% in two weeks. Second, when a customer is exposed to a display impression, her probability of directly visiting the company's website (i.e., by typing the company's URL in the browser) increases by 20%. The baseline (i.e., without seeing a display impression) probability of a customer to visit the retailer's website is 0.01% in two weeks. The click through rate on a typical search ad is 4%, which we will assume can be attributed fully to the search ad.

The average CPM for display impressions is $2. A customer who arrives at the retailer's website through a click on a display ad converts to a purchase with an average rate of 10%, and the average margin on a conversion is $18. A customer who arrives at the retailer's website through a click on a search ad is further down in the "purchase funnel" (as compared to one arriving through a click on a display ad); such a customer has a higher average conversion rate of 20% and also purchases more so that the average margin on the conversion is $27. For search ads, payment is only for clicks and the average cost per click (CPC) on search ads is $0.2. A customer who arrives at the retailer's website by directly typing the website link in the URL is even further down in the "purchase funnel"; such a customer has an average conversion rate of 35% and the average margin on the conversion is $35.

Find the ROI on display advertising accounting for both click throughs and view throughs.