I. Gretchen Gallup has been developing genetically modified, six-legged polo ponies in her spare time. Gretchen expects the technology she’s working on should have all the glitches worked out in three (3) years (rumor has it that some of the ponies have grown six heads instead of six legs). She goes on Shark Tank and is offered the following deals. Deal 1: A partnership with one of the hosts. No money right now, but once the kinks are worked out, she will be paid $100,000 per year while the patent is on. Patents like this are good for twenty years. After that, Gretchen will earn $20,000 forever. Deal 2: One million dollars today with the expectation she will turn the patent over to the host when it is ready (assume the patent will happen, so no risk there). If the appropriate discount rate is 10%, which deal is best for Gretchen? Notes: (i) the first payment in Deal 1 will come at the beginning of year 3 and (ii) use the 10% discount rate throughout the problem. Drawing a timeline will really help here.
II. Redo question I, but this time assume that along with the $100K for 20 years and $20K in perpetuity, there is an annual growth rate of the payments only, g, of 4% beginning when the first payment ($100K) begins and continuing on through perpetuity.