Suppose there is a series of cashflows that lasts n + 1 periods, {at}t , 0 ≤ t ≤ n, and that is growing at constant rate g, i. e. at = (1 + g) ta0, ∀t. the discount rate is fixed at r and assume g < r. find an expression for the discounted present value of the cashflows at time 0. formally, find an expression for s = a0 + a1 1+r + + an (1+r) n

Robert black, regional manager for ford in texas and oklahoma, faced a dilemma. the ford f-150 pickup truck was the best-selling pickup ever, yet ford's headquarters in detroit had decided to introduce a completely redesigned f-150. how could mr. black sell both trucks at the same time? he still had "old" f-150s in stock. in his advertising, mr. black referred to the new f-150s as follows: "not a better f-150. just the only truck good enough to be the next f-150." this statement represents ford's of the new f-150.