dividend discount model equations confusion

Davis Company, Inc. earned $5 a share last year and paid a dividend of $2/share. The company is expected to grow by 8% annually and continue its payout ratio for the foreseeable future. An investor with an 11% required rate of return expects to sell the stock at $75 two years from now. The maximum amount that an investor should be willing to pay for the stock today is CLOSEST to: A. $58.68 B. $64.71 C. $66.67 D. $70.47 The answer is B, and I know how to get there, but am really comfused about when to uses which formula for valuing stocks. In this case, the answering people used the multiple period holding valuation: D1/1+k + P1/1+k- just extend it out to another period by squaring the D1 and 1+k1. However, I immediately thought of using the infinite period growth model: D0(1+g)/k-g I wanted to use that equation because the question stated that the company was expected to grow at 8% and continue its payout policy- thus indicating to me that the company is no longer in a growth phase. However, I was wrong (according to the “answer people”). I have always been a bit confused about which equation to use. Any ideas?

You are correct about using the infinite period growth model - the only difference in this problem is - they have given the expected stock price two years from now. Whenever the expected stock price is given, we need to use the multi-period formulas. If not, use the infinite period growth model.

basically they are just discounting the the cash flows. DDM is only appropriate if you are assuming you are going to hold on to the asset for a very very long time ie infintely. (the price will converge onto the value calculated by DDM). If the time period is limited to just 1 or 2 years, just discount the cash flows.

CF1 = 2 * 1.08 CF2 = 2 * 1.08^2 + 75 I=12 Solve for NPV = 64.71 Ans