Reverse Engineering and Interpreting the PB Ratio The mid-2016 market capitalization for Alphabet Inc., formerly Google Inc. was $532.69 billion, its book value of equity was $127.88 billion, and its trailing four-quarters ROE was 14.99%. Its historical five-year average sales growth was 20.66%, its historical five-year average EPS growth was 11.58%, and analysts were forecasting a 14% annual earnings growth rate for industry over the next five years. Following are three different cases to help interpret and reverse engineer its PB ratio, including some unknown values.

PB* (equals PB ratio observed ???? 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ?

Case 1: Solve for implied growth rate Assumed parameters ROE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15%

Discount rate, r

e. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10%

Implied parameter Growth rate, ( r e1 [PB* ???? r e]????????????ROE)/PB*. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ?

Case 2: Solve for implied discount rate Assumed parameters ROE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15%

Growth rate, g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8%

Implied parameter Discount rate, (ROE????1????[PB* ???? g])/(1 1????PB*). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ?

Case 3: Solve for implied future ROE Assumed parameters Discount rate, r

e. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10%

Growth rate, g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8%

Implied parameter ROE, (PB* ???? [ r e????????g]) 1????r e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ?

Required

a. For Case 1, compute the growth rate implied by Alphabet’s PB ratio.

b. For Case 2, compute the discount rate implied by Alphabet’s PB ratio.

c. For Case 3, compute the ROE implied by Alphabet’s PB ratio.

d. Based on your results in parts a through

c, do you believe Alphabet’s observed PB ratio implies reasonable expectations about its future performance? Explain.