In: Finance
Zach has been appointed fiscal coordinator for the stanford narcolepsy institute. He has the task of valuing 3M. 3M will pay a dividend of $2.25 next quarter. Zach estimates that the firm will grow at 6% per quarter for 4 years, at 3% per quarter for 3 years, then at 1% per quarter thereafter. The cost of equity is 16% with annual compounding. Find the correct stock price for 3M.
As a first step we need to find the rate per period i.e. effective rate per quarter, R that will be used for discounting.
(1 + R)4 = 1 + 16%
Hence, R = 1.161/4 - 1 = 3.78%
Stage 1 (Year 1 to Year 4):
Growth rate, g1 = 6% per period (quarter), D1 = $ 2.25, R = 3.78%, N = number of quarters in 4 years = 4 x 4 = 16
Sum of PV of growing annuity
= 40.85
Stage 2 (Year 5 to Year 7):
Growth rate, g2 = 3% per period (quarter), D17 = D1 x (1 + g1)15 x (1 + g2) = $ 2.25 x (1 + 6%)15 x (1 + 3%) = $ 5.55, R = 3.78%, N = number of quarters in 3 years = 4 x 3 = 12
Sum of PV of growing annuity at t = 16 (i.e. end of 4th year)
= 61.63
Hence, PVStage 2, t = 0 = PVstage 2, t = 16 / (1 + R)16 = 61.63 / (1 + 3.78%)16 = 34.04
Stage 3 (Year 8 onward)
Terminal growth rate, g = 1% per quarter
D29 = D17 x (1 + g2)11 x (1 + g) = 5.55 x (1 + 3%)11 x (1 + 1%) = 9.27
Horizon value of future dividends at t = 28 (i.e. end of 7 years) = DHV, t = 28 = D29 / (R - g) = 9.27 / (3.78% - 1%) = 333.49
Hence PV of horizon value today = DHV, t = 0 = DHV, t = 28 / (1 + R)28 = 333.49 / (1 + 3.78%)28 = 118
Hence, the correct stock price for 3M = Sum of PV of all future dividends = PVStage 1, t = 0 + PVStage 2, t = 0 + DHV, t = 0 = 40.85 + 34.04 + 118 = $ 192.89