Question

In: Finance

Zach has been appointed fiscal coordinator for the stanford narcolepsy institute. He has the task of...

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.

Solutions

Expert Solution

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


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