Question

Apple Inc. pays quarterly dividends. The next dividend will be paid 2 months from now. The last dividend was paid 1 month ago and the amount was $0.73 per share. Suppose the concensus belief is that the dividend will be growing at a rate of 1% per dividend. If we assume an annual discount rate of 6% (expressed as EAR), what is the fair value of Apple's stock?

plz

I don't clear what's 'fair value' mean in this question

Answer 1

Fair value is calculated through any of the equity valuation model like dividend discount model or discounted cash flow model. It is different than the market value. The investors may not know the real or fair value of a security. So, an equity valuation model is used to know the intrinsic or fair value of a security and then we compare it to the market value to know if it's under priced or over priced in the market.

We will use dividend discount model to calculate fair value of Apple's stock.

Dividend discount model = expected dividend/(discount rate - growth rate)

First we need to calculate expected dividend for 3 quarters (quarter 2 to 4) of current year and first quarter of next year to get annual expected dividend. dividend growth rate is 1% per dividend means per quarter.

Expected dividend = dividend paid in 1st quarter*(1+dividend growth rate) + dividend in 2nd quarter*(1+dividend growth rate) + dividend in 3rd quarter*(1+dividend growth rate) + dividend paid in 4th quarter*(1+dividend growth rate)

Expected dividend in 2nd quarter = $0.73*(1+0.01) = $0.73*1.01 = $0.7373

Expected dividend in 3rd quarter = $0.7373*(1+0.01) = $0.7373*1.01 = $0.744673

Expected dividend in 4th quarter = $0.744673*(1+0.01) = $0.744673*1.01 = $0.75211973

Expected dividend in 1st quarter of next year = $0.75211973*(1+0.01) = $0.75211973*1.01 = $0.7596409273‬

Total annual dividend = $0.7373+$0.744673+$0.75211973+$0.7596409273‬ = $2.99

Now we need to calculate annual growth rate as below:

(1+Quarterly growth rate)^{no. of quarters} - 1 = (1+0.01)⁴ - 1 = 1.01⁴ - 1 = 1.0406 - 1 = 0.0406 or 4.06%

Fair value = $2.99/(0.06 - 0.0406) = $2.99/0.0194 = $154.12