To determine the present value of a share of Cava stock today, we need to consider the expected future cash flows from the stock and discount them back to their present value using the appropriate discount rate. In this case, the relevant information includes the expected dividend payments, their growth rate, and the discount rate.
First Dividend (Year 6): The first dividend from Cava stock is expected to be $3 per share, which will be paid 6 years from today. To find the present value of this dividend, we can use the formula for the present value of a single future cash flow:
PV = FV / (1 + r)^t
Where PV is the present value, FV is the future value, r is the discount rate, and t is the time period. In this case, PV = $3 / (1 + 0.13)^6 = $1.46 (rounded to two decimal places).
Second Dividend (Year 7): In the seventh year, the dividend is expected to grow by 20%. So, the dividend in year 7 will be $3 * 1.20 = $3.60 per share. To find the present value of this dividend, we use the same formula:
PV = $3.60 / (1 + 0.13)^7 = $1.38 (rounded to two decimal places).
Constant Growth Dividends (Year 8 and Beyond): Starting from year 8, the dividends are expected to grow at a constant rate of 3% per year. This is a perpetuity, and we can use the Gordon Growth Model to calculate the present value of these dividends:
PV = D / (r – g)
Where D is the next dividend, r is the discount rate, and g is the growth rate. In this case, D = $3.60 and g = 0.03.
PV = $3.60 / (0.13 – 0.03) = $36.00.
Total Present Value: To find the total present value of all expected future cash flows, we sum up the present values of the individual components:
Total PV = $1.46 (Year 6) + $1.38 (Year 7) + $36.00 (Constant Growth) = $38.84 (rounded to two decimal places).
So, a share of Cava stock should sell for approximately $38.84 today, based on the given information and a discount rate of 13%. This is the estimated intrinsic value of the stock, and it represents the present value of all expected future cash flows to the shareholder. Investors can use this value as a reference when making investment decisions, such as buying or selling Cava stock in the market.
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