Trentham Estate Ltd expects to grow at a rate of 22 per cent for the next 5 years and then settle to a constant-growth rate of 6 per cent.

The company’s most recent dividend was $2.35.

The required rate of return is 15 per cent.

a Find the present value of the dividends during the rapid growth period.

b What is the price of the share at the end of year 5?

c What is the price of the share today?

Solutions

Expert Solution

PV of dividends during rapid growth period:

PV of Dividends = 2.35 x (1+22%)^1/(1+15%)^1 + 2.35 x (1+22%)^2/(1+15%)^2 + 2.35 x (1+22%)^3/(1+15%)^3 + 2.35 x (1+22%)^4/(1+15%)^4 + 2.35 x (1+22%)^5/(1+15%)^5

PV of Dividends = 14.07794

PV of Dividends = $14.08

Price of share at end of 5^th year = 2.35 x (1+22%)^5 x (1+6%) / (15%-6%)

Price of share at end of 5^th year = 74.80496

Price of share at end of 5^th year = $74.80

Price of share today = PV of Dividends + PV of (Price of share at end of 5^th year)

Price of share today = 14.07794 + (74.80496)/(1+15%)^5

Price of share today = 51.26923

Price of share today = $51.27

jeff jeffy answered 2 years ago

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