Auto Transmissions is expected to pay no dividend in the next two years. From year 3 until infinity, the business is looking to pay a constant annual dividend of $2.30 per share. What is the value of this share at a required return of 15%?

The value of this share is = $[shareprice]

If you struggle with this question, please review our week 7 module. We have done this question in our week 7 practice quiz

Question

Auto Transmissions is expected to pay no dividend in the next two years. From year 3 until infinity, the business is looking to pay a constant annual dividend of $2.30 per share. What is the value of this share at a required return of 15%?

The value of this share is = $[shareprice]

If you struggle with this question, please review our week 7 module. We have done this question in our week 7 practice quiz

BlackTom AI · Accepted Answer

First, parse the dividend schedule: there are no dividends in years 1 and 2, and from year 3 onward there is a constant dividend of 2.30 per year.
Next, recognize this is a perpetuity that starts receiving payments two years from now. The value of a perpetuity immediately after year 2 (i.e., at t = 2) is D / r, where D is the annual dividend and r is the required return.
So, at t = 2, the value of the perpetual dividends from year 3 onward is 2.30 / 0.15 = 15.333...
To obtain the present value today (t = 0), discount that amount back two years at the required return of 15%: PV0 = 15.333... / (1.15)^2.
Calculating (1.15)^2 gives 1.3225, so PV0 ≈ 15.333... / 1.3225 ≈ 11.61.
An alternative approach is to use the general formula for a perpetuity starting after a delay: PV0 = (D / r) / (1 + r)^n, where n is the number of years with no dividends before the perpetuity begins. Here n = 2, D = 2.30, r = 0.15, yielding the same result: PV0 ≈ 11.61.
If you see a different value like 13.15, that result would arise from either using a different timing convention (for example discounting by only one year instead of two) or misplacing the first payment in time. It's important to align the first cash flow date with the correct present-value timing to avoid such discrepancies.
Note: Because there are no options provided for this numerical question, we follow the standard perpetuity-with-delay valuation steps and show the concrete arithmetic leading to approximately 11.61 as the present value.

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