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.

Similar Questions

ABC, Inc. just paid a dividend of $2. ABC expects dividends to grow at 10% annually forever. The return on shares like ABC, Inc. is typically around 12%. What is the most you would pay for ABC’s share?

ALP’s most recent dividend was $2.00 per share and is selling today for $70. The dividend is expected to grow at 7% per year for the foreseeable future. Should you purchase the share if the market return is 10% on investments with comparable risk?

Using a dividend discount model, find the intrinsic value (price at time zero) for a firm whose expected dividend is $1.92 and growth in dividends for year 2, 3, and 4 is 23.2% and constant growth afterwards is 0.54%. The cost of equity is 9.21%. (Answer in 2 decimal places, 6.21 for $6.21).

Using a dividend discount model, find the intrinsic value (price at time zero) for a firm whose expected dividend is $1.37 and growth in dividends for year 2, 3, and 4 is 13.8% and constant growth afterwards is 1.42%. The cost of equity is 6.67%.

AWSM has just paid a dividend of $1.24 and is expected to increase the future dividends at a rate of 3% per year indefinitely. If you, as a shareholder, require 12% per year, what is the current price per share?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler