Problem 5.3. A stock that does not pay dividend is trading at $100. The stock price will increase by 10% or decrease by 10% in one year. After that, the stock price will increase or decrease by 20% in the second year. The risk-free interest rate is 5% per annum with continuous compounding. Value a two-year American put option with strike price of $102. Note that risk-neutral probabilities or replicating portfolios may differ across two periods. You must also check for early exercise.

The Product Life Cycle

Every product goes through the various life cycle phases of introduction, growth, maturity and decline.

Key Points

Depending on its current stage in the product life cycle, a product will have different marketing, financing, manufacturing, purchasing and human resource requirements.

In the market introduction stage (following product development ), the product is released on to the market.

Sales are low and costs are high in the market introduction stage, thus, no profits are made. There is little to no competition and demand must be created through heavy promotion.

Key Terms

decline stage: when a product is not predicted to continue to be successful or upgraded

product life cycle: The process wherein a product is introduced to a market, grows in popularity, and is then removed as demand drops gradually to zero.

maturity stage: when a product is no longer in the growth stage, but not yet in the decline stage

Product Life Cycle: Overview

The product life cycle (PLC) describes the life of a product in the market with respect to business/commercial costs and sales measures. It proceeds through multiple phases, involves many professional disciplines and requires a multitude of skills, tools and processes.

This is not to say that product lives cannot be extended – there are many good examples of this – but rather, each product has a ‘natural’ life through which it is expected to pass.

The stages of the product life cycle are:

Introduction

Growth

Maturity

Decline

PLC management makes these three assumptions:

Products have a limited life and, thus, every product has a life cycle.

Product sales pass through distinct stages, each of which poses different challenges, problems and opportunities to its parent company.

Products will have different marketing, financing, manufacturing, purchasing and human resource requirements at the various stages of its life cycle.

The product life cycle begins with the introduction stage (see ). Just because a product successfully completes the launch stage and starts its life cycle, the company cannot take its success for granted.