Valuation and Capital Return as Inverse Problems

Petri P Kärenlampi

doi:10.5772/intechopen.101943

Abstract

The capital return rate is the relative time change rate of value. Correspondingly, the current value can be produced in terms of value change rate divided by capital return rate. There is a variety of ways to approximate the expected capital return rate. These are briefly discussed. The approximation of the value change rate is still more variant, depending on the type of businesses discussed. A variety of businesses may appear within a firm, in which case the value change rates must be integrated. An example is provided of a real estate firm benefiting from the growth of multiannual plants of varying age. It is found that the application of a duration-dependent reference capital return rate increases the value increment rate of juvenile stands and decreases that of mature stands, however increasing the valuation result of both.

Highlights

The capital return rate is the relative time change rate of value
The reference capital return rate according to Eq (13) increasing with increasing time to maturity, it is found that mature stands show greater value than the reference curves, whereas juvenile stands show lower value
The capital return rate and firm valuation have been discussed as inverse problems

Summary

Introduction

The capital return rate is the relative time change rate of value. We choose to write rðtÞ 1⁄4 dκ (1). KðtÞdt where κ in the numerator considers value growth, operative expenses, interests and amortizations, but neglects investments and withdrawals In other words, it is the change of capitalization on an economic profit/loss basis. Does it possibly provide the definition of valuation as a function of the required capital return rate? The quantities appearing on the right-hand side of Eq (1) are observable in a variety of ways, including profit-loss—statement, balance sheet, and market valuation. The capital return rate appearing on the right-hand side of Eq (2) can be determined from comparable reference investments. In the remaining part of this chapter, we will first discuss the practical implementation of the determination of capital return rate and firm value using Eqs. We will discuss the determination of the values of the quantities appearing in Eqs. A few applications are discussed, as well as interpolation techniques

Application to stands of multiannual plants

Determination of stand capitalization

Determination of a reference capital return rate

Determination of stand value increment rate

Further valuation attempts

Discussion