Question

(1)A US based MNC plans to invest in a new project EITHER in US or in Mexico. The new project is expected to take up a quarter of the firm’s total investment fund. The balance of the corporation’s investment is exclusively in an existing US project. The features of the proposed new project are as follows:

                                                          Existing US project US project (new) Mexico project (new)

Expected rate of return E(R) 10% 15% 15%

Standard deviation of E(R) 0.10 0.11 0.12

Correlation of returns from new

project with returns on existing

US project - 0.95 - 0.05

Based on considerations of risk and return, determine the portfolio the MNC should choose if the goal is to generate more stable returns.

Answer 1

	The new project is expected to take up a quarter of the firm’s total investment fund.
	That means 25% or 0.25 of Total Investment fund is invested in new project
	and balance i.e. 75% or 0.75 is invested in existing US Project.
a)	If New Project plans to invest in US
	Given,
	Expected Rate of Return of Existing US Project = E(RUe) = 10%
	Expected Rate of Return of New US Project = E(RUn) = 15%
	So,
	Expected Rate of Retun of Portfolio
	= % Invested in existing project*Expected Rate of Return of Existing US Project
	+ % Invested in New US project*Expected Rate of Return of New US Project
	= 0.75*10%+0.25*15%
	= 7.5% + 3.75%
	= 11.25%
	Standard Deviation of Existing US Project = σUe = 0.10
	Standard Deviation of New US Project = σUn = 0.11
	Correlation = r = -0.95
	So,
	Standard Deviation of Portfolio
	= √W1^2*σUe^2 + W2^2*σUn^2 + 2*r*W1*W2*σUe*σUn
	= √(0.75)^2*(0.10)^2 + (0.25)^2*(0.11)^2 + 2*(-0.95)*0.75*0.25*0.10*0.11
	= √0.5625*0.01 + 0.0625*0.0121 + (-0.00391875)
	= √0.005625 + 0.00075625 - 0.00391875
	= √0.0024625
	= 0.0496
b)	If New Project plans to invest in Mexico
	Given,
	Expected Rate of Return of Existing US Project = E(RUe) = 10%
	Expected Rate of Return of New Mexico Project = E(RMn) = 15%
	So,
	Expected Rate of Retun of Portfolio
	= % Invested in existing project*Expected Rate of Return of Existing US Project
	+ % Invested in New Mexico project*Expected Rate of Return of New Mexico Project
	= 0.75*10%+0.25*15%
	= 7.5% + 3.75%
	= 11.25%
	Standard Deviation of Existing US Project = σUe = 0.10
	Standard Deviation of New Mexico Project = σMn = 0.12
	Correlation = r = -0.05
	So,
	Standard Deviation of Portfolio
	= √W1^2*σUe^2 + W2^2*σMn^2 + 2*r*W1*W2*σUe*σMn
	= √(0.75)^2*(0.10)^2 + (0.25)^2*(0.12)^2 + 2*(-0.05)*0.75*0.25*0.10*0.12
	= √0.5625*0.01 + 0.0625*0.0144 + (-0.000225)
	= √0.005625 + 0.0009 - 0.000225
	= √0.0063
	= 0.0794
	As we calculated above
		US	Mexico
	Expected Return	11.25%	11.25%
	Standard Deviation	0.0496	0.0794
	Goal of the Company is to generate more stable returns,
	so project should be invested in US as both gives same returns
	but US has lower standard deviation than Mexico i.e. more
	stable returns than Mexico