Fundamentals of Financial Management

Differences Between Wealth Maximization and Profit Maximization

Profit maximization is the traditional goal of a firm, which means maximizing the net profit (total revenue minus total cost) of the firm over a given period, usually one fiscal year. Wealth maximization is the modern goal of a firm, which means maximizing the net present value (NPV) or the market value of the owners' equity (shareholders' wealth) over the long run.

The major differences between these two goals are as follows:

Which Goal Is Superior?

Wealth maximization is superior to profit maximization. The reasons are:

1. Considers time value of money: Wealth maximization discounts future cash flows to their present value, so it correctly compares cash received at different points in time. Profit maximization treats a rupee earned today and a rupee earned after five years as equal, which is incorrect.

2. Considers risk and uncertainty: Business decisions involve varying degrees of risk. Wealth maximization uses the required rate of return (discount rate) that reflects risk, whereas profit maximization ignores risk entirely. A high-profit project with very high risk may reduce shareholders' wealth.

3. Focuses on cash flows, not accounting profit: Accounting profit can be manipulated through accounting policies (depreciation methods, inventory valuation, etc.) and does not represent actual cash available to shareholders. Wealth maximization is based on real cash flows, which determine the true value of the firm.

4. Ensures long-term survival and growth: Profit maximization encourages short-term decisions (e.g., cutting research and development, avoiding maintenance) that may raise current profit but harm the firm's future. Wealth maximization balances current returns with future growth, ensuring the firm's long-term survival.

5. Aligns with shareholders' interest: The primary objective of a company is to maximize the wealth of its shareholders. Wealth maximization directly measures this through the market price of shares, which reflects the shareholders' actual return.

6. Socially desirable: Wealth maximization benefits not only shareholders but also other stakeholders (employees, creditors, government, society) because a firm that creates value also pays taxes, wages, and interest. Profit maximization may lead to exploitation of stakeholders to boost profit.

Conclusion: Although profit is necessary for the survival of a firm, it is not a sufficient goal. Wealth maximization is a broader, more complete, and more rational objective because it incorporates time value of money, risk, and cash flows. Hence, wealth maximization is considered the superior goal of financial management.

Given: Initial investment Rs 225,000 each; required return 12%; life 5 years.

(a) Payback period

Project A (equal annual inflows): $\text{Payback}=\frac{225{,}000}{75{,}000}=3\text{ years}$

Project B (uneven inflows), cumulative cash flow: Year 1 = 90,000; Year 2 = 160,000; Year 3 = 210,000; the remaining 15,000 is recovered in Year 4. $\text{Payback}=3+\frac{15{,}000}{80{,}000}=3.19\text{ years}$

Project A has the shorter payback.

(b) NPV at 12%

Project A: annuity factor (12%, 5 years) = 3.6048, so PV = $75{,}000\times3.6048 = 270{,}360$.

$NPV_A = 270{,}360-225{,}000 = \text{Rs }45{,}360$ $NPV_B = 273{,}661-225{,}000 = \text{Rs }48{,}661$

Both are positive, but Project B has the higher NPV, so it adds more to shareholders' wealth. Recommend B.

(c) IRR

Project A: the present value factor is $225{,}000/75{,}000 = 3.000$. From annuity tables for 5 years, the factor is 3.0576 at 19% and 2.9906 at 20%. $IRR_A = 19+\frac{3.0576-3.0000}{3.0576-2.9906}\approx 19.86\%$

Project B: by trial and error, NPV = Rs 2,300 at 20% and Rs (2,570) at 21%. $IRR_B = 20+\frac{2{,}300}{2{,}300+2{,}570}\approx 20.47\%$

Both exceed the 12% required return, but Project B has the higher IRR (20.47% against 19.86%). Recommend B.

(d) Conflict in ranking

There is no conflict between the two discounted-cash-flow methods: NPV and IRR both rank B first. Only the payback period favours A, but payback ignores the time value of money and cash flows after the payback date, so it is a weaker criterion. NPV is the most reliable method for mutually exclusive projects, as it measures the absolute increase in wealth. Therefore the company should accept Project B.

Given

Working in percentage points, so variance is in (%^2).

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a. Expected return and standard deviation

Stock A

[ E(R_A)=\sum P_iR_{Ai} ]

[ E(R_A)=0.4(10)+0.4(15)+0.2(20) ]

[ E(R_A)=4+6+4=14% ]

Variance:

[ \sigma_A^2=\sum P_i(R_{Ai}-E(R_A))^2 ]

[ \sigma_A^2=0.4(10-14)^2+0.4(15-14)^2+0.2(20-14)^2 ]

[ \sigma_A^2=0.4(16)+0.4(1)+0.2(36) ]

[ \sigma_A^2=6.4+0.4+7.2=14 ]

[ \sigma_A=\sqrt{14}=3.74% ]

Stock B

[ E(R_B)=0.4(30)+0.4(20)+0.2(20) ]

[ E(R_B)=12+8+4=24% ]

Variance:

[ \sigma_B^2=0.4(30-24)^2+0.4(20-24)^2+0.2(20-24)^2 ]

[ \sigma_B^2=0.4(36)+0.4(16)+0.2(16) ]

[ \sigma_B^2=14.4+6.4+3.2=24 ]

[ \sigma_B=\sqrt{24}=4.90% ]

Answer:

[ E(R_A)=14%,\quad \sigma_A=3.74% ]

[ E(R_B)=24%,\quad \sigma_B=4.90% ]

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b. Covariance and correlation coefficient

Covariance

[ Cov(A,B)=\sum P_i(R_{Ai}-E(R_A))(R_{Bi}-E(R_B)) ]

[ Cov(A,B)=0.4(10-14)(30-24)+0.4(15-14)(20-24)+0.2(20-14)(20-24) ]

[ Cov(A,B)=0.4(-4)(6)+0.4(1)(-4)+0.2(6)(-4) ]

[ Cov(A,B)=-9.6-1.6-4.8=-16 ]

[ Cov(A,B)=-16\ (%^2) ]

Correlation coefficient

[ \rho_{AB}=\frac{Cov(A,B)}{\sigma_A\sigma_B} ]

[ \rho_{AB}=\frac{-16}{(3.74)(4.90)} ]

[ \rho_{AB}=\frac{-16}{18.33}=-0.873 ]

Answer:

[ Cov(A,B)=-16\ (%^2) ]

[ \rho_{AB}=-0.873 ]

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c. Does forming a portfolio reduce risk?

Yes. The correlation coefficient between Stock A and Stock B is:

[ \rho_{AB}=-0.873 ]

This is a strong negative correlation. When two stocks are negatively correlated, their returns tend to move in opposite directions. Therefore, the negative covariance term in the portfolio variance formula offsets a large part of the individual risks.

The 50–50 portfolio standard deviation is only:

[ \sigma_p=1.22% ]

This is lower than both Stock A’s standard deviation (3.74%) and Stock B’s standard deviation (4.90%). Hence, forming a portfolio of these two stocks definitely reduces risk.

If the correlation were (+1), there would be no risk reduction. But here, because the correlation is strongly negative, diversification reduces risk substantially.

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d. Portfolio return and risk for 50% in A and 50% in B

Portfolio expected return

[ E(R_p)=w_AE(R_A)+w_BE(R_B) ]

[ E(R_p)=0.5(14)+0.5(24) ]

[ E(R_p)=7+12=19% ]

Portfolio variance

[ \sigma_p^2=w_A^2\sigma_A^2+w_B^2\sigma_B^2+2w_Aw_B Cov(A,B) ]

[ \sigma_p^2=(0.5)^2(14)+(0.5)^2(24)+2(0.5)(0.5)(-16) ]

[ \sigma_p^2=0.25(14)+0.25(24)-8 ]

[ \sigma_p^2=3.5+6-8=1.5 ]

[ \sigma_p=\sqrt{1.5}=1.22% ]

Portfolio:

[ E(R_p)=19%,\quad \sigma_p=1.22% ]

Comparison

Preference

I would prefer the portfolio.

Reason:

• It gives a higher expected return than Stock A: (19% > 14%).
• It has much lower risk than both Stock A and Stock B: (1.22%) versus (3.74%) and (4.90%).
• Its coefficient of variation is the lowest, meaning it gives the best return per unit of risk.

Therefore, on a risk-adjusted basis, the 50–50 portfolio is the best choice. Only an aggressive investor seeking the highest possible return and willing to accept higher risk might choose Stock B.