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Given Information
Particulars 
Amount (In £) 
Initial Capital Investment 
£ 600000 
Cashflow Year 1 
£ 300000 
Cashflow Year 2 
£ 300000 
Cashflow Year 3 
£ 100000 
It is a tool used to evaluate an investment proposal. It helps in determining the period required to cover the entire cost of initial investment from the cashflows generated from investments. Shorter the period more ludicrous an investment proposal as money is invested for a shorter duration of time. It is relatively simple and easy to understand and gives a rough idea about the investment proposal. Suitable for companies with a weaker liquidity position.
>1 + Cf_{2} + Cf_{3} + …… + Cf_{t} in year t
Year 
Cashflow 
Cumulative Cashflow 
Initial Investment 
£ (600000) 
£ (600000) 
1 
£ 300000 
£ (300000) 
2 
£ 300000 
0 
3 
£ 100000 
£ 100000 
As in the second year, the initial investment is fully recovered and there is zero profit. it is termed the payback period. Thus, the Payback period is of 2 years.
It is another important capital budgeting concept that gives equal weightage to all Cashflows. As money today is more than money tomorrow, here all the future cash flows from an investment proposal is discounted at a required rate. The required rate varies according to the time and risk factors associated with the cash flow. It is used to determine the profitability of an investment proposal.( Chan, K., & Rate, E. A. I. (2020)).
>1 + Cf_{2 } + Cf_{3 } + …………………...….. – Z_{0}
(1+ r) (1+r)^2 ( 1+r)^3
Cf : Cashflows
R : time period
Z_{0} : Initial Investment
Cost of>
Year 
Cash flows 
Discounting Factor 
Product 
Initial Investment 
£ (600000) 
1 
£ (600000) 
1 
£ 300000 
0.925925926 
£ 277778 
2 
£ 300000 
0.85733882 
£ 257202 
3 
£ 100000 
0.793832241 
£ 79383 
Net Present Value 
£ 14363 
is a valuation metric used to evaluate the profitability of an investment proposal. IRR is the discount rate at which the net present value from all future operations is becomes zero. Generally, the higher the internal rate of return better the investment proposal. It is used to rank various proposals with the proposal having the highest IRR is termed the best. However, IRR doesn’t account for the changes in the risk and thus should not be used for the long term. The formula used is the same as we use in the case of Net Present Value, but here we equate it to zero. (Santandrea, M., Sironi, A., Grassi, L., & Giorgino, M. (2017))
= Cf_{1 } + Cf_{2 } + Cf_{3 } + …………………...….. – Z_{0}
(1+ r) (1+r)^2 ( 1+r)^3
Cf : Cashflows
R : time period
Z_{0} : Initial Investment
Years 
Cash Flows 
Initial 
£ (600000) 
1 
£ 300000 
2 
£ 300000 
3 
£100000 
Internal Rate of Return – 10%
It helps in identifying the period of time after which we will be able to receive our initial investment. This metric incorporates the concept of the time value of money, thus, giving equal weightage to all the future cash flows. Shorter the payback period better the investment proposal as money will be invested for a shorter period of time.
Investment>1 + Cf_{2 } + Cf_{3 } + …………………...….. + Cf_{t}
(1+ r) (1+r)^2 ( 1+r)^3 ( 1+r )^t
Discounted Payback 
Period 

Assumed Rate 
8% 

Years 
Cashflows 
Discounting factor 
Product 
Cumulative cashflows 
Initial Investment 
£ (600000) 
1 
£ (600000)0 
£ (600000) 
£ 300000 
0.925925926 
£277778 
£ (322222) 
) 
£ 300000 
0.85733882 
£257202 
£ (65021) 

£ 100000 
0.793832241 
£ 79383 
£ 14363 
Discounted Payback year + (Remaining Amount to be recovered ) / Annual Income
For next year
Discounted Payback + 65021 />
Thus, the discounted payback period for Project Rainbowwhich 2.81 years
The payback period for the project is of 2 years and the discounted payback period is of 2.81 years. If the company has a weaker liquidity position and does not want the risks associated with longterm investment project Rainbowwhich is a viable investment opportunity. The project has a Net Present Value of £ 14363 and has an Internal Rate of return of 10% which is decent. Due to the shorter time period, the risk associated is a lot less likely during the period of time. Thus, the IRR value becomes much more reliable. Thus, in all the projects Rainbowwhich is viable and should be accepted
Merits 
Demerits 
It is simple and easy to understand. It requires few inputs and is relatively easy to calculate. 
It doesn’t discount the cash flows in the future to its present value. 
As it is easy, the managers can get a rough idea about a project which helps in making quick decisions 
It doesn’t take the profitability of the project into account. Cash flows may reduce or even stop after the payback period. 
It gives importance to the speedy recovery of investments. Thus helpful for companies with weak liquidity positions. 
It does not attempt to measure the rate of return. The rate of return is an important measure used by the investor to evaluate an investment proposal. 
Net Present Value
Merits 
Demerits 
It considers the concept of the time value of money. Thus, gives equal weightage to all the cash flows. 
Assumptions about the required rate of return have to be made to calculate NPV. Slight changes to it can significantly affect the final value 
It factors in the risk of the project by giving the flexibility to assume the discount rate. 
It neglects the hidden costs incurred for the project. This sometimes can be very high which necessitates its inclusion. 
It helps in determining the actual profitability of the project. 
Two investment proposal of different size cannot be compared using this method. 
It takes all the cash flows of a project into consideration while estimating the net present value of a project. 
This method ignores sunk cost while determining the value. 
The risk for an investment can change with the passage of timing affecting the net present value. 
Internal Rate of Return
Merits 
Demerits 
It incorporates the concept of the time value of money by identifying the rate through discounting future cash flows even or uneven 
This concept ignores futures costs that may be incurred while generating cash flows. 
There is no need to predetermine the required rate of return thus eliminates the risk of misappropriation. 
It makes an implicit assumption that the future cash flows can be reinvested at the internal rate of return which is not practical. 
Various investment proposals can easily be ranked as it provides us with percentage return. 
If there are two projects varying in the amount of capital being invested generally the larger project is undervalued 
It gives more importance to the profitability of the project. 
The calculations are a bit tedious for an average person who wants to use this method 
Discounted Pay back
Merits 
Demerits 
It incorporates the concept of the time value of money. Thus, giving equal weightage to all the future cash flows. 
This method fails to determine whether the project will increase the firm’s value or not 
It gives importance to the speedy recovery of investments. Thus, helpful for companies with weak liquidity positions. 
It ignores the calculation beyond the payback period. The cash flows may reduce or even stop after payback 
The concept behind the method is easy to understand. 
There is a definite standard as to how short the payback period should be to accept a proposal 
Given information:
Particulars 
Value 
Invested Amoumt 
£ 1000 
Time Period 
3 years 
Rate of return 
6% 
It refers to the annual rate of interest received on the invested amount after taking the compounding effect into considerations it provides us with a better understanding of the returns being derived on the amount invested and helps us in decision making.
Formula;
Effective annual + (nominal rate/number of compounding periods)}^number . of compounding period] 1
Here number of compounding periods *> 1 + (6/100*36)}^36] 1
>
Effective annual rate is 6.178%
Value of the investment after a period of 3 years (Santos Júnior, M. (2019))
R/100*12)^t
Where P : Principle Amount Invested
R: Nominate rate of interest
t: time period
>>
Value of investment after the period of 3 years will be £ 1196.68
Principle required to be invested so that the final amount is equal to £ 4000. Here the interest is compounded semi annually
Formula,
R/100*2)^t
Where P : Principle Amount Invested
R: Nominate rate of interest
t: time period
>>
Thus, an amount of £ 3350 is required to be invested for initially for the resultant amount be £ 4000
The interest rate required for the amount invested such that the final amount received is £ 2000. Interest being compounded annually.
Formula,
R/100)^t
Where P : Principle Amount Invested
R: Nominate rate of interest
t: time period
^3>
Thus, interest rateof 25.99% is for the amount to double itself after the period of 3 years.
Time period after which the amount invested will double itself at a nominal interest rate of 12% p.a. Interest is compounded quarterly
Formula,
R/100*4)^t
Where P : Principle Amount Invested
R: Nominate rate of interest
t: time period
(100*4))^(t*4)>
Thus, the amount will be double itself if the amount is invested for 5.86 years.
This means maximizing the net present values of the course of actions taken by a firm i.e., the difference between the present value of the benefits and costs of a course of action. The Wealth created is reflected in the market value of the firm. Thus, wealth maximizations also mean maximizing the market value of the firm. (Khan, Z. A., &Hussanie, I. (2018).)
Profit Maximization: means deriving maximum return on investment through optimal utilization of resources. Here profits provide the rationale behind decision making and are used as the basis for measuring the performance of the company.
Wealth maximization is better than profit maximization because:
An agent is a person who is entrusted with the powers to act in the best interest of its principle and sometimes, the interests of agents differ from that of its principle. This inherent conflict of interest between the two parties leads to agency problems. (Panda, B., &Leepsa, N. M. (2017).)
In the above case study, the nature of the agency problem is of
Management Vs Stockholders: here, the stockholders of the company appoint management to run the operation of the business enterprise with the purpose of maximization of the stockholder’s wealth. And management is sometimes faced with decisions that will be beneficial for them but maybe against the interest of stockholders. Thus, agency problem
In the above case, the CEO has to decide whether to buy a company, Emerald PLC. If the CEO is to accept the proposal, then it will lead to improvement in his perquisites and prestige as then he will be CEO of a much larger company. On the other hand, it will reduce the wealth of the stockholders as the company is overvalued and they will be paying the extra amount which will give no value addition to the stockholders
Unless the company acquired is its competitor and may give enough benefit to the host company to cover the extra amount bring paid for acquiring the company. The CEO should keep aside his personal interest and act in favor of the interest of its stockholders as he has been appointed for the very purpose and it is his ethical responsibility that in case of any conflict arising during the decisionmaking process, he should act in a way that is always beneficial for the company’s stockholders.
Here, the CEO should reject the proposal as it will lead to a reduction in the share value of stockholders. Also, such decisions may have a positive impact on the CEO in short term, but will negatively affect the benefits of stockholders in long term.
Reference
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