Question

Explain, in your own words, the concept of the time value of money in a relationship to both the simple direct investment and timing for maximizing the value of a corporations excess cash as well as for cash flows of projects and capital/project investment analysis. Be sure to discuss the limitation of time value analysis in terms of the component financial data points used in the underlying formulas and financial analysis results.

Answer 1

The concept of time value of money says that the value of a given amount in future shall be less than it;s value today.

This can be understood with the following example:

If you are offered the choice between having $10000 today and having $10000 at a future date, you will usally prefere to have $10000 now. Similarly if the choice is between payin $10000 now and paying $10000 at a later date, you will prefere to pay later. In the first case by receiving $10000 early, you can invest $10000 and earn interest on the same. Similarly in the second case by deferring the payment,you can earn interest by keeping the money in the bank.

Therefore the time gap allowed help us to make some money. This incremental gain is the time value of money.

Otherthan interest there are some other reasons why the money in future is worth less than similar money today.

(i) Preference for Present consumption: Individuals have prefrence for present consumption in comparison to future consumption.

(ii) Inflation:Due to inflation,purchasing power of the money reduces and more money is required to buy the same amount of goods as could have been baught if the payment had been received earlier.

(iii) Risk: Risk of uncertainity in the future lowers the value of money. eg. Risk of Non Payment, Uncertainity of investor's life.

Concept of the time value of money in a relationship to the simple direct investment and timing for maximizing the value of a corporations excess cash:

If the corporation have excess cash than instead of keeping it idle, corporation can invest it somewhere(after analyzing variious investment options available) and earn interest on the same hence it can maximize the value of corporations' excess cash. Example:

Say company have excess cash of $10000 and it dose not need this for one year. Hence it can invest it in a good investment option. Suppose company has following three options available.

Option1st: Rate of interest 12% p.a.

Option2nd: Rate of interest 6.5% semiannually.

Option3rd: Rate of interest 12% p.a. compounded quarterly

we shall find out effective annual rate (EAR)for al the above three options.

EAR (option1); 12%

EAR(option2): 13.4225% (i.e.1.065^{^2}-1=.134225 or 13.4225%)

EAR(option3):12.551% (i.e.1.03^{^4}-1=.12551 or 12.551%)

EAR is maximum in option 2nd hence option 2nd should be choosen.

The value of $10000 after one year in option2nd=11342.25 [i.e.10000*(1.065)^{^2}]

Concept of the time value of money in a relationship to  cash flows of projects and capital/project investment analysis:

if we have to determine whether the money invested in a project will be profitable or not or we have to determine which out of various projects will be most profitable, we find the present value of future cash flows of the projects(or projects) than compare it with the initial investment( in case of single project) if the Present value of future cash flows is higher than the intial investment then project is acceptable otherwise not. Difference between present value of future cash flows and the intial investment is called Net Present value(NPV). If we have to analyse various projects then we shall choose one having highest NPV.

Example Initial investment $90000

annual cash flow $10000

life of project 10 years

Risk free Rate of interest 10%

Calculation of NPV:

PV of cash flows=Annual cash flow*PV factor of annuity

PV factor of annuity= [(1+r)^{^n}-1] / [(1+r)^{^n}*r]

=[(1+.1)^{^10}-1] / [(1+.1)^{^10}*.1]

=6.1446

PV of cash flow=10000*6.1445

=61445

NPV=90000-61445

=28555

NPV is positive hence project is acceptable.

Limitation of time value analysis:

(i) Taking risk free rate(discounting rate) is not easy: In the above example we took 10% as risk free rate. But in practical there is no criteria of choosing risk free rate.

(ii)Inflation rate can not be predetermined: Know one know what shall be the inflation rate in the country. Hence it becomes the limitaion of time value of money.

I hope the concept is clear now.

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