1. Write a short essay each of the following questions. For each question, illustrate with an appropriate example in your answer.
a. ‘Risk aversion implies that corporate managers will only invest in low risk investments’. Critically evaluate this statement (indicate whether you agree or disagree in your answer).
b. Is it possible for an ordinary annuity to have the same present value as perpetuity if the cash flows and discount rates are identical? Explain.
1.a) The Investment process has a degree of inherited risks that cannot be avoided. Risk is defined in terms of variability of return from a given investments. It is also defined as the probability that the expected return will differ from the actual return. The greater risk implies a greater variability of outcomes whereas lesser risk implies a lesser variability of returns (DeFusco et al., 2015). The risks that are faced by corporate managers can be classified into specific risks and systematic risks. The risk associated with an individual investment can be termed as specific risk and it can be eliminated through proper diversifications. There is always a risk that secured investments can also lose value and this type of risk is called systematic risks (Nakano et al., 2014). The understanding of the relationship between risk and return is very important for investment and they are:
- If the investor were willing to take more risk then, the investor would expect higher returns.
- If the investor is unwilling to take higher risks then the investor should accept lower returns.
The relationship between the risk and return therefore provides that if an investment has more risk then, it should offer higher returns. Otherwise, it would be prudent to invest in risk free investment where it can get low return for low risks. The degree of risk that a corporation is willing to take depends on how risk averse is the investing manager of that corporation. There are certain individuals that undertake a higher degree of risk for generating a little extra return. The risk averse corporate managers on the other hand are not unwilling to take risks but they requires a higher return for risky investments. The risk averse corporate managers insist that there should be a premium or additional compensation for taking risks (Brealey et al., 2012).
The statement provided in the question that risk averse corporate managers will only invest in low risk investment is not correct. As it can be seen from the discussion above that a risk averse corporate managers require a higher return for taking higher risk. In conclusion, it can be said that risk aversion therefore does not imply that no risky investment will be made. It only suggests that risky investment should be adequately compensated with higher returns to justify the higher risk. For example if there are two investment opportunity A and B. The beta of A being 1.2 is risky investment and beta of B 0.80 is low risk investment. Therefore, if the return from both the investment is same then a risk averse corporate manager will invest in B because it will receive same return with low risks. A risk averse corporate manager will only invest in A if it offers a higher return than B.
1. b) The present value represents the current monetary value of payments that is to be received in future. It describes the future sum of money that is worth today. This principal of present value can be applied to the finite series of annual payments that is annuity. It can also be applied theoretically to infinite number of future payments that is perpetuity (Kashyap, 2014).
An annuity may be defined as the series of equal cash flows that is received at equal intervals for a finite number of periods. The Annuities are of two types depending on the timing of the payment ordinary annuities and annuity due. In case of ordinary annuities, payments are made at the end of the specific time period. For example if $1000.00 is to be received yearly in the form of annuity. Then in the case of ordinary annuity, this $1000.00 is to be received after one year and in case of annuity due this $1000.00 will be received at the beginning of the year. The annuities whether ordinary annuity or annuity due does not continue forever and they are for specific period. Perpetuity on the other hand does not have any specific period. Perpetuity can be explained as a series of equal payments that is to be received forever (Xingyun, 2015).
The present value of an annuity is calculated by using the following formula:
PV= (P/r) (1-(1+r) ^ -n)
Here P stands for payment received each period, n stands for number of period and r stands for the interest rate or discounting factor.
For example, if an annuity of $1500.00 is received annually for 10 years. If the rate of interest per annum is 3.5% then the Present value of the annuity will be:
When the annual payment continues forever then the annuity becomes perpetuity (Wicksell, 2013). The present value of perpetuity is calculated by using the following formula:
Here P stands for payment received at the end of each period and r is the discounting rate or interest rate. Continuing with the above example the present value of perpetuity for $1500.00 at 3.5% rate would be:
Based on the above discussion and by the help of the example it can be concluded that present value of annuity and perpetuity cannot be identical even if the rate of interest and the cash flows are identical.
Brealey, R. A., Myers, S. C., Allen, F., & Mohanty, P. (2012). Principles of corporate finance. Tata McGraw-Hill Education.
DeFusco, R. A., McLeavey, D. W., Pinto, J. E., Anson, M. J., & Runkle, D. E. (2015). Quantitative investment analysis. John Wiley & Sons.
Kashyap, A. (2014). Capital Allocating Decisions: Time Value of Money.Asian Journal of Management, 5(1), 106-110.
Nakano, M., Otsubo, F., & Takasu, Y. (2014). Effects of Accounting Conservatism on Corporate Investment Levels, Risk Taking, and Shareholder Value (No. 14-E-10). Institute for Monetary and Economic Studies, Bank of Japan.
Wicksell, K. (2013). Interest and prices: a study of the causes regulating the value of money. Read Books Ltd.
Xingyun, P. E. N. G. (2015). Time Value of Money. World Scientific Book Chapters, 49-70.