19.d Evaluating Investments
We can evaluate whether or not an investment is worthwhile, or determine which investment is most beneficial when selecting among mutually exclusive investments by using the formula for the present value of an annuity:
PV=B/(1+R)+B/(1+R)^2+B/(1+R)^3+……B/(1+R)^N
B= The amount of the payment received each year
R= The rate of interest on the payment received in that particular year
N= The number of years that will elapse before that payment is received
-$50 +$30 +$30
N=0 N=1 N=2 N=3
Figure 19.d.1
-$100 +$40 +$40 +$40
N=0 N=1 N=2 N=3
Figure 19.d.2
Figure 19.d.1 and 19.d.2 are graphical illustrations of the present value of an annuity. The negative dollar amount in the period N=0 represents the initial payment that is invested, $50 in figure 19.d.1 and $100 in figure 19.d.2. The positive dollar values in the following periods, N=1, N=2, and N=3 represent the return we will receive on our investment expressed in the future value of dollars. The initial investment in N=0 is already expressed in today’s dollars so we take that value as given. For the following periods, N=1, N=2, and N=3, we must calculate the present value of the payment received in each period.
For the investment shown in figure 19.d.1, if we assume an interest rate of 10%, the calculation is as follows:
PV= -50+30/(1.1)+30/(1.1)^2
= -50+27+24
= 1
Because the present value is greater than 0, we will accept this investment
For the investment shown in figure 19.d.2, if we assume an interest rate of 10%, the calculation is as follows:
PV= -100+40/(1.1)+40/(1.1)^2+40/(1.1)^3
= -100+36+32+28
= -4
Because the present value is less than 0, we will reject this investment
The general rule in evaluating investments is as follows:
If present value>0, accept the investment
If present value<0, reject the investment
This generalization makes sense intuitively, if we expect to receive a net positive return in the future, we will participate and invest. If we expect to receive a net negative loss in the future, we will not participate in this investment opportunity.
In the case of mutually exclusive investments, where we must choose between a number of options of investments, we should choose the investment that yields the highest present value according to the above calculation. An example of a mutually exclusive investment is the case where we own a parcel of land on which we can only build one enterprise. We should choose the enterprise that yields the highest return expressed by the greatest net present value.
Evaluating Investments Review Questions
1) If the present value of an investment is 3 will we accept it or reject it?
2) If the present value of an investment is –27, will we accept it or reject it?
3) How do we select an investment among alternative mutually exclusive investments?
4) What is the present value of an investment with the following payment and returns;
N=0, 100; N=1, 50; N=2, 50; assume an interest rate of 10%
Answers:
1) Accept it
2) Reject it
3) Pick the investment with the highest present value
4) PV=100+50/(1.1)+50/(1.1)^2