Question

Consider the streams of income given in the following​ table:

Income Stream  
End of Year A B
1 $5,000   $2,000
2 $4,000   $3,000
3 $3,000   $4,000
4 $2,000   $5,000
Total $14,000   $14,000

a.Find the present value of each income​ stream, using a discount rate of 1%,then repeat those calculations using a discount rate of 8 %

b. Compare the calculated present values and discuss them in light of the fact that the undiscounted total income amounts to $14,000 in each case.

Answer 1

a. Present value of A at discount rate of 1% is computed as follows:

= $ 5,000 / 1.01¹ + $ 4,000 / 1.01² + $ 3,000 / 1.01³ + $ 2,000 / 1.01⁴

= $ 13,705.41 Approximately

Present value of B at discount rate of 1% is computed as follows:

= $ 2,000 / 1.01¹ + $ 3,000 / 1.01² + $ 4,000 / 1.01³ + $ 5,000 / 1.01⁴

= $ 13,608.35 Approximately  

Present value of A at discount rate of 8% is computed as follows:

= $ 5,000 / 1.08¹ + $ 4,000 / 1.08² + $ 3,000 / 1.08³ + $ 2,000 / 1.08⁴

= $ 11,910.54 Approximately

Present value of B at discount rate of 8% is computed as follows:

= $ 2,000 / 1.08¹ + $ 3,000 / 1.08² + $ 4,000 / 1.08³ + $ 5,000 / 1.08⁴

= $ 11,274.35 Approximately

b. As can be seen that the present value of A is greater than the present value of B. The reason for the same is that the higher cash flows in A are occuring at initial years and hence are discounted at higher present value factor as compared to investment B where larger cash flows are occuring in later period and hence are discounted at lower present value factor, which is resulting in lower present value.

Even if undiscounted cash flows of both projects are $ 14,000, we should invest in investment A since the undiscounted cash flows does not take in to account the time value of money and hence are not the determining factor in selecting the investment.