Question

Assume that there two investments of different risk. A return of 0.05 is required on one investment: on the other a return of 0.10 is required. Compare the present values obtained for each investment for expected cash flows of $1 billion 1 year, 20 years, and 50 years from now at the required rates of return.

Answer 1

Ans:

Present value of cash flow at 5% rate (note 1)	1416474162
Present value of cash flow at 10% rate (note 2)	1066253088

Note 1:

	Find the present value of cash flows at 5% rate.
Year	Present value factor (1/(1+rate)^n	Present value factor (A)	Cash flows (B)	Present value (A*B)
1	1/(1+5%)	0.9524	1000000000	952380952.38
2	1/(1+5%)^20	0.3769	1000000000	376889482.87
3	1/(1+5%)^50	0.0872	1000000000	87203726.97
			Present value of cash flows	1416474162.23

Note 2:

	Find the present value of cash flows at 10% rate.
Year	Present value factor (1/(1+rate)^n	Present value factor (A)	Cash flows (B)	Present value (A*B)
1	1/(1+10%)	0.9091	1000000000	909090909.09
2	1/(1+10%)^20	0.1486	1000000000	148643628.02
3	1/(1+10%)^50	0.0085	1000000000	8518551.28
			Present value of cash flows	1066253088.39