Question

Calculate the present value of the following cash flows given a discount rate of 12%:

	Year 1	Year 2	Year 3	Year 4
Cash Flows	$1,500	$8,500	$12,500	$11,000

Calculate the internal rate of return for a project that has upfront costs of $7 million and cash flows of $2.5 million per year for each of the next four years. The risk adjusted project discount rate is 12%.

Answer 1

1)

Present value = 1,500 / (1 + 0.12)¹ + 8,500 / (1 + 0.12)² + 12,500/ (1 + 0.12)³ + 11,000 / (1 + 0.12)⁴

Present value = 1,339.2857 + 6,776.148 + 8,897.2531 + 6,990.6989

Present value = $24,003.39

2)

IRR is the rate of return that makes initial investment equal to present value of cash inflows.

Initial investment = Annuity * [1 - 1 / (1 + r)ⁿ] / r

7,000,000 = 2,500,000 * [1 - 1 / (1 + r)⁴] / r

Using trial and error method, i.e after trying various values for R, let's try R as 15.97%

7,000,000 = 2,500,000 * [1 - 1 / (1 + 0.1597)⁴] / 0.1597

7,000,000 = 2,500,000 * 2.799857

7,000,000 = 7,000,000

Therefore, IRR is 15.97%