Question

CEO McIntosh is considering an investment option: (20 points) Time Cash Flow A Year0 $-4000 Year 1 $-2000 Year 2 $2000 Year 3 $400 Year 4 $8000 Year 5 $-2000 His firm only likes investments with an IRR of 10% or more, in order to decide whether this option is acceptable, the CEO first decides to calculate the IRR of the cash flow stream. He does this by calculating the NPV(Y) of the cash flow stream given a rate of return (x) and plots the result (generally the point where this plot crosses the x axis is the IRR). The equation he plots is (Y=): His plot looks like this: Input: 2000 2000 400 8000 2000 Plots: -4000 - 250000 2000do 150000 10000 sogoo Note: In the above equation, x represents (1+r) i.e. When you gain interest, you multiply your money by (1+r), this is what x represents in the above equation. (x from-1.7 to 5) 2 3 4 5 -50000 12 50000 (this was done in wolfram alpha: link) Unfortunately, this plot crosses the X axis at 3 places! So, it has multiple possible rates of return. These can be seen in the graph, though the exact values show up in the link. The zeroes are approximately: x= (-1.49,0.24, 1.12). The CEO wants to understand what each of these numbers mean. He knows that since x is (1+r) if he were to invest $1 and get an interest rate of 'x', his money after a single period would become x. So, for the first rate, i.e. -1.49, this means his $1 of money (assets), would become $1.49 of debt. Similarly, if he waits another period, it would turn into $2.22 of assets. The CEO knows this is impossible, otherwise he could get rid of all his company's debt by investing it here for 1 period. Real interest rates either shrink or grow the investment, they cannot negate it, i.e. 0 < 1+r. Thus, he knows the first rate can be ignored as a result of the mathematical model not lining up with reality. For the second rate (0.24), if he invests $1 at time o, his dollar would become 24 cents after 1 period, and continue shrinking on and on. Although this is not a good rate for an investment, he knows he has to take it seriously
Please show work using formulas

Answer 1

a) Withholding all the cash at the begining will result in changing the cash flow and thus the IRR. Cashflow will be as shown below and IRR will be 7.7% in such case.

Year	0	1	2	3	4	5
Cashflow	-8000	0	2000	400	8000	0

For IRR calculation, refer to screenshot below

B) Investing the intial cash will help in getting higher return than 7.7%. This will add to cashflow in terms of interest

Year	0	1	2	3	4		5
Cashflow	-8000	0	2000	400	8000		0
Interest (r%)		4000*r%	(2000)*r%	2000*r%	2000*r%		2000*r%
Cash Invested		4000	2000	2000	2000		2000 (becomes 0 later)
Interest Earned		247.9	123.93	123.93	123.93		123.93
Net Cash Flow	-8000	247.9	2123.93	523.93	8123.93		123.93

Through the use of solver if r=6.2% then IRR will be 10% (Values updated). This is based on assumption that the interest earned is withdrawn each year. If it does not and withdraws interest only at the end of the 5 years then investment rate needed shall be 6.7%

C) IRR of -1 or lesser is not possible as in that case we will be loosing the entire investment every year thus it will represent either a worst case liability scenario (shall be covered via insurance) or does not include complete time period of investment.