Question

In an excel file, You are presented with two options for receiving cash flows: Option A – No payments in the first five years and annual payments of $5,000 at the end of year 6 through year 13. Option B – A one-time lump-sum payment of $10,000 at the end of the first year.

a. If the annual interest rate is 5%, which option would you prefer? [4 points]

b. Consider the cash flows of option A minus Option B. Compute the IRR of this stream of cash flows.

C. If the discount rate is greater than the IRR which investment should you chose? If the discount rate is less than the IRR which investment should you chose? [5 points]

d. Use economic intuition, to explain why the appeal of Option 1 relative to Option 2

Answer 1

A)

Interest Rate = 5%

OPTION A	OPTION B
Cash Flows	Year	PV = Cash Flow / (1+int%)^Year	Cash Flows	Year	PV = Cash Flow / (1+ int%)^Year
0	1	0.00	10,000	1	10,000
0	2	0.00	0	2	0
0	3	0.00	0	3	0
0	4	0.00	0	4	0
0	5	0.00	0	5	0
5000	6	3731.08	0	6	0
5000	7	3553.41	0	7	0
5000	8	3384.20	0	8	0
5000	9	3223.04	0	9	0
5000	10	3069.57	0	10	0
5000	11	2923.40	0	11	0
5000	12	2784.19	0	12	0
5000	13	2651.61	0	13	0
	Sum of PV=	25320.48		Sum of PV=	10000.00

We will select Option A since we will get a higher present value from this option.

B)

If we consider the difference in cash flows betwen Option A we can calculate the IRR:

OPTION A	OPTION B
Year	PV = Cash Flow / (1.05)^Year	Year	PV = Cash Flow / (1.05)^Year	Difference in CF (A-B)
1	0	1	10,000	-10,000
2	0	2	0	0
3	0	3	0	0
4	0	4	0	0
5	0	5	0	0
6	3731.076983	6	0	3,731
7	3553.406651	7	0	3,553
8	3384.19681	8	0	3,384
9	3223.044581	9	0	3,223
10	3069.566268	10	0	3,070
11	2923.396445	11	0	2,923
12	2784.187091	12	0	2,784
13	2651.606753	13	0	2,652
			IRR=	12.40%

Using IRR function over difference in Cash flows we get 12.40%.

Remember, IRR is the rate of return at which NPV = 0 i.e. the initial cash outlay is equal to the present value of cash inflows.

C)

If Discount Rate > IRR, then we should discard the project and If Discount Rate < IRR, we should accept the project.

hence if Discount rate > IRR, we should choose Option B and take 10,000 now and if Discount rate < IRR ,we should choose Option A.

This is because if the IRR is not greater than the project, then there is no point in investing and taking risk in the project as we can simply earn the discount rate (interest rate) by investing the money in risk free or low risk profile.

D)

Economin intuition is the ability to understand or make sense of something without conscious reasoning. Option 1 is more appealing as per Option 2 because it makes the person more financially secure in the long run with a benefit of higher cash inflows as compared to Option 2.