Question

Your firm has been hired to develop new software for the​ university's class registration system. Under the​ contract, you will receive $501,000 as an upfront payment. You expect the development costs to be $436,000 per year for the next 3 years. Once the new system is in​ place, you will receive a final payment of $847,000 from the university 4 years from now. a. What are the IRRs of this​ opportunity?  ​(Hint​: Build an Excel model which tests the NPV at​ 1% intervals from​ 1% to​ 40%. Then zero in on the rates at which the NPV changes​ signs.) b. If your cost of capital is 10% ​, is the opportunity​ attractive? Suppose you are able to renegotiate the terms of the contract so that your final payment in year 4 will be $1.2 million. c. What is the IRR of the opportunity​ now? d. Is it attractive at the new​ terms?

Answer 1

The cash flow associated with this question is shown below:

Year	Cash flows
0	501,000
1	-        436,000
2	-        436,000
3	-        436,000
4	847,000

(a): IRR is the rate which makes NPV as nil.  Now the excel table for testing the NPVs from 1% to 40% (at 1% intervals) is shown below:

r	NPV
1%	32,680.80
2%	26,123.97
3%	20,273.98
4%	15,079.46
5%	10,492.86
6%	6,470.12
7%	2,970.45
8%	-         44.00
9%	-   2,608.32
10%	-   4,755.07
11%	-   6,514.48
12%	-   7,914.62
13%	-   8,981.57
14%	-   9,739.57
15%	- 10,211.15
16%	- 10,417.28
17%	- 10,377.45
18%	- 10,109.82
19%	-   9,631.28
20%	-   8,957.56
21%	-   8,103.33
22%	-   7,082.23
23%	-   5,907.00
24%	-   4,589.50
25%	-   3,140.80
26%	-   1,571.21
27%	109.66
28%	1,892.81
29%	3,769.87
30%	5,733.03
31%	7,774.99
32%	9,888.94
33%	12,068.52
34%	14,307.80
35%	16,601.24
36%	18,943.67
37%	21,330.26
38%	23,756.50
39%	26,218.18
40%	28,711.37

We can see that there are 2 IRRs. One that lies between 7% and 8% and one that lies bewteen 26% and 27%.

On doing the calculations we get the IRRs as 7.98% and 26.94% (both rounded to 2 decimal place)

(b): No the opportunity is not attractive when the cost of capital is 10%. This is because it is apparent from the table that at 10% cost of capital NPV is negative (-$4,755.07)

(c): Here the scenario is:

Year	Cash flows	1+r	PVIF	PV
0	501,000	1.4600	1.0000	501,000.00
1	-        436,000		0.6849	- 298,630.14
2	-        436,000		0.4691	- 204,541.19
3	-        436,000		0.3213	- 140,096.71
4	1,200,000		0.2201	264,100.86
			NPV	121,832.83

The above scenario has no IRR because no rate is making NPV as nil.

(d): It will be attractive at the new terms as NPV is positive in all cases irrespective of the cost of capital.