Question

Your firm has been hired to develop new software for the​university's class registration system. Under the​ contract, you will receive $ 497,000 as an upfront payment. You expect the development costs to be $ 439,000 per year for the next 3 years. Once the new system is in​ place, you will receive a final payment of $ 860,000 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.) Round to two decimal places

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

a. IRR is the rate of return where present value of Cash outflows is equal to present value of cash inflows:

Net NPV = (497000+(860000XPVF of Year4)- (439000XPVF of year1)-(439000XPVF of year 2)-(439000XPVF of year3)

Cost of Capital	Years	1	2	3	4	NPV
1%	1.01	0.99	0.98	0.97	0.96	32,350.59
2%	1.02	0.98	0.96	0.94	0.92	25,482.31
3%	1.03	0.97	0.94	0.92	0.89	19,338.48
4%	1.04	0.96	0.92	0.89	0.85	13,866.64
5%	1.05	0.95	0.91	0.86	0.82	9,018.24
6%	1.06	0.94	0.89	0.84	0.79	4,748.30
7%	1.07	0.93	0.87	0.82	0.76	1,015.14
7.30%	1.073	0.93	0.87	0.81	0.75	-5.99
8%	1.08	0.93	0.86	0.79	0.74	-2,219.90
9%	1.09	0.92	0.84	0.77	0.71	-4,992.68
10%	1.10	0.91	0.83	0.75	0.68	-7,336.45

Hence the IRR is 7.3%

(b) At 10% Cost of Capital,

NPV = (497000+(860000X.68)-(439000X.91)-(439000X.83)-(439000X.75))

= -7336.45

NPV is negative, so opportunity is not attractive.

(c) We cannot get IRR of this opportunity as PV of cash inflows shall not be equal to PV of Cash outflow at any rate of cost of capital.

(d) Yes, definitely it is attractive at new terms because NPV is $224888 at 10% cost of capital.

Cost of Capital	Years	1	2	3	4	NPV
1%	1.01	0.99	0.98	0.97	0.96	3,59,083.91
2%	1.02	0.98	0.96	0.94	0.92	3,39,589.75
3%	1.03	0.97	0.94	0.92	0.89	3,21,424.07
4%	1.04	0.96	0.92	0.89	0.85	3,04,500.07
5%	1.05	0.95	0.91	0.86	0.82	2,88,737.08
6%	1.06	0.94	0.89	0.84	0.79	2,74,060.15
7%	1.07	0.93	0.87	0.82	0.76	2,60,399.51
7.30%	1.073	0.93	0.87	0.81	0.75	2,56,489.67
8%	1.08	0.93	0.86	0.79	0.74	2,47,690.25
9%	1.09	0.92	0.84	0.77	0.71	2,35,871.89
10%	1.10	0.91	0.83	0.75	0.68	2,24,888.12