Question

Your firm has been hired to develop new software for the​ university's class registration system. Under the​ contract, you will receive $ 508,000 as an upfront payment. You expect the development costs to be $ 431,000 per year for the next 3 years. Once the new system is in​ place, you will receive a final payment of $ 825,000 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

As given in the question, cash flow for the software is as follow;

	Year 0	Year 1	Year 2	Year 3	Year 4
Upfront Payment	508,000.00
(Development Cost)		(431,000.00)	(431,000.00)	(431,000.00)
Final Payment					825,000.00
Total Cashflow	508,000.00	(431,000.00)	(431,000.00)	(431,000.00)	825,000.00

Now, let r be the IRR of the opportunity.

Hence, we have;

$0=508,000-\frac{431,000}{1+r}-\frac{431,000}{(1+r)^{2}} - \frac{431,000}{(1+r)^{3}} + \frac{825,000}{(1+r)^{4}}$

Solving for r, we get, r = 10%

b., since the cost of capital is equal to the IRR, the project is not yielding any returns. Hence, it may not be a attractive proposal.

c. If the final payment is 1.2 million, the cashflow of the project will be;

	Year 0	Year 1	Year 2	Year 3	Year 4
Upfront Payment	508,000.00
(Development Cost)		(431,000.00)	(431,000.00)	(431,000.00)
Final Payment					1,200,000.00
Total Cashflow	508,000.00	(431,000.00)	(431,000.00)	(431,000.00)	1,200,000.00

Hence, let r be the IRR in this case also, we have;

$0=508,000-\frac{431,000}{1+r}-\frac{431,000}{(1+r)^{2}} - \frac{431,000}{(1+r)^{3}} + \frac{1200,000}{(1+r)^{4}}$

Now, for no real values of r, RHS is 0. Hence, in this case, there is no real IRR.

However, to evaluate if proposal is attractive or not, we may find NPV at the cost of capital.

NPV at r = 10% is;

$NPV = 508,000-\frac{431,000}{1+0.1}-\frac{431,000}{(1+0.1)^{2}} - \frac{431,000}{(1+0.1)^{3}} + \frac{1200,000}{(1+0.1)^{4}}= $232,529.94$

As NPV of the project is positive, the revised opportunity is attractive.