Question

Innovation Co. is thinking about marketing a new software product.

The initial set-up cost is $5M (and is paid at t=0).

At the end of every year for the next 10 years (i.e., at t=1,2,…,10), the product will generate revenue of $1M.

After that, the product will be outdated and will not be offered in the market anymore.

However, the company will have to provide customer support in perpetuity, which will cost $0.1M at the end of every year (i.e., at t=1,2,…,∞).

The cost of capital is 10% and there is annual compounding frequency.

What is the present value of the project’s total cost? (3 points)

What is the future value of the project’s total revenue when it ends (at t=10)? (3 points)

What is the Modified IRR for this project? Based on that rule, will you take the project? (4 points) 4 (10 points): The United States Space Force is looking to buy supercomputers.

Answer 1

a)Present Value of the project's total cost

Project cost every year = 0.1m or $100,000

This amount is perpetiuity i.e. never ending.

Present Value of perpetuity = Amount/rate, where amount = 100,000, r = 10%

=100,000/0.1 = $1,000,000

Hence, present value of project's total cost = $1,000,000

b)Future Value of project's total revenue

Every year revenue = $1,000,000

Future value of an annuity = A((1+r)t - 1)/r, where A = 1,000,000 , r = 10%, t = 10

=1,000,000((1.1)10 - 1)/0.1 = $15,947,424.60

c)MIRR

MIRR = (Future value of positive cash flow/Present value of negative cash flow)(1/t) - 1

We have calculated required values and t = 10

MIRR = (15,947,424.60/1,000,000)(1/10) - 1 = 0.59 or 59%

Clearly the MIRR > Cost of capital..We should accept the project.

If you have any doubt ask me in the comment section please.