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year for the next 10 years (i.e., at t=1,2,...,10), the productwill generate revenueof$1M.Afterthat,the product will be outdated and will not be offered in the market anymore.However,the company will have to provide customer supportin perpetuity, which will cost $0.1M at the end of everyyear (i.e., at t=1,2,...,∞).The cost of capital is10%and there is annual compounding frequency.

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

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

hat is theModified IRRfor this project?Based on that rule, will you take the project? (4 points)

Answer 1

Computation of the present value of the total project cost

Given in the question that the company is required to pay $ 0.1M at the end of every year to provide customer suppourt up to infinity period

Present value of the Customer suppourt perpetuity= $ 0.1 Million/10%

= $ 1 Million

So the present value of the perpetuity is $ 1 million

S.No	Particulars	Amount
A	Initial set up cost	$ 5 M
B	PV of perpetuity	$ 1 M
	Total p.v	$ 6 M

Hence the total value of the project cost is $ 6 millions

Computation of the Future value of the projects total revenue

Year	Cash flow( M)	Disc @ 10%	Future value( M)
1	2	3	4(2*3)
1	$1	(1.10)^9	$2.3579
2	$1	(1.10)^8	$2.1436
3	$1	(1.10)^7	$1.9487
4	$1	(1.10)^6	$1.7716
5	$1	(1.10)^5	$1.6105
6	$1	(1.10)^4	$1.4641
7	$1	(1.10)^3	$1.3310
8	$1	(1.10)^2	$1.2100
9	$1	(1.10)^1	$1.1000
10	$1	(1.10)^0	$1.0000
		Total	$15.9374

Computation of the Modified internal rate of return

We know that Present value of cash outflow= Present value of the Terminal cash inflows at MIRR

$ 6 million = $ 15.9374/( 1+i)^10

(1+i)^10 = $ 15.9374/$ 6

( 1+i)^ 10=$ 2.656233

By using calculator we get 10th root of $ 2.656233 is 1.1026

By Solving the equation we get 1+i=1.1026

i = 10.26%

Since, my MIRR(i.e 10.26%) is greater than my Cost of Capital( i.e 10%), I will accept the Project.

Alternative Method to Calculate MIRR:

Year	Cash flow
0	($6)
1	$1
2	$1
3	$1
4	$1
5	$1
6	$1
7	$1
8	$1
9	$1
10	$1

We can alsoget MIRR by using MIRR Function in excel

MIRR ( Values, Interest rate, reinvestment rate)

= 10.2622%

Here values= Series of Cash flows( Hint: Drag from top to bottom)

Interest rate = 10%, Reinvestment rate = 10%.