Question

Your company is considering two mutually exclusive projects, X and Y, whose costs and cash flows are shown below:

Year	X	Y
0	−$2,000	−$2,000
1	200	2,000
2	600	200
3	800	100
4	2,400	75

The projects are equally risky, and the firm's required rate of return is 12 percent. You must make a recommendation, and you must base it on the modified IRR. What is the MIRR of the best project?

	a.	12.00%
	b.	12.89%
	c.	11.46%
	d.	13.59%
	e.	21.29%

Answer 1

Answer :- e) 21.29%

Explanation :-

Modified IRR = [FV(positive cash flows, cost of capital) / (-PV (negative cash flows, finance rate))]^1/n - 1

Here only cost of capital is given. The cost of capital is therefore only considered to be the rate of finance.

Cost of capital = 12%

n = Number of years

Computation of Modified IRR of project X:

FV (positive cash flows, reinvestment rate)

= (200 (1+0.12)^3) + (600 (1+0.12)^2) + (800(1+0.12)^1) + (2400 (1+0.12)^0)

=$4329.62

PV (negative cash flows, finance rate)

=$2000/(1+0.12)^0

=$2000

Modified IRR = [FV(positive cash flows, cost of capital) / (-PV (negative cash flows, finance rate))]^1/n - 1

= ($4329.62/2000)^1/4 - 1

=1

2.16^1/4-1

=1.2123- 1

=0.212or 21.2% (approx.)

Computation of Modified IRR of project Y:

FV (positive cash flows, reinvestment rate)

= (2000 (1+0.12)^3) + (200 (1+0.12)^2) + (100(1+0.12)^1) + (75(1+0.12)^0)

=$3247.73

PV (negative cash flows, finance rate)

=$2000/(1+0.12)^0

=$2000

Modified IRR = [FV(positive cash flows, cost of capital) / (-PV (negative cash flows, finance rate))]^1/n - 1

= ($3247.73/2000)^1/4 - 1

=1.623^1/4-1

=1.1288- 1

=0.1289 or 12.89%(approx.)

Modified IRR of Project X = 21.29%

Modified IRR of Project Y = 12.89%

Recommendation: As modified IRR of Project x is greater than that of Project y, Project x should be accepted.