Question

A firm is considering two mutually exclusive projects, X and Y, with the following cash flows:

0 1 2 3 4

Project X: -$1,000 $90 $300 $430 $700

Project Y: -$1,000 $1,100 $100 $55 $55

The projects are equally risky, and their WACC is 13.0%. What is the MIRR of the project that maximizes shareholder value? Round your answer to two decimal places.

Answer 1

Present value of inflows=cash inflow*Present value of discounting factor(rate%,time period)

X:

Present value of inflows=90/1.13+300/1.13^2+430/1.13^3+700/1.13^4

=$1041.92

NPV=Present value of inflows-Present value of outflows

=$1041.92-$1000

=$41.92(Approx).

Y:

Present value of inflows=1100/1.13+100/1.13^2+55/1.13^3+55/1.13^4

=$1123.62

NPV=Present value of inflows-Present value of outflows

=$1123.62-$1000

=$123.62(Approx).

Hence Y is better project having higher NPV.

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

Hence future value of inflows=1100*(1.13)^3+100*(1.13)^2+55*(1.13)+55

=$1832.0267

MIRR=[Future value of inflows/Present value of outflows]^(1/time period)-1

=[$1832.0267/1000]^(1/4)-1

which is equal to

=16.34%(Approx).