Question

1. What is the reinvestment rate assumption and how does it affect the NPV vs. IRR conflicts?

2. What is the rationale behind the MIRR method?

3. ​​​​​​​Would the MIRR change if the required rate of return changed?

Answer 1

1. REINVESTMENT RATE ASSUMPTION

The IRR has a reinvestment rate assumption that assumes that the company will reinvest cash inflows at the IRR's rate of return for the lifetime of the project. If the reinvesment rate is too high to be feasible, then the IRR of the project will fall. If the reinvestment rate is higher than IRR's rate of return, then the IRR of the project is feasible.

Mutually exclusive projects where IRR and NPV rankings are often in conflict and the problem of multiple IRRs arise. This assumption may solve the problems by turning a sufficient condition into an implict assumption.

2. RATIONALE BEHIND THE MIRR METHOD

One of the points advanced in favor of the IRR approach is that IRR is expressed as a percentage and decision makers may prefer to think percentage terms. But IRR has also been criticized on the grounds that it is a percentage that contains thae implicit assumption that returns are reinvested at a rate equal to the IRR. There has been much discussion about this point. It may not be possible for a firm to reinvest intermediate cash flows at a rate of return equal to the project's internal rate of return. The analysts favouring the use of IRR but concerned about the impact of the reinvestment debate have been provided a modified device, also consistent with NPV, which circumvents any reinvestment worries. This is called the Modified Internal Rate of Return (MIRR). The MIRR of an investment is that rate of compunding whic if applied to the initial outlay produces the terminal value of the project returns.

MIRR can be calculated as follows:

MIRR =

where Future Value (positive cash flows, reinvestment rate)=Positive Annual cash flow * (1 + r₂ )^n-t;r₂=reinvestment rate at year

Present Value (negative cash flows,finance rate)=Initial Investment + Negative Annual cash Flow/(1 + r₁ )ⁿ ; r₁= required rate of return

3. EFFECT OF CHANGE IN REQUIRED RATE OF RETURN ON MIRR

MIRR at

r₁(required rate of return)=8% and r₂(reinvestment rate of return) = 11%,

Cash Flows for the year

0(initial investment)= - $ 1000

1= - $ 2000

2= $ 4000

3 = $ 7000

substituting the values

Present Value = $1000 + $2000/(1+0.08 )

= $2851.852

Future Value = $4000/(1+0.11)² + $7000/(1+0.11)³

= $3246.49+ $5118.34

= $8364.8290

MIRR =

=

=1.4309-1

= 0.4309 or 43.09%

Let the required rate of return r₁, increases from 8% to 9%, and reinvestement rate of return r₂ remains unchanged, then the new MIRR is calculated as follows:

Present Value = $1000 + $2000/(1+0.09)

=$1000 + $1834.862

= $2834.862

Future Value remains unchanged i.e., $8364.8290 as r₂ is constant, thus the new MIRR

=

=

= 1.4338-1

=0.4338 or 43.38%

Therefore, it is proved that, if the reinvestement rate remains unchanged, and required rate of return increases r1 increases from 8% to 9%, then MIRR also increases from 43.09% to 43.38%.