NPV IRR reinvestment assumption

“Mathematically, whenever you discount a cash flow at a particular discount rate, you
are implicitly assuming that you can reinvest a cash flow at that same discount rate.” Can anyone please explain to me what this means? When you discount a cashflow in 1 period, you stop at that. You do not add it to the next cashflow and discount it over 2 periods. So, then why does the reinvestment assumption come in?

The math says that if you buy an EBITDA machine for \$1 million and it generates a 7.2% return for 10 years you will have \$2 million at the end of your holding period. That 7.2% assumption assumes you reinvest your dividends from the EBITDA machine at the same rate (7.2%) instead of just sitting in your bank account earning next to nothing.

So, if the price of EBITDA machines skyrockets 5 years into your investment you will not be able to reinvest your dividends at that 7.2% so your actual ending value will be less than the \$2 million you have targeted.

You can test this in Excel by modeling these cash flows and re-investment assumptions. There is actually an Excel function for the modified IRR (MIRR) that will allow you to make different reinvestment assumptions.

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That makes sense. Thank you for the answer. So, please correct me if i’m wrong, in a simplistic way both the IRR & NPV intrinsically assume any cash flow that an investment generates is ‘re-invested’ in the respective rates and not just left lying around. If so, how are these assumptions mathematically incorporated? For instance, NPV is simply the present value of all the cashflows. How does this assume that the amounts are re-invested? Please do help me out. Kinda confused.

Here is an Excel example of how this works.

With cash flows reinvested at the project return:

Return on Investment 7.2%
Return on Reinvestment 7.2%
Year 0 1 2 3 4 5 6 7 8 9 10
Investments (1,000,000)
Terminal Value 1,000,000
Beginning Balance - - 72,000 149,184 231,925 320,624 415,709 517,640 626,910 744,047 869,619
Dividends - 72,000 72,000 72,000 72,000 72,000 72,000 72,000 72,000 72,000 72,000
Interest on Dividends - - 5,184 10,741 16,699 23,085 29,931 37,270 45,138 53,571 62,613
Ending Balance - 72,000 149,184 231,925 320,624 415,709 517,640 626,910 744,047 869,619 1,004,231
Ending Value Value 2,004,231

With cash flows reinvested at 3%:

Return on Investment 7.2%
Return on Reinvestment 3.0%
Year 0 1 2 3 4 5 6 7 8 9 10
Investments (1,000,000)
Terminal Value 1,000,000
Beginning Balance - - 72,000 146,160 222,545 301,221 382,258 465,726 551,697 640,248 731,456
Dividends - 72,000 72,000 72,000 72,000 72,000 72,000 72,000 72,000 72,000 72,000
Interest on Dividends - - 2,160 4,385 6,676 9,037 11,468 13,972 16,551 19,207 21,944
Ending Balance - 72,000 146,160 222,545 301,221 382,258 465,726 551,697 640,248 731,456 825,399
Ending Value Value 1,825,399
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There are two schools of thought on this:

• One believes that interim cash outflows are removed from the investment, so there is no reinvestment assumption
• The other believes that interim cash flows are still considered to be part of the investment through the end of the investment, so there is an implicit reinvestment assumption

The author of that quote clearly belongs to the second school. Note that what he wrote is an opinion, not a theorem.

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You can also use the TVM worksheet on the BAII to do the same thing!

Thanks. I think my BAII still has the same batteries from my L1 exam in 1999 if that is any indication of how often I use it.

Ah, riiight. Got it. Thankyou!!

Yep, definitely got the picture now. Thanks a lot!!
Not to ask for much, But is it possible for you to attach this excel sheet? Would like to know how the MIRR formula and calculations work.