Question

It is sometimes stated that “the net present value approach assumes reinvestment of the intermediate cash flows at the required return.” Is this claim correct? To answer, suppose you calculate the NPV of a project in the usual way. Next, suppose you do the following:

a. Calculate the future value (as of the end of the project) of all the cash flows other than the initial outlay assuming they are reinvested at the required return, producing a single future value figure for the project.

b. Calculate the NPV of the project using the single future value calculated in the previous step and the initial outlay. It is easy to verify that you will get the same NPV as in your original calculation only if you use the required return as the reinvestment rate in the previous step.

Answer 1

It is sometimes stated that “the net present value approach assumes reinvestment of the intermediate cash flows at the required return.” Is this claim correct?

Yes , the above cliam is correct.

.

Let us assume the following cash flows for a project and required rate of return of the project to be 10%:

Year	Cash Flows
0	-10,000
1	4,500
2	4,500
3	4,500

.

Calculation of NPV in usual way:

Year	Cash Flows	DF @ 10%	Present Value
0	-10,000	1	-10,000.00
1	4,500	0.909090909	4,090.91
2	4,500	0.826446281	3,719.01
3	4,500	0.751314801	3,380.92
		NPV:	1,190.83

.

Part-a:

Future value (as of the end of the project) of all the cash flows other than the initial outlay assuming they are reinvested at the required return is as follows:

Year	Cash Flows	Working	Future Value
1	4,500	4500*1.10^2	5,445
2	4,500	4500*1.10^1	4,950
3	4,500	4500*1.10^0	4,500
		Future Value	14,895

.

Part-b:

NPV of the project using the single future value calculated in the previous step and the initial outlay = Present Value of Future value (as of the end of the project) of all the cash flows as computed in part-a – Initial Investment

= 14,895/1.10^3 – 10,000

= 11,190.83 – 10,000

= $1,190.83

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So, in both the cases NPV is coming $1,190.83 which proves the claim hat “the net present value approach assumes reinvestment of the intermediate cash flows at the required return.” is correct.