<p>Assuming the present is taken to be period 0, your approach is correct, subject to one caveat.</p>
<p>As you suggest, the internal rate of return is the discount rate at which the discounted present values of all the costs and all the benefits of a project sum to zero.  In this case, you are given the stream of benefits, and the right hand side of your equation correctly represents the discounted present value of that stream.</p>
<p>So far as the left hand side is concerned, instead of being given a stream of costs to treat in the same manner, you are just given the net present value of costs.  If the question is from a textbook and that is all the information given, you can hardly do anything else than use that net present value.</p>
<p>The caveat is that it's unclear how that net present value of the costs has been obtained. If it was calculated using any discount rate other than the true internal rate of return, eg an organisation's standard discount rate for evaluating the net present value of proposed projects, then (except by coincidence) your approach will not give the correct internal rate of return (and the given answer will be wrong).</p>

CC BY-SA 4.0
2021-05-21T11:19:37.443Z
2021-05-21T14:49:38.730Z
2021-05-21T14:49:38.730Z
Adam Bailey
<p>Trying to finding the internal rate of return R:</p>
<ul>
<li><p>Net present value of costs is <span class="math-container">$\ Y(s)$</span></p>
</li>
<li><p>Net benefit is <span class="math-container">$\ Y(s+1)-Y(s)$</span> in every period t up to<span class="math-container">$\ \infty $</span></p>
</li>
</ul>
<p>The answer is given as <span class="math-container">$\ R=\frac{Y(s+1)-Y(s)}{Y(s)} $</span></p>
<p>Is this the correct approach (NPV = 0)?:</p>
<p><span class="math-container">$\ Y(s) = \sum_{t=1}^{\infty}\frac{Y(s+1)-Y(s)}{(1+R)^t} $</span></p>

CC BY-SA 4.0
2021-05-21T17:13:34.920Z
Hi, please do not delete questions for which you get useful answer. Deletion of useful material goes against the principles of SE
1muflon1
<finance>
Internal rate of return
user918814
# Internal rate of return

(Asked by: username_0 on 2021-05-20)

Trying to finding the internal rate of return R:

* Net present value of costs is $\ Y(s)$
* Net benefit is $\ Y(s+1)-Y(s)$ in every period t up to$\ \infty $

The answer is given as $\ R=\frac{Y(s+1)-Y(s)}{Y(s)} $

Is this the correct approach (NPV = 0)?:

$\ Y(s) = \sum\_{t=1}^{\infty}\frac{Y(s+1)-Y(s)}{(1+R)^t} $

**Tags:** finance

> **Comments:**
> **username_1**: Hi, please do not delete questions for which you get useful answer. Deletion of useful material goes against the principles of SE  

---

## 1 answers

### Answer by username_2 on 2021-05-21. Score: 2

Assuming the present is taken to be period 0, your approach is correct, subject to one caveat.

As you suggest, the internal rate of return is the discount rate at which the discounted present values of all the costs and all the benefits of a project sum to zero. In this case, you are given the stream of benefits, and the right hand side of your equation correctly represents the discounted present value of that stream.

So far as the left hand side is concerned, instead of being given a stream of costs to treat in the same manner, you are just given the net present value of costs. If the question is from a textbook and that is all the information given, you can hardly do anything else than use that net present value.

The caveat is that it's unclear how that net present value of the costs has been obtained. If it was calculated using any discount rate other than the true internal rate of return, eg an organisation's standard discount rate for evaluating the net present value of proposed projects, then (except by coincidence) your approach will not give the correct internal rate of return (and the given answer will be wrong).


---

