Question

28 -81.6 + r* 1 (1-(+r0 NPV

What are the steps to solve for zero! Please show all work! Thanks.

Answer 1

This can be done using spreadsheet programs such as Excel. Otherwise, manually we have to do it using trial and error

For example,
Lets say r*=10%
NPV=-81.6+28/10%*(1-1/1.1^4)=7.15623250

Now as NPV is positive, we increase r* to r*=15%
NPV=-81.6+28/15%*(1-1/1.15^4)=-1.66060584

Now as NPV is negative, we decrease r* to r=12.5%
NPV=-81.6+28/12.5%*(1-1/1.125^4)=2.55790276

Now as NPV is positive, we increase r* to r=13.5%
NPV=-81.6+28/13.5%*(1-1/1.135^4)=0.82732211

Now as NPV is positive, we increase r* to r=14%
NPV=-81.6+28/14%*(1-1/1.14^4)=-0.01605547

So, r* is approximately 14%

Alternatively, using Excel
=RATE(4,-28,81.6)
=13.99%

or
=IRR({-81.6;28;28;28;28})
=13.99%

Alternatively using financial calculator
N=4
PMT=-28
PV=81.6
FV=0
CPT I/Y=13.99%