Finance future/present value question

Question

Somebody makes you the following offer-they will give you $500 per month, (at the end of each month), for the next five years if you pay them back $500 at the end of each month for the following ten years. Assuming your monthly opportunity cost is 1%, evaluate whether or not you should accept the offer.

 

 

Thanks! 

Answer 1

Yes, take the deal. On a gross basis it does not look good but a TVM basis it is a deal.

 

Benefit in  $500/ month X  60 months = $30,000

Cost out    $500 / Month  X 120 months = ($60,000)  but this is unadjusted for TVM

 

What is the PV of the "in"

N=  60    (5 years X 12 months/ year)

I=   1%   (given, make sure you do not use .01, the calculator wants a percent not decimal)

PV= ? (what we are looking for)

PMT= $500/ month (given)

FV= 0  (payments in stop, make sure you enter the ZERO. You need it, the computer wants it.)

 

now hit PV      You get a negative $22,477.52 That is the present value of the $30,000 gross unadjusted amount.

 

 

Now what is your cost?

Gross unadjusted is easy. $60,000      (120 months at $500/ month)

 

But want is the PV?

 

This is a two step problem.

First what is the PV of $500/ month for 10 years?

N=120        (10 X12)

I=1%          (% not decimal)

PV= ?         (what we are looking for)

PMT= $500   (cash out to other party)

FV= 0           (do not forget this)

 

Hit PV and you get a negative $34,850.26. It looks bad for the deal. PV in $22,477.52  PV out $34,850.26

 

But this is the PV 5 years from now.

What is this worth TODAY?

 

N= 60   (5X12   watch out it is not 120 time peroids)

I= 1%   (% not decimal)

PV= ?  (what we are looking for)

PMT= 0  (nothing but the PV of the future cash stream)

FV=  $34,850.26  (PV value of the $60,000 to be paid out)

 

hit PV= $19,183.31    

 

 Summary you will get a PV of $22,477.52

 

You will have to pay $60,000 but this is only worth $19,183.31 in present value at 1% per month opportunity cost.

 

In NPV terms you are ahead.