[marc9482]

The following example was posed in a text that we're using in Intermediate Accounting, but the problem is that when I do the calculation on my HP-12C business calculator I keep getting a different answer and the professor can't explain why as she states she doesn't have a HP-12C. If anyone can explain this I'd be most appreciative.

Problem:
Sutter Company purchases a specially built robot sprayer painter for its production line. The company issues a $ 100,000, five year, zero-interest-bearing note to Wrigley Robotics, Inc. for the new equipment. The prevailing market rate of interest for obligations of this nature is 10%. Sutter is to pay off the note in five $ 20,000 installments, made at the end of each year. Sutter cannot readily determine the fair value of this specially built robot. Therefore Sutter approximates the robot's value by establishing the fair value (present value) of the note. What are the entries for the date of purchase and the dates of payments?

Aside Note: My HP-12C calculates the PV as $ 62,092.13. The problem shows the PV to be $ 75,816. Can anyone explain the difference?

[ArcSine]

Assuming only what's stated in the problem, along with an assumption of annual compounding, 75,816 is the correct answer.

What are you inputting, such that you're getting back 62,092?

[marc9482]

Input into HP-12C:

FV = $ 100,000
n = 5
I = 10%
PV = ?

and HP-12C shows PV = 62,092.13

so please explain how $ 75,816 is the correct answer

[ArcSine]

Ah, clear now. Your inputs are telling the HP to calc the PV of a single future amount of 100K, to which the machine responds...

which is indeed 62,092.1323.

But remember that in this problem you're finding the PV not of a single future amount, but rather of a sequence of multiple, equal amounts (20K, annually, 5 payments, beginning one year hence).

It can be solved pretty quickly mathematically (there's a shortcut formula available when all the future cash flows are the same amount; aka an "annuity"), but to knock it out on your HP, pull out the manual and look up the instructions for calculating annuities.

[marc9482]

Ah, OK, I get it now!! For those wondering the entry into the HP-12C is
20,000 cFj
20,000 cFj
20,000 cFj
20,000 cFj
20,000 cFj
10 (I)
f(NPV) = 75,816

[marc9482]

Or...
0 cFo
20000 cFj
5 Nj
10 I
f(NPV)