当值Y-值Z = 0时如何查找值X

Question

I live abroad and I want to send some money back home. The bank will only let me send it in the local currency or 12 other currencies, and mine is not on their list. Therefore I only have the option of sending the local currency, which is Japanese Yen, or Euros. I want to create a spreadsheet, showing me when it would be worth sending in Euros and when it would be worth it sending in Yen. So I have:

Option 1: Send Euros
Option 2: Send Yen

Option 1 will require:
2,000 Yen handling fee
Two currency exchange transactions (Yen ---> Euros ---> Swedish Kroner)

Option 2 will require:
2,000 Yen handling fee + 0.1% of amount (minimum 1,500 Yen)
One currency transaction (Yen ---> Swedish Kroner)

So I made the following spreadsheet:

Exchange Rate
JPY/EUR: 143.21
EUR/SEK: 8.209
JPY/SEK: 0.058065

Handling Fee
EURO: 2000
JPY: 3500

Amount : 300,000

Option 1 : 17081.782
Option 2 : 17216.273

Amount X: ???

Here the Amount is set to 300,000 Yen

Option 1 is:

        ((300,000 - 2,000) / 143.21) * 8.209
        ((Amount - Handling) / JPY/EUR) * EUR/SEK

Option 2 is:

        (300,000 - 3,500) * 0.058065
        (Amount - Handling) * JPY/SEK

(Handling fee in Option 2 is 2,000 + 0.1% of amount, but minimum 1,500, and since 0.1% of 300,000 is 300, it will always be 1,500 for smaller amounts like 300,000.)

What I want to find out is Amount X, which is the amount where Option 1 - Option 2 = 0.

Does anyone have any suggestions to how I can obtain Amount X through a formula in Excel so that I will always be given the minimal amount I need to send before Option 1 is better than Option 2.

Answer 1

With a layout as below and suitable formulae which you clearly can manage, the results in C9 are 17,081.78 kr and in E10 17,216.27 kr . The balance point is when D2 is ¥119,132 .

This can be achieved with algebra by solving for when:

=B9*(D2-D3)/B8  

equals:

=B10*(D2-D3-MAX(1500,E2*0.001))  

but since the fixed handling fee is common to both options it is slightly easier to calculate the D4 'break-even' value and then add ¥2,000 to it. This would be:

 =E5/(1-B9/(B8*B10))  

Where, as you suggested, E5 might as well be replaced by 1500 . However to spare the algebra involved in solving for D4 Excel has a feature to help. With the first formula above say in G2 and the second in H2 then in I2:

=G2-H2  

is Option1 - Option2 which is -134.49 where D2 is ¥300,000. You want this to be 0 , so go to DATA > Data Tools - What-If Analysis, Goal Seek..., and Set cell: I2 , to value: 0 , By changing cell: D2 , OK. Excel will then apply a lot of sensible guesswork and in this case should find the answer, which will show in D2 if you click OK again.