Present value - getting stuck!

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gmblng

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US corp expects to receive 3 pounds/share dividend this year from a British subsidiary. End of year exchange rate = $1.60/pound. Pound is expected to depreciate 5%/year against the dollar indefinitely. The dividend (in pounds) expected to appreciate 10%/year indefinitely.

Parent US corp owns 10 million shares of the subsidiary. What is the present value in dollars of its equity ownership in the subsidiary?

Assume a cost of capital of 15% for the subsidiary.
********************************************************************


What I”ve done so far:

10 million shares at 3 pounds = L 30,000,000. Convert to dollars =
$1.60 x 30,000,000 = $480,000,000.

5% depreciation of the pound against the dollar
= 1.60 x .05 = .08 $1.60 - .05 = $1.52/pound.

10% appreciation of dividend (in pounds) = 3 x .10 = 3 + .30 = L3.30 /share

I don't know how to incorporate the 5% depreciation and the 10% appreciation, as well as the cost of capital (15%).

I know the present value will be LESS than the $480,000,000 amount because of the depreciation but I don't know the formula to calculate it.

Any help you can provide would be GREATLY appreciated. Thanks for your time. :(
 
gmblng said:
US corp expects to receive 3 pounds/share dividend this year from a British subsidiary. End of year exchange rate = $1.60/pound. Pound is expected to depreciate 5%/year against the dollar indefinitely. The dividend (in pounds) expected to appreciate 10%/year indefinitely.

Parent US corp owns 10 million shares of the subsidiary. What is the present value in dollars of its equity ownership in the subsidiary?

Assume a cost of capital of 15% for the subsidiary.
Click to expand...
I don;t know what to do with the cost of capital, either. The rest might go like this:

Without depreciation in exchange and without appreciation in dividends

3*1.6
3*1.6
3*1.6
3*1.6
3*1.6
just 3/share every year.

Add the appreciation

3*1.6
3*1.6*(1.1)
3*1.6*(1.1)<sup>2</sup>
3*1.6*(1.1)<sup>3</sup>
3*1.6*(1.1)<sup>4</sup>
...

Add the depreciation

3*1.6
3*(1.1)*1.6*(0.95)
3*(1.1)<sup>2</sup>*1.6*(0.95)<sup>2</sup>
3*(1.1)<sup>3</sup>*1.6*(0.95)<sup>3</sup>
3*(1.1)<sup>4</sup>*1.6*(0.95)<sup>4</sup>
...

What to do with Cost of Capital...Hmmm...Well, we don;t yet have a discount rate. Maybe that's what it means.

With Cost of Capital annual discounting

3*1.6*1.15<sup>-1</sup>
3*(1.1)*1.6*(0.95)*1.15<sup>-2</sup>
3*(1.1)<sup>2</sup>*1.6*(0.95)<sup>2</sup>*1.15<sup>-3</sup>
3*(1.1)<sup>3</sup>*1.6*(0.95)<sup>3</sup>*1.15<sup>-4</sup>
3*(1.1)<sup>4</sup>*1.6*(0.95)<sup>4</sup>*1.15<sup>-5</sup>
...

That's kind of a mess, but it's just an Infinte Geometric Series. You should be able to add that up.

3*1.15<sup>-1</sup>*1.6 / (1 - [(1.1)*(0.95)*1.15<sup>-1</sup>]) = 45 + 5/7. Are we $$?
 
I think I'm on the right track thanx to help here - but

. . . I can't figure out the + 5/7 at the end of the inifinite series (where is that fraction coming from?) :?
 
Re: I think I'm on the right track thanx to help here - but

gmblng said:
. . . I can't figure out the + 5/7 at the end of the inifinite series (where is that fraction coming from?) :?
Click to expand...

3*1.15^-1*1.6 / (1 - [(1.1)*(0.95)*1.15^-1]) = 45 + 5/7

Well, just do the calculation of the left side: you'll get 45.7142857~
which is 45 5/7

You can actually do rearrangements, cancellations and end up with 320/7
 
AH - I had read that as 45 + 5, divided by 7. Now I see it was the fraction rep of the decimal.
Still having a problem - my calculations above (I went back and checked them and they were slightly off so I corrected them) STILL are not coming up to the book answer. I have $457,142,857.14 . . . and the book has $468,837,209. I'm off by 11,694,352 and I can't find out how that happened!
 
gmblng said:
What I”ve done so far:
10 million shares at 3 pounds = L 30,000,000.
Convert to dollars = $1.60 x 30,000,000 = $480,000,000.
Click to expand...

????
 
gmblng said:
US corp expects to receive 3 pounds/share dividend this year from a British subsidiary. End of year exchange rate = $1.60/pound. Pound is expected to depreciate 5%/year against the dollar indefinitely. The dividend (in pounds) expected to appreciate 10%/year indefinitely.

Parent US corp owns 10 million shares of the subsidiary. What is the present value in dollars of its equity ownership in the subsidiary?

Assume a cost of capital of 15% for the subsidiary.
Click to expand...
Click to expand...
********************************************************************

Right - the US corp owns $480,000,000 of the subsidiary (in US dollars). I have to find the present value of equity ownership; so of course I had to convert the 10,000,000 shares from pounds to dollars.

I know the answer has to be less than $480,000,000 because of (1) depreciation and because of (2) the calculations I've been doing with people's help (thanks to all).

My answer ($457,124,857.14), though, is not matching the book's present value answer ($468,837,209)
 
"What I”ve done so far:
10 million shares at 3 pounds = L 30,000,000.
Convert to dollars = $1.60 x 30,000,000 = $480,000,000."

You missed my point; look at that AGAIN; $1.60 * 30,000,000 = ????
 
$1.60 x 30,000,000 = OHHH! It's $48,000,000. Darn that extra zero!

Great. Well, in all honesty, I don't know what the conversion has to do with the formula for an infinite series that i was given, so it brings me back to the same issue - my answer the the books' are off and I don't know how to correct it. I can't find the error.
 
Well, TK's 45,714,285.71 is definitely correct.

Could be your book's answer is wrong, or uses rounding of the pennies.

To change TK's to your book's (46,883,720.90), increasing the rate
by .00003 (to 15.003) will do it within a few bucks.
So you can see it don't take much.
 
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