Cost Basis vs. Investment Value

CFA Level III
#1

This is in reference to Schewser page 258-259.

The book provides limited explaination on how this cost-basis formula would theortically apply to a real life situation.

Heres the formula

FVIFcgt, MV<>Basis = (1+R)^N(1-TCG) + TcgB

Where b = Cost Basis / Market Value

In what investing situation would the the ‘investment’ purchase price and cost basis differ? Is this formula trying to take into account situation where facevalue would differ from market? I.e, bonds trading a discount to Par.

The forumla is simple but I want to ensure i understand how this relates

#2

Purchase price and cost bases should be same…

The formula I think is using the cost basis and " current" market value. (the differnce is capital gain)

#3

Galli

you have the formula wrong

it should be

FVIFcgt, MV<>Basis = (1+R)^N( 1 -TCG) + TcgB

Please look at the right formula (T-Tcg) is replaced by (1-Tcg)

#4

and there is another way to do the entire formula thing. (without using the formula above).

Say you had $1 invested earning R% for N years.

End of period value = (1+r)^n

if Cost basis were B - your capital gain = (1+r)^n -B

and you pay Tcg tax on that.

Tax paid = [(1+r)^n-B] * Tcg

End balance after taxes = (1+r)^n - [(1+r)^n-B] * Tcg

= (1+r)^n(1-Tcg) + B*Tcg

which is what is shown above.

#5

Opps, Thanks. I wrote the original formula wrong.

I think I understand the basics of taxing capital gains but why do they provide two seperate formalas which results in basically the same answer? One simply assumes capital appreciation and the other doesn’t? Seems strange to me that they even bothered having two seperate sections in the book to explain both

Cost-Basis Taxing: (1+r)^n(1-Tcg) + B*Tcg

and

Deferred Capital Gains Taxing: (1+r)^n(1-Tcg) + Tcg

#6

2nd one is the same as the first when the Basis = 1. (that is currrent market value of the asset is the same as the price at which it was acquired). .

And if you did not take a short cut of reading Schweser alone - the text explains this as well.

This is from my 2014 book - the reading number has now become 10 in the 2015 books, but I am pretty sure this is present there as well.