# [OPE-L:4343] Re: Problems in Vol. III

Allin Cottrel (cottrell@wfu.edu)
Mon, 10 Mar 1997 20:19:50 -0800 (PST)

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> > Allin suggests (OPE 4337) another way of coming at this. My
> > question to you, Allin, is "What is the rate of return for
> > CAPITAL 2?"

Please disregard my last question, which was not properly
thought out.

I make the IRR to be .10 in both cases. Cap1 has a present cost
of \$1000, followed by a \$100 profit each year, while Cap2 has
a present cost of \$2000 followed by \$200 profit each year for
ten years, at which point its machine must be replaced. Make
the comparison over the ten years.

For Cap1, the IRR solves

1000 = sum(t = 1 to 9)[100/(1 + r)^t] + 1100/[(1 + r)^10]

At the end of year 10 the capitalist has \$1100 in hand after
meeting his wage-bill -- his year-10 profit plus the funds to
purchase another year's materials if he chooses. r = .10

For Cap2, the IRR solves

2000 = sum(t = 1 to 9)[200/(1 + r)^t] + 2200/[(1 + r)^10]

At the end of year 10 the capitalist has \$2200 in hand after
meeting his wage-bill -- his year-10 profit of \$200, as stipulated,
plus the funds to purchase another year's materials, plus the
funds to replace his machine, which have been set aside as
depreciation allowance over the ten years. r = .10

Allin.