Consider a firm with existing assets that generate an EPS of $5. If the firm doe

Question

Consider a firm with existing assets that generate an EPS of $5. If the firm

does not invest except to maintain existing assets, EPS is expected to remain

constant at $5 a year. However starting next year the firm has the chance to

invest $3 per share a year in developing a newly discovered geothermal

steam source for electricity generation. Each investment is expected to

generate a permanent 20% return and discount rate is 12%. However, the

source will be fully developed by the fifth year. What will be the stock price

at time t=0? Solve the problem using standard valuation method, i. e., stock

price equals the present value of future dividends. Excel Spread sheet

Explanation / Answer

I'm guessing that you're working off the assumption that any earnings NOT reinvested in the project are paid out as dividends.

$3 * 1.20 = 3.60 - 3.00 = .60<<the additional cash flow(earnings) created by the $3 investment for years 1 -5
earnings not invested - paid out as dividends = 5 - 3 = 2 <<for years 1 - 5

I'm not sure from the question if each $3 investment earns 20% each year - ie. compounds, if so..
1.)IF COMPOUNDS if each $3 investment earns 20% EACH year (i.e. IF it compounds) then you need to calc what EACH investment adds to earnings EACH year. You must calc each $3 investments contribution for each year and add it to earnings. So, for example the first $3 investment contributes to earnings as follows:
yr 1 = $0.60
yr2 = (0.60 * 1.20) = 0.72
yr3 = 0.60 * 1.20^3 = 1.0368 or 1.04 rounded
yr4 = 0.60 * 1.20^4 = 1.24
yr5 = 0.60 * 1.20^5 = 2.49
The second years $3 initial investment will compound for n-1 = 4 years total
3rd for n-2=3years, etc, etc. each would need to be added to each appropriate year..you'll need a spreadsheet

1.) IF DOES NOT COMPOUND - much simpler
Lay out the "cash flows" ($2 = the earnings of the original $5 EPS that are not invested, but are assumed to be distributed as dividends)
Calc Dividends per share
Yr 1 = 2 +0.60 = $2.60
yr 2 = 2 +0.60 +0.60 = $3.20
yr3 = 2 +0.60 +0.60 +0.60 = $3.80
yr4 = etc = $4.40
yr 5 = etc = 5.00
terminus cash flow (investment stops) = orig $5 EPS + incremental earnings from the investments(5 investments yielding $0.60 each=) $3 = $8

2.) discount the dividends for each of the 5 years at 12%...CFt/(1+r)^t +...+
2.60/(1.12)^1 + 3.20/1.12^2 + 3.80/1.12^3 + 4.40/1.12^4 + 5.00/1.12^5
sum these figures = $13.21

3.) add to the sum in number 2 the perpetuity value at year six
perpetuity formula = Div1/r where r is in decimal form and D1 is the next dividend

YR 6 EPS/dividend is now $8
$8/0.12 = $66.67 <<perpetuity value
perp value + DCF value in #2 = price today
66.67 + 13.21 = $79.88

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