You are considering buying a share of stock in the tech company Neutrino, LLC for $250. You expect the stock to pay a dividend of $2 after 3 years and $10 after 4 years, but no dividends in years 1 and 2. You also expect to sell the stock after 4 years for $270.
(a) If your bank account pays an interest rate of 3 percent, is Neutrino, LLC a good invest- ment? What about if your bank pays an interest rate of 4 percent?
(b) If your bank account pays an interest rate of 4 percent, what would the future sale price of stock in Neutrino, LLC have to be after 4 years for the current stock price of $250 to be fair value?

(a)-$14.86, If NPV is negative, it is not considered a good investment. (b) $287.38

Explanation:

Solution

Recall that,

(a) The sale price expected=$270

The price of purchase=$250

The dividend after year 3=$2

The dividend after year 4=$3

The NPV of investment= -250+2/(1+i)^3+(3+270)/(1+i)^4

Then,

If the interest is =3%

The NPV of investment=-250+2/(1+3%)^3+(3+270)/(1+3%)^4=-$5.61

When the NPV is negative, this is not considered  a good investment.

Thus,

If  the interest is =4%

The NPV of investment=-250+2/(1+4%)^3+(3+270)/(1+4%)^4=-$14.86

If NPV is negative, it is not considered  a good investment.

(b) Let  say the sale price be X

Then,

The NPV of investment=-250+2/(1+4%)^3+(3+X)/(1+4%)^4

If $250 is a fair price,  the NPV is taken as zero

so,

=-250+2/(1+4%)^3+(3+X)/(1+4%)^4=0

= -250+1.777993+(3+X)*0.854804=0

=(3+X)*0.854804=248.222007

=3+X=290.38

Therefore.

X=$287.38

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