Step 1: Discount the future value of the company to obtain the post-money valuation (POST).

POST = future value / (1 + r)^{investment period}

POST for Melton = $51 million / (1 + 13.7%)⁵ = $26.839 million.
POST for Apple = $29 million / (1 + 13.7%)¹⁰ = $8.031 million.

Step 2: Calculate pre-money valuation.

PRE = POST − investment.

PRE for Melton = $26.839 million − $7 million = $19.839 million.
PRE for Apple = $8.031 million − $5 million = $3.031 million.

Step 3: Determine the fractional ownership.

F = INV / POST

F for Melton = $7 million / $26.839 million = 26.08%.
F for Apple = $5 million / $8.039 million = 62.26%.

Step 4: Determine the number of shares the firm must buy.

Stake = Entrepreneurs’ shares × [ F / (1 − F)].

Stake for Melton = 1.5 million / [26.08% / (1 − 26.08%)] = 529,258 shares.
Stake for Apple = 80,000 / [62.26% / (1 − 62.26%)] = 131,951 shares.

Step 5: Calculate stock price per share.

P = INV / Stake

P for Melton = $7 million / 529,258 = $13.23
P for Apple = $5 million / 131,951 = $37.89

Melton’s calculated value is 22% below the current offer price. Apple’s is 9.8% below the current offer price. Richmond Group should not buy either stake. (Study Session 13, LOS 46.j)