Question 17.4: Rexton Oil is an all-equity firm with 100 million shares out...

Plan

We can use the perpetuity formula to value Rexton under the two scenarios. The repurchase will take place at market prices, so the repurchase itself will have no effect on Rexton’s share price. The main question is whether spending $150 million now (instead of repurchasing) to increase cash flows by $7.8 million per year is a positive-NPV project.

Execute

Invest: Using the perpetuity formula, if Rexton invests the $150 million to expand, its market value will be $72.8 million ÷ 10% = $728 million, or $7.28 per share with 100 million shares outstanding.

Repurchase: If Rexton does not expand, the value of its future free cash flows will be
$65 million ÷ 10% = $650 million. Adding the $150 million in cash it currently has, Rexton’s market value is $800 million, or $8.00 per share.

If Rexton repurchases shares, there will be no change to the share price: It will repurchase $150 million ÷ $8.00 per share = 18.75 million shares, so it will have assets worth $650 million with 81.25 million shares outstanding (100 million shares – 18.75 million shares repurchased). That implies a share price of $650 million ÷ 81.25 million shares = $8.00 per share.

In this case, cutting investment and growth to fund a share repurchase increases the share price by $0.72 per share ($8.00 – $7.28).

Evaluate

The share price is higher with the repurchase because the alternative of expansion has a negative NPV: It costs $150 million, but increases future free cash flows by only $7.8 million per year forever, for an NPV of:

-$150 million + $7.8 million/10% = -$72 million, or -$0.72 per share

Thus, by avoiding the expansion, the repurchase keeps the shares from suffering the $0.72 loss.