Chapter 3
Arbitrage and Financial Decision Making
3-1. The benefit of the rebate is that Honda will sell more vehicles and earn a profit on each additional vehicle sold:
Benefit = Profit of $6,000 per vehicle × 15,000 additional vehicles sold = $90 million.
The cost of the rebate is that Honda will make less on the vehicles it would have sold:
Cost = Loss of $2,000 per vehicle × 40,000 vehicles that would have sold without rebate = $80 million.
Thus, Benefit – Cost = $90 million – $80 million = $10 million, and offering the rebate looks attractive.
(Alternatively, we could view it in terms of total, rather than incremental, profits. The benefit as $6000/vehicle × 55,000 sold = $330 million, and the cost is $8,000/vehicle × 40,000 sold = $320 million.)
The value of the deal is $78,431 – 72,727 = $5704 today.
3-3.
a. Stock bonus = 100 × $63 = $6,300
Cash bonus = $5,000
Since you can sell (or buy) the stock for $6,300 in cash today, its value is $6,300 which is better than the cash bonus.
b. Because you could buy the stock today for $6,300 if you wanted to, the value of the stock bonus cannot be more than $6,300. But if you are not allowed to sell the company’s stock for the next year, its value to you could be less than $6,300. Its value will depend on what you expect the stock to be worth in one year, as well as how you feel about the risk involved. You might decide that it is better to take the $5,000 in cash then wait for the uncertain value of the stock in one year.
3-4.
a. Having $200 today is equivalent to having 200 × 1.04 = $208 in one year.
b. Having $200 in one year is equivalent to having 200 / 1.04 = $192.31 today.
c. Because money today is worth more than money in the future, $200 today is preferred to $200 in one year. This answer is correct even if you don’t need the money today, because by investing the $200 you receive today at the current interest rate, you will have more than $200 in one year.
3.5. Cost = $1 million today
The NPV is positive, so it is a good investment opportunity.
3.6.
a.
b. The firm can borrow $18.18 million today, and pay it back with 10% interest using the $20 million it will receive from the government (18.18 × 1.10 = 20). The firm can use $10 million of the 18.18 million to cover its costs today, and save $4.55 million in the bank earn 10% interest to cover its cost of 4.55 × 1.10 = $5 million next year. This leaves 18.18 – 10 – 4.55 = $3.63 million in cash for the firm today.
3.7.
a.
b. If only one of the projects can be chosen, project C is the best choice because it has the highest NPV.
c. If two of the projects can be chosen, projects B and C are the best choice because they offer a higher total NPV than any other combinations.
3.8.
a.
Costs are lower under the first supplier’s offer, so it is better choice.
b. The firm can borrow $100,000 at 6% from a bank for one year to make the initial payment to the first supplier. One year later, the firm will pay back the bank $106,000 (100,000 × 1.06) and the first supplier $100,000 (10 × 10,000), for a total of $206,000. This amount is less than the $210,000 (21 × 10,000) the second supplier asked for.
3.9.
a. Take a loan from Bank Onethe Royal Bank at 5.5% and save the money in Bank Enn Scotiabank at 6%.
b. Bank One Royal Bank would experience a surge in the demand for loans, while Bank Enn Scotiabank would receive a surge in deposits.
c. Bank One Royal Bank would increase the interest rate, and/or Bank Enn Scotiabank would decrease its rate.
3.10. There is exchange rate risk. Engaging in such transactions may incur a loss if the value of the dollar falls relative to the yen. Because a profit is not guaranteed, this strategy is not an arbitrage opportunity.
3.11. We can trade one share of Nokia CN Rail stock for $1749.96 85 USD
