1. Chapter 3 Additional Time Value of Money Problems

2. Example 3.1a Competitive Market Prices Determine Value Problem: You have just won a radio contest and are disappointed to learn that the prize is 6 tickets to the Lady Antebellum tour (face value $50 each). Not being a fan of country music, you have no intention of going to the show. However, it turns out that there is a second choice: four tickets to your favorite band’s sold-out show (face value $40 each). You notice that on Ebay, tickets to the Lady Antebellum show are being bought and sold for $45 apiece and tickets to your favorite band’s show are being bought and sold at $60 each. What should you do?

3. Example 3.1a Competitive Market Prices Determine Value Solution: Plan: Market prices, not your personal preferences (nor the face value of the tickets), are relevant here: – 6 Lady Antebellum tickets at $45 apiece – 4 of your favorite band’s tickets at $60 apiece You need to compare the market value of each option and choose the one with the highest market value.

4. Example 3.1a Competitive Market Prices Determine Value Execute: The Lady Antebellum tickets have a total value of $270 (6  $45) versus the $240 total value of the other 4 tickets (4  $60). Instead of taking the tickets to your favorite band, you should accept the Lady Antebellum tickets, sell them on Ebay, and use the proceeds to buy 4 tickets to your favorite band’s show. You’ll even have $30 left over to buy a t-shirt.

5. Example 3.1a Competitive Market Prices Determine Value Evaluate: Even though you prefer your favorite band, you should still take the opportunity to get the Lady Antebellum tickets instead. a As we emphasized earlier, whether this opportunity is attractive depends on its net value using market prices. Because the net value of taking the Lady Antebellum tickets, selling them, and buying your favorite band’s tickets is positive $30, the opportunity is appealing.

6. Example 3.1b Competitive Market Prices Determine Value Problem: You have just won a contest and are disappointed to learn that the prize is a gift certificate for dinner and drinks for four at a local sushi restaurant. The face value of the gift certificate is $200. Unfortunately, you are not a fan of eating raw fish and would prefer a thick Angus steak. It turns out that there is a second choice: You see that on Ebay, a $200 gift certificate from the sushi restaurant is selling for $175 while dinner and drinks for two at your favorite steak house runs $150. What should you do?

7. Example 3.1b Competitive Market Prices Determine Value Solution: Plan: Market prices, not your personal preference (nor the face value of the tickets), are relevant here: – Dinner for four at the sushi restaurant at $175 – Dinner at your favorite steak house at $150 You need to compare the market value of each option and choose the one with the highest market value.

8. Example 3.1b Competitive Market Prices Determine Value Execute: The sushi restaurant gift certificate has a value of $175 You should accept the sushi restaurant gift certificate, sell it on Ebay for $175, and use the proceeds to buy dinner for two at your favorite steak house You’ll even have $25 left over to pay for the valet parking

9. Example 3.1b Competitive Market Prices Determine Value Evaluate: Even though you prefer steak, you should still take the opportunity to get the sushi instead. As we emphasized earlier, whether this opportunity is attractive depends on its net value using market prices. Because the net value of taking the sushi gift certificate, selling it, and buying a steak dinner is positive $25, the opportunity is appealing.

10. Example 3.2a Applying the Valuation Principle Problem: You are the operations manager at your firm. Due to a pre-existing contract, you have the opportunity to acquire 500 barrels of oil and 4,000 pounds of copper for a total of $50,000. The current market price of oil is $75 per barrel and for copper is $2.50 per pound. You are not sure that you need all of the oil and copper, so you are wondering if you should you take this opportunity. How valuable is it? Would your decision change if you believed the value of oil or copper would plummet over the next month?

11. Example 3.2a Applying the Valuation Principle Solution: Plan: We need to quantify the costs and benefits using market prices. We are comparing $50,000 with: – 500 barrels of oil at $75 per barrel – 4,000 pounds of copper at $2.50 per pound

12. Example 3.2a Applying the Valuation Principle Execute: Using the competitive market prices we have: – (500 barrels) × ($75/barrel today) = $37,500 today – (4,000 pounds of copper) × ($2.50/pound today) = $10,000 today The value of the opportunity is the value of the oil plus the value of the copper less the cost of the opportunity, $37,500 + $10,000 - $50,000 = - $2,500 today. Because the value is negative, we should not take it

13. Example 3.2a Applying the Valuation Principle Evaluate: Since we are transacting today, only the current prices in a competitive market matter Our own use for or opinion about the future prospects of oil or copper do not alter the value of the decision today This decision is not good for the firm, and will decrease its value by $2,500

14. Example 3.2b Applying the Valuation Principle Problem: You are the operations manager at your firm. Due to a pre-existing contract, you have the opportunity to acquire 500 ounces of platinum and 50,000 mmBTUs of natural gas for of $1,000,000. The current market price of platinum is $1,450 per ounce and for natural gas is $3.60 per mmBTU. You are not sure that you need all of the platinum and natural gas, so you are wondering if you should you take this opportunity. How valuable is it? Would your decision change if you believed the value of platinum or natural gas would skyrocket over the next month?

15. Example 3.2b Applying the Valuation Principle Solution: Plan: We need to quantify the costs and benefits using market prices. We are comparing $1,000,000 with: – 500 ounces of platinum at $1,450 per ounce – 50,000 mmBTUs of natural gas at $3.60 per mmBTU

16. Example 3.2b Applying the Valuation Principle Execute: Using the competitive market prices we have: – (500 ounces) × ($1,450/ounces) = $725,000 today – (50,000 mmBTUs) × ($3.60/mmBTU) = $180,000 today The value of the opportunity is the value of the platinum plus the value of the natural gas less the cost of the opportunity, $725,000 + $180,000 - $1,000,000 = -$95,000 today. Because the value is negative, we should not take it

17. Example 3.2b Applying the Valuation Principle Evaluate: Since we are transacting today, only the current prices in a competitive market matter Our own use for or opinion about the future prospects of platinum and natural gas do not alter the value of the decision today This decision is bad for the firm, and will decrease its value by $95,000

18. Example 3.3a Comparing Revenues at Different Points in Time Evaluate: Delaying the project for one year was equivalent to giving up $1.16 billion in cash. In this example, we focused only on the effect on the first year’s revenues. However, delaying the launch delays the entire revenue stream by one year, so the total cost would be calculated in the same way by summing the cost of delay for each year of revenues.

19. Example 3.4a Present Value of a Single Future Cash Flow Problem: XYZ Company expects to receive a cash flow of $2 million in five years. If the competitive market interest rate is fixed at 4% per year, how much can they borrow today in order to be able to repay the loan in its entirety with that cash flow?

20. Example 3.4a Present Value of a Single Future Cash Flow Solution: Plan: First set up your timeline. The cash flows for the loan are represented by the following timeline: Thus, XYZ Company will be able to repay the loan with its expected $2 million cash flow in five years. To determine the value today, we compute the present value using Eq. 3.2 and our interest rate of 4%.

21. Example 3.4a Present Value of a Single Future Cash Flow Execute: Given:5402,000,000 Solve for:-1,643,854.21 Excel Formula: =PV(RATE,NPER, PMT, FV) = PV(0.04,5,0,2000000)

22. Example 3.4a Present Value of a Single Future Cash Flow Evaluate: The loan is much less than the $2 million the company will pay back because of the time value of money.

23. Example 3.4b Present Value of a Single Future Cash Flow Problem: You are considering investing in a savings bond that will pay $20,000 in twenty years. If the competitive market interest rate is fixed at 5% per year, what is the bond worth today?

24. Example 3.4b Present Value of a Single Future Cash Flow Solution Plan: First set up your timeline. The cash flows for this bond are represented by the following timeline: Thus, the bond is worth $20,000 in twenty years. To determine the value today, we compute the present value using Eq. 3.2 and our interest rate of 5%.

25. Example 3.4b Present Value of a Single Future Cash Flow Execute: Given:205020,000 Solve for:-7,357.79 Excel Formula: =PV(RATE,NPER, PMT, FV) = PV(0.05,20,0,20000)

26. Example 3.4b Present Value of a Single Future Cash Flow Evaluate: The bond is worth much less today than its final payoff because of the time value of money.