Case This case is based on an actual incident. Eric recently took a trip to Hawaii and visited a "Vacation Club" or timeshare. The club offered to sell Eric one week per year at their resort for the next 20 years for a cost of $35,200 plus a $700 yearly maintenance fee (payable at the end of each year, payable for the first time at the end of period 1). The maintenance fee grows at 3% per year (starting at $700 at the end of period 1). Eric plans on taking a one week vacation every year at this location. If he ever does decide to try another location he can trade his week for an equivalent resort. Is this a good deal? The sales pitch went as follows: Sales Consultant (SC): Let's assume you are going to take a one week, seven-night, vacation every year at a cost of $200 per night. Eric (E): Okay. Sounds reasonable. SC: We expect the cost of hotel lodging to increase at a rate of 5% per year for the next twenty years. For example, next year we expect a room that is currently $200ight to be $210ight. E: Okay. I can buy that. SC: I thought you would. You seem like a smart guy. E: Yes, thank you. SC: So the cost of a room next year will be $210 and the year after that it be $220.50 and so on. Twenty years from now the cost will be $530.66/per night. Since you will be staying seven niglts per year, that will cost you $3,715. E: Wow. That sounds like a lot. SC: Yes it is, but it gets worse: If you multiply the cost per night by the seven nights for each of the next 20 years and then add up the twenty years of hotel payments you will spend almost $50,000 (assume E's first payment is in period 0) on your dream vacation! E: Oh man. I want to live the dream. What can I do? SC: Well, we are offering you the ability to lock in your dream vacation now for only $35,200 today. E: $35,200 plus the annual maintenance fee. SC: Oh ya. But think about having your dream vacation locked in. We are saving you almost $20,000. Frankly, I don't see how we pay the bills around here. E: Hmmm... something seems funny to me. The way you added the numbers up seems strange. Are you sure that is right? SC: Oh yes. I have a B.S. in mechanical engineering and my friend is in the finance group of Hooters [he actually said this). He doubled checked the numbers for me. This is a great deal. E: I better think about it. SC: This offer is only good today. I can't offer it to you later. E: I don't have $35,200 today. SC: No problem. We will loan you the $35,200 at 15%/yr compound interest (20-year term). You will just make (uniform) yearly payments, based on these terms. Can you believe that? What a deal! You can start living the dream today! E: I better think this over. Something does not seem quite right to me. SC: As I said, this deal is too good. I can't offer it to you if you don't take it right now. E: Hmmm... seems like you don't want me to think about. I'll take my chances and wait this one out. Questions: 1. Read the sales pitch again. What do you think about the SC's reasoning? Has he calculated the true cost of the vacation? Is he trying to mislead E? 2. How much will the yearly maintenance fee cost E (what is the present value)? Use an interest rate of 7%/yr compounded yearly (Note: this rate is E's discount rate, not the rate at which the maintenance fees will increase). 3. What would E's annual payments on the $35,200 loan be? 4. Assume E could deposit a lump sum amount now in a savings account earning 7% per year compounded yearly. How much would he have to deposit now to finance his dream vacation for the next 20 years? In this case, E would buy hotel rooms each year, but not pay maintenance fees. Assume that the hotel room rate will increase at 5% as the SC stipulated. Compare this amount to the cost of the timeshare. 5. Maybe E should take the loan. Is it a good idea to take out the 15% loan to avoid a 5%/yr increase in the cost of the vacation? Explain. 6. Is the SC offering E a good deal? Should he sign up? Case This case is based on an actual incident. Eric recently took a trip to Hawaii and visited a "Vacation Club" or timeshare. The club offered to sell Eric one week per year at their resort for the next 20 years for a cost of $35,200 plus a $700 yearly maintenance fee (payable at the end of each year, payable for the first time at the end of period 1). The maintenance fee grows at 3% per year (starting at $700 at the end of period 1). Eric plans on taking a one week vacation every year at this location. If he ever does decide to try another location he can trade his week for an equivalent resort. Is this a good deal? The sales pitch went as follows: Sales Consultant (SC): Let's assume you are going to take a one week, seven-night, vacation every year at a cost of $200 per night. Eric (E): Okay. Sounds reasonable. SC: We expect the cost of hotel lodging to increase at a rate of 5% per year for the next twenty years. For example, next year we expect a room that is currently $200ight to be $210ight. E: Okay. I can buy that. SC: I thought you would. You seem like a smart guy. E: Yes, thank you. SC: So the cost of a room next year will be $210 and the year after that it be $220.50 and so on. Twenty years from now the cost will be $530.66/per night. Since you will be staying seven niglts per year, that will cost you $3,715. E: Wow. That sounds like a lot. SC: Yes it is, but it gets worse: If you multiply the cost per night by the seven nights for each of the next 20 years and then add up the twenty years of hotel payments you will spend almost $50,000 (assume E's first payment is in period 0) on your dream vacation! E: Oh man. I want to live the dream. What can I do? SC: Well, we are offering you the ability to lock in your dream vacation now for only $35,200 today. E: $35,200 plus the annual maintenance fee. SC: Oh ya. But think about having your dream vacation locked in. We are saving you almost $20,000. Frankly, I don't see how we pay the bills around here. E: Hmmm... something seems funny to me. The way you added the numbers up seems strange. Are you sure that is right? SC: Oh yes. I have a B.S. in mechanical engineering and my friend is in the finance group of Hooters [he actually said this). He doubled checked the numbers for me. This is a great deal. E: I better think about it. SC: This offer is only good today. I can't offer it to you later. E: I don't have $35,200 today. SC: No problem. We will loan you the $35,200 at 15%/yr compound interest (20-year term). You will just make (uniform) yearly payments, based on these terms. Can you believe that? What a deal! You can start living the dream today! E: I better think this over. Something does not seem quite right to me. SC: As I said, this deal is too good. I can't offer it to you if you don't take it right now. E: Hmmm... seems like you don't want me to think about. I'll take my chances and wait this one out. Questions: 1. Read the sales pitch again. What do you think about the SC's reasoning? Has he calculated the true cost of the vacation? Is he trying to mislead E? 2. How much will the yearly maintenance fee cost E (what is the present value)? Use an interest rate of 7%/yr compounded yearly (Note: this rate is E's discount rate, not the rate at which the maintenance fees will increase). 3. What would E's annual payments on the $35,200 loan be? 4. Assume E could deposit a lump sum amount now in a savings account earning 7% per year compounded yearly. How much would he have to deposit now to finance his dream vacation for the next 20 years? In this case, E would buy hotel rooms each year, but not pay maintenance fees. Assume that the hotel room rate will increase at 5% as the SC stipulated. Compare this amount to the cost of the timeshare. 5. Maybe E should take the loan. Is it a good idea to take out the 15% loan to avoid a 5%/yr increase in the cost of the vacation? Explain. 6. Is the SC offering E a good deal? Should he sign up