Question

1. The local BMW dealer offers to sell you the new 7 series vehicle for 60 monthly payments of $735 (first payment 30 days from now). Given your FICO credit rating of 555 the BMW credit manager states the interest rate on this loan will be 6.5% per annum or .5416% monthly. At the time you sign the loan documents what “value” are you paying for the BMW?

2. After purchasing the BMW, you tell Sally about the great deal you received on the car. Sally loves the car and decides to visit the same BMW dealer. Sally is offered to purchase the exact same vehicle model at the same monthly payment of $735 (for 60 months) as you. Sally’s FICO credit rating is 710 and the financing agreement states the interest rate on this loan will be 5.5% per annum or .4583% monthly. At the time Sally sign the loan documents, what “value” is Sally paying for the BMW?

3. What explanation can you give for the difference in “value” between your BMW purchase and Sally’s? Did she get a better or worse deal than you? What advice would you give to Sally about purchasing her car?

4. After graduating from the Merage School of Business, you take a job with a real estate investment company specializing purchasing and managing rental property focused on the student housing market. During the first week on the job, you are asked to determine whether an apartment building, with an asking price of $8.0 million (nonnegotiable), is a good investment opportunity for the company.   The required rate of return on all your Company’s real estate investments is 6.75%.   Your market research and financial modeling concludes the following:

1. Annual net cash flows (gross rents collected less all expenses) are as follows:

Year 1: $500,000

Year 2: $525,000

Year 3: $550,000

Year 4: $560,000   (data continued next page)

Year 5: $575,000               

Year 6 and thereafter: $580,000

                  Based upon you investment return requirements, should you purchase the apartment building?

5. A few weeks after completing your initial analysis you learn that the city in which the apartment building is located may adopt a building moratorium (curtail new building construction) due to a persistent water shortage brought on by the drought in California. You believe future growth in student enrollment at the nearby university combined with the reduction in available housing supply in the future will allow rent increases in the first four years of ownership higher than originally forecasted. Updating your financial model:

1. Annual net cash flows (gross rents collected less all expenses) are as follows:

Year 1: $575,000

Year 2: $600,000

Year 3: $640,000

Year 4: $650,000

Year 5: $670,000

Year 6 and thereafter: $695,000

Based upon your investment return requirements, should you purchase the apartment building (the seller has not adjusted their asking price despite the potential building moratorium)?

6. Immediately after completing your analysis for Question 4, your company’s finance director notifies you that the company has increased its required rate of return to 7.5% on all new real estate investments. The finance director states that the increase in the required rate of return stems from the increase in interest rates brought on by the Federal Reserve Banks recent actions to increase interest rates. Using the cash flow data from Question 4, what is your recommendation regarding whether the building should be purchased at the seller’s asking price of $8.0 million.

Answer 1

Since you have asked multiple questions, I will address the first one with all its sub-parts.

1. The local BMW dealer offers to sell you the new 7 series vehicle for 60 monthly payments of $735 (first payment 30 days from now). Given your FICO credit rating of 555 the BMW credit manager states the interest rate on this loan will be 6.5% per annum or .5416% monthly. At the time you sign the loan documents what “value” are you paying for the BMW?

Monthly payment, P = 735

Interest rate per period, i = 6.5% / 12 = 0.5417%

Nos. of period, N = 60

Hence, value you are paying = Present value of all the future payments

$=\frac{P}{i}\times (1-(1+i)^{-N}) = \frac{735}{0.005417}\times (1-(1+0.005417)^{-60})$

= $ 37,565

2. After purchasing the BMW, you tell Sally about the great deal you received on the car. Sally loves the car and decides to visit the same BMW dealer. Sally is offered to purchase the exact same vehicle model at the same monthly payment of $735 (for 60 months) as you. Sally’s FICO credit rating is 710 and the financing agreement states the interest rate on this loan will be 5.5% per annum or .4583% monthly. At the time Sally sign the loan documents, what “value” is Sally paying for the BMW?

Interest rate per period, i = 5.5% / 12 = 0.4583%

Hence, value Sally is paying = Present value of all the future payments

$=\frac{P}{i}\times (1-(1+i)^{-N}) = \frac{735}{0.004583}\times (1-(1+0.004583)^{-60})$

= $ 38,479

3. What explanation can you give for the difference in “value” between your BMW purchase and Sally’s?

The difference in value is originating on account of different interest rate you and Sally are subjected to. Since Sally's credit rating is better than yours, the riskiness of future payments from her is lower than the riskiness of future payment from you. Hence, the discount rate applicable to the series of cash flows from Sally is lower. Since monthly payment is same in both the cases, the lower discount rate is giving a higher value for Sally.

3. Did she get a better or worse deal than you? What advice would you give to Sally about purchasing her car?

Sally is getting a worse deal than you.

Advice: Sally should negotiate for a lower monthly payment emanating out of the value to you. So her monthly payment should be such a payment whose present value over 60 months at annual interest of 5.5% turns out to be same as the value to you that is $ 37,565.

In this case, the monthly payment, P should be worked out from the following equation:

$37565=\frac{P}{i}\times (1-(1+i)^{-N}) = \frac{P}{0.004583}\times (1-(1+0.004583)^{-60}) = 52.35P$

Hence, P = 37,565 / 52.35 = $ 717.53