Question 1 Assume you are 30 years old at t=0 and you will retire...

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Question 1
Assume you are 30 years old at t=0 and you will retire at the age of 62. Your first payment from your retirement account to you will be paid when you are 63. You expect to pass away when you are 90 years old.
• Your goal is to have your retirement account payout $175,000 per year in real terms during your retirement.
• During your working years you plan to save a growing amount each year, starting when you are 31, with the growth rate of your savings equal to the inflation rate.
• Assume you will earn a nominal APR on your retirement savings of 5% with monthly compounding.
• The expected inflation rate is 2.2%.

a) How much will you save when you are 31?
b) How much will you save when you are 62?
c) How much will you have in your retirement account at the end of your 62nd year?
d) How much will you have in your retirement account at the end of your 76th year?
e) How much will you have in your retirement account at the end of your 90th year?

Question 2
You are looking to buy a car that (without any special deals) costs $24,000, but only have $3,000.
A car dealer offers you three options.
• Option 1: Pay $3,000 down and finance the rest with a four-year loan from the dealer at 4% APR, compounded monthly. The loan payments are made monthly, with the first payment due in one month.
• Option 2: Pay $3,000 down and lease the car from the dealer. The lease would be for three years with the option to buy the car for $11,250 at the end of the leasing period. The monthly lease payment would be $300. The first lease payment is due in one month.
• Option 3: Pay cash and get a $500 rebate.

Your opportunity cost of capital is an APR of 6% with monthly compounding. You can borrow and invest at this APR of 6% at a local bank and expect this to be the case in the future.

a) Which of the three options do you prefer? When evaluating the leasing option, assume that you buy the car at the end of the leasing period, and note that option 3 would involve borrowing from the bank.
b) At what monthly lease payment do options 1 and 2 look equally attractive, keeping all other features the same?

Question 3
After completing your education, you are considering developing and selling the kDrone, a remote-controlled aerial camera capable of capturing HD quality video that when not in flight, also serves as a fitness monitor, calendar, and voice-activated link to over 10 million websites simply by saying, “Hey Wildcat!”
Here are the details of the project:

• At time 0, you will purchase the manufacturing equipment needed for $12,000,000. The equipment can be depreciated to zero using straight line depreciation over six years. At time t=5, when production comes to an end, you will sell the equipment for $2,100,000.
• You anticipate selling 25,000 kDrones in the first year (t=1) and the number of kDrones you sell will increase by 10% per year through the fifth year of sales (t=5). After five years, the product will be obsolete and sales will be zero beginning in the sixth year (t=6).
• Each kDrone sells for $400. The sales price is constant through time.
• The total cost making each kDrone is $200 in the first year (t=1), but the cost per unit will increase by 5% each subsequent year.
• You offer your very best customers the opportunity to pay for their kDrone one year after purchase. You anticipate that 15% of your customers will take advantage of this offer.
• 30% of next-year’s sales will be held as inventory.
• Your tax rate is 40%.
• The appropriate nominal discount rate for this project is 15%.
• Assume all cash flows are nominal.
Should you invest in the project? Why?

Question 4
You observe the following bond prices:
• The price of a six-month zero-coupon bond with $1,000 face value is $981.50.
• The price of a one-year 6% coupon bond with $1,000 face value is $1018.37.
• The price of a 1.5-year 5.5% coupon bond with $1,000 face value is $1009.83.

a) What are the six-month, one-year, and 1.5-year spot rates?
b) What should the price of a one-year zero coupon bond with $1,000 face value be?
c) What should the yield to maturity of a 1.5-year 11% coupon bond with a $1,000 face value be?

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