1. Michael wants to finally buy a brand new car. A nice Corvette costs $55,000…
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Question
1. Michael wants to finally buy a brand new car. A nice Corvette costs $55,000… A convertible BMW costs $35,000… A long-lasting Japanese Honda costs $20,000… Michael decided that he will need to take a 2-year car loan which requires fixed payments at the end of each month. He has also calculated that with his current job he will be able to spend not more than $1,300 per month on car loan payments. He already has $5,000 saved in his savings account which he plans to use as a downpayment.
If the annual interest rate on the car loan is 12%, compounded monthly, which one of the three cars can Michael afford?
2. Today is Kristin’s birthday and she decides to start saving for her 3-year long MBA education. She will start the MBA program on her 28th birthday. She will need $25,000 to pay for the tuition and living expenses at the end of the first year of the program. She is expecting this cost to increase by 5% each year (i.e., in year 2 it will be 5% higher than in year 1, in year 3 it will be 5% higher than in year 2), due to rising tuition and housing prices.
Kristin will make her first deposit into an account paying 10% annually in the amount of $6,553.30 one year from today, and she will continue to make an identical deposit each year up to the day she turns 28 and starts her MBA degree.
What birthday is Kristin celebrating today?
3. Rebecca bought a corporate bond with the time to maturity of 6 years, yield to maturity of 10%, and face value of $1,000. It pays semiannual coupons and the coupon rate of 8%.
Was Rebecca’s purchased bond sold at a premium, discount, or par?
Andrew bought a different financial asset (not a bond). It pays him equal annual payments for 6 years at the end of each year. The discount rate for this asset is 15%. If he paid the same amount for this security as Rebecca paid for her bond, how much are Andrew’s annual payments?
4. What is the Present Value of the following stream of cash flows if R=10%?
0 1 2 3 4 5 …
$1 $2 $3 $4 $5 …(and so on)
(Hint 1: It’s not equal to infinity. Hint 2: This is equivalent to a stream of $1 perpetuities, first one starting its payments in year 1, second one starting its payments in year 2, and so on forever.)
Explanation / Answer
1.)
Buying a new Corvette car costing $55000 is out of question and is to be ruled out as it is beyond the affordability of Micheal because even if we multiply $1300 per month with 24 months, we get $31,200, which is nowhere near to the balance cost of the new car of $50000 after making down-payment of $5000.
Buying a convertible BMW car costing $35,000 is also out of question and is to be ruled out as it is again beyond Micheal's affordability; expained as follows: With $5000 dow-payment, the balance amount of $30000 will have to be paid as 24 monthly principal installments of $1250 each. With that, Micheal is left only with $50 towards first Interest payment in first EMI, which represents just 2.00% per annum of interest payment as against required 12% per annum demanded by the bank for Car Loan. The first monthly interest payment in first EMI will work out to atleast $3600 @12% per annum..
Buying a long-lasting Japanese Honda car costing $20,000 is well within the reach of Micheal's affordability because: after making down-payment of $5000, the balance of $15000 will be the car loan amount; which when divided by 24 months, we get monthly principal installment of $625 each,and interest @ 12% per annum compounded monthly basis will ask interest portion of the installment to be just $150; thus total EMI will work out to $775; this will leave ample room for savings of ($1300-$775= $525 per month) for Micheal.
2.) Total 3-year MBA Course fees= $25000 + [$25000*(1+0.05)1] + [$25000*(1+0.05)2]= $78812.50
Kristin is celebrating her 19th birthday today and thus after 9 years from now [in fact at the beginning of the she will be able to have an accumulated corpus of $88990.39 which is far higher than the required MBA total Course fees of $78812.50. In fact, at the beginning of 9th birthday year from now she will be having the required MBA-Course Fees total amount. Thus ANSWER is= 28th Birthday year - 9 years from now= 19th birthday year.
For detailed workings, please find attached herewith the image file i.e. BMP file, of MS Excel spreadsheet where this problem is solved. The said image file has been uploaded on Chegg server using Image Uploader function in its tool bar of Q&A Board.
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