Question

1- On March 28, 2008, Toyota Motor Credit Corporation (TMCC), a subsidiary of Toyota Motor, offered some securities for sale to the public. Under the terms of the deal, TMCC promised to repay the owner of one of these securities $100,000 on March 28, 2038, but investors would receive nothing until then. Investors paid TMCC $24,099 for each of these securities; so they gave up $24,099 on March 28, 2008, for the promise of a $100,000 payment 30 years later. Why would TMCC be willing to accept such a small amount today ($24,099) in exchange for a promise to repay about four times that amount ($100,000) in the future?

2- As you increase the length of time involved, what happens to the present value of an annuity? What happens to the future value?

3- Tri-State Megabucks Lottery advertises a 10 million grand prize. The winner receives $500,000 today and 19 annual payments of $500,000. A lump sum option of $5 million payable immediately is also available. Is this deceptive advertising?

4- Suppose you won the Tri-State Megabucks Lottery in the previous question. What factors should you take into account in deciding whether you should take the annuity option or the lump sum option?

5- What is compounding? What is discounting?

Answer 1

Answer 1)

Repayment	100,000
Repayment Date	28-Mar-38
Paid	24,099
Payment Date	28-Mar-08
Term (Years)	30

TMCC will be willing to accept 24,099 today with a promise to repay 100,000 at the end of the 30 years because:

TMCC needs to raise funds from the market in order to run its operations. By accepting 24,099 today it managed to receive funds with a promise to pay 100,000 after 30 years. The rate at which the funds were raised = 4.86%.

(This can be calculated by PV = FV / (1+int%)^n

24,099 = -100,000 / (1+int%)^30

Int % = 4.86%)

TMCC believes it can earn more than 4.86% over this time period on the money raised by sale of securities. This can help TMCC realise profits on funds which have been raised from the public.

Answer 2) As we increase the time period involved, the future value will keep on increasing. This is becuase with each additional time period added, interest is accrued for that period resulting in a higher future value which will need to be repaid. (DIRECT RELATION)

The present value of an annuity will reduce . This is because it will be discounted by more time periods i.e. n will increase. Hence the present value of annual installments decrease when raising funds for a longer time interval as the annual installments themselves get scattered over longer periods and reduce. (INVERSE RELATION)

Answer 3)

Grand Prize	10,000,000
Winnings Today	500,000
Annual Payments	500,000
Number of Years	19
Lump Sum Amount	5,000,000

This is not deceptive advertising since the lottery company gives a fair option to the winner to take a lesser lump sum amount today or take the full amount in annual installments. This concept is based on the time value of money. The winner will accept the lump sum amount if he believes he can earn a higher return on 5 million that the amount after 19 years is more than 10 million.

Answer 4)

The main factor that would determine the choice is the Rate of Return. The current rate of return being offered on the lottery can be calculated through:

PV = FV/(1+int%)^n

5,000,000 = -10,000,000/ (1+int%)^19

Int% = 3.72%

If the winner believes he can earn a return of more than 3.72% on this lottery , then it will be desirable for him to take the lump sum amount of 5 million but if he believes he will not be able to earn more than 3.72% then he will be take the annuity option to win 10,000,000.

Other Factors can be the need for money today. if the winner needs the money today for personal purposes then he would choose to take the lump sum amount. He may also desire steady income flow over the time period than a one time income.

Answer 5) Compounding is the process of computing the future value of an investment . It takes into account the value that is added through the accruing of interest.

FV = PV * (1+int%)^n

Discounting is the process of computing the present value of a cash flows which will be received over a period of time.

PV = FV/(1+int%)^n