3: The Time Value of MoneyP3-18 Consumer Insurance Pty Ltd sells extended warranties on appliances that provide coverage after
the manufacturers’ warranties expire. An analyst for the company forecasts that the company will
have to pay warranty claims of $5 million per year for three years, with the first claims expected
to occur four years from today. The company wants to set aside a lump sum today to cover these
costs, and money invested today will earn 10%. How much does the company need to invest now?
P3-19 Ed Lowman, the 20-year-old star opening batsman for his university cricket team, is approached
about skipping the last two years of his four-year university degree and entering the professional
cricket industry. Ed expects that his cricket career will be over by the time he is 32 years old. Talent
scouts for Cricket Australia estimate that Ed could receive a signing bonus of $1 million today,
along with a five-year contract for $3 million per year (payable at the end of each year). They further
estimate that he could negotiate a contract for $5 million per year for the remaining seven years
of his career. The scouts believe, however, that Ed will have a much better chance of selection for
the Australian Test team if he improves by playing two more years of university cricket. If he stays at
university, he is expected to receive a $2 million signing bonus in two years, along with a five-year
contract for $5 million per year. After that, the scouts expect Ed to obtain a five-year contract for
$6 million per year to take him into retirement. Assume that Ed can earn a 10% return over this
time. Should Ed stay or go?
P3-20 Jill Chu wants to choose the best of four immediate retirement annuities available to her. In each
case, in exchange for paying a single premium today, she will receive equal annual end-of-year
cash benefits for a specified number of years. She considers the annuities to be equally risky and
is not concerned about their differing lives. Her decision will be based solely on the rate of return
she will earn on each annuity. The key terms of each of the four annuities are shown in the following
table:
AnnuityPremium paid
today Annual benefit Life (years)
A $30,000 $3,100 20
B 25,000 3,900 10
C 40,000 4,200 15
D 35,000 4,000 12a Calculate to the nearest 1% the rate of return on each of the four annuities Jill is considering.
b Given Jill’s stated decision criterion, which annuity would you recommend?P3-21 Evaluate each of the following three investments, each costing $1,000 today and providing the
returns noted below, over the next five years.
Investment 1: $2,000 lump sum to be received in five years
Investment 2: $300 at the end of each of the next five years
Investment 3: $250 at the beginning of each of the next five years
a Which investment offers the highest return?
b Which offers the highest return if the payouts are doubled (that is, $4,000, $600 and $500)?
c What causes the big change in the returns on the annuities?