3: The Time Value of MoneyP3-27 Determine the annual deposit required to fund a future annual annuity of $12,000 per year. You will
fund this future liability over the next five years, with the first deposit to occur one year from today.
The future $12,000 liability will last for four years, with the first payment to occur seven years from
today. If you can earn 8% on this account each year, how much will you have to deposit each year
over the next five years to fund the future liability?
P3-28 Mary Chong, capital expenditure manager for PDA Manufacturing, knows that her company is
facing a series of monthly expenses associated with installation and calibration of new production
equipment. The company has $1 million in a bank account right now that it can draw on to meet
these expenses. Funds in this account earn 6% interest annually, with monthly compounding. Ms
Chong is preparing a budget that will require the company to make equal monthly deposits into
their bank account, starting next month, to ensure that they can pay the repair costs they anticipate
over the next 24 months (shown as follows). How much should the monthly bank deposit be?
Months Repair costs per month
1–4 $100,000
5–12 200,000
13–24 500,000P3-29 Joan Messineo borrowed $15,000 at a 14% annual interest rate to be repaid over three years. The
loan is amortised into three equal annual end-of-year payments.
a Calculate the annual end-of-year loan payment.
b Prepare a loan amortisation schedule showing the interest and principal breakdown of each of
the three loan payments.
c Explain why the interest portion of each payment declines with the passage of time.
P3-30 You are planning to purchase a caravan for $40,000, and you have $10,000 to apply as a down
payment. You may borrow the remainder under the following terms: a 10-year loan with semiannual
repayments and a stated interest rate of 6%. You intend to make $6,000 in payments, applying the
excess over your required payment to the reduction of the principal balance.
a Given these terms, how long (in years) will it take you to fully repay your loan?
b What will be your total interest cost?
c What would be your interest cost if you made no prepayments and repaid your loan by strictly
adhering to the terms of the loan?
P3-31 You are the pension fund manager for Tanju’s Toffees. The fund collects contributions (inflows) from
workers each year and pays benefits (outflows) to retirees. Your CFO wants to know the minimum
annual return required on the superannuation fund in order to make all required payments over
the next five years and not diminish the existing asset base. The fund currently has assets of $500
million.
a Determine the required return if outflows are expected to exceed inflows by $50 million per year.
b Determine the required return with the following fund cash flows.
End of year Inflows Outflows
1 $55,000,000 $100,000,000
2 60,000,000 110,000,000
3 60,000,000 120,000,000
4 60,000,000 135,000,000
5 64,000,000 145,000,000c Consider the cash flows in part (b). What will happen to your asset base if you earn 10%?
What about 20%?